DYNAMICS OF VERGENCE EYE MOVEMENTS IN PRE-VERGENCE ADAPTATION AND POST-VERGENCE ADAPTATION CONDITIONS

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By PremNandhini Satgunam, B.S (Optom), M.S * * * * * The Ohio State University 2007

Dissertation Committee: Approved By Dr. Nicklaus Fogt, Advisor

Dr. Michael Earley

Dr. Marjean Taylor Kulp

Dr. Thomas Raasch

______Advisor Vision Science Graduate Program

ABSTRACT

Objects at different distances are viewed using vergence eye movements. These eye movements are brought about by a negative feedback vergence controller that monitors the eye and the target position. The vergence controller contains a fast vergence component and a slow vergence component. The fast vergence component has an initial open-loop portion that elicits the vergence movement followed by a closed-loop component that completes the vergence movement. Sustained vergence posture is maintained by the slow vergence component, the neural innervation of which is responsible for vergence adaptation. Control system models predict that for sustained viewing, the slow vergence controller relieves the fast vergence controller. The fast vergence controller is then available to respond to novel stimuli. The purpose of the current dissertation was to experimentally assess interactions between the slow and fast vergence components. Specifically, vergence parameters including vergence latency, vergence amplitude and vergence velocity were studied before and after vergence adaptation.

Twenty subjects were enrolled with informed consent. A haploscopic arrangement was used to present computer generated vergence targets. Subjects viewed a 12 degree vergence target initially for 5 seconds (pre-vergence adaptation) and subsequently for 5 minutes (post-vergence adaptation). Subjects made a divergence or convergence movement of 4 degrees from the 12 degree vergence position for both the viewing durations (5 seconds and 5 minutes). Phoria measures were made at three different time intervals in a given trial to monitor vergence adaptation. Twenty trials were measured on different days (10 trials for convergence and 10 trials for divergence) for each subject.

ii It was found that the divergence latency increased by 11.5 %, while divergence velocity and amplitude decreased by 43.8 % and 34 % after vergence adaptation. This trend was present after sustained vergence regardless of the presence of positive vergence adaptation. For convergence, the velocity (8.2 %) and amplitude (17.7 %) were found to be significantly higher after a period of sustained convergence only if vergence adaptation occurred.

The change in vergence amplitude and velocity brought about by vergence adaptation followed the main sequence ratio (1:4) established in the literature. This suggests that the increase in neural innervation from the slow vergence controller interacted with the disparity detectors. Specifically, these data suggest that there is a decline in the divergent disparity detectors after sustained vergence. Finally, these data suggest that slow vergence innervation is gated during a fast vergence movement.

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Dedicated to my Mom and people like her, who never had an opportunity for education, yet struggle to give it to their children

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ACKNOWLEDGMENTS

I take this opportunity to thank everyone who has been a source of inspiration, support and of tremendous help in my graduate school years at OSU. First of all, is my adviser, Dr. Nick Fogt, who believed that I could complete this work in time when I had my own doubts. Without his deep insightful discussions and patient corrections of my many ‘unreadable’ drafts this dissertation would have never seen light. He has been tirelessly helping me for all these five years and constantly thinking in my best interest for my future career. Dr. Angela Brown has been another well-wisher and I am indebted to her for her words of wisdom. I thank Dr. Andrew Toole for sharing his expertise in computer code nuances. This project would have never been completed if my subjects had not come 20 times to complete the study; I thank them for their perseverance. Dr. Karla Zadnik, for her timely assistance in clearing the required paper work. Finally, my committee members Dr. Mike Earley, Dr. Marjean Kulp and Dr. Tom Raasch for their discussion and comments.

I have the blessing of good friends to talk and listen to me that buffered me well during the stressful periods in my graduate study. I will not be able to name them all but in particular, I am grateful to Deepa, Indu, Vidhya, Sowjanya, Priya and Barbara Pyle for their moral support and prayers and in reminding me that I am neither the only one nor the first one to go through this. Finally, my parents, Vaidehi akka, brothers and sisters- in-law for their phone calls, encouragement and prayers.

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VITA

May 8, 1977……………………………………………. Date of Birth

1999……………………………………………………. B.S. Optometry, Elite School of Optometry India

1999 – 2002……………………………………………..Faculty-cum-clinical instructor, Elite School of Optometry India

2002 – 2004……………………………………………. M.S. Vision Science, The Ohio State University

PUBLICATIONS

Satgunam, P., Fogt, N. (2005). Saccadic latencies for achromatic and chromatic targets. Vision Research , 45: 3356-3364.

Brown, A., Lindsey, D., Satgunam, P., Miracle, J. (2007). Critical immaturities limiting infant binocular stereopsis. Investigative Ophthalmology and Visual Science, 48: 1424-1434.

FIELDS OF STUDY

Major Field: Vision Science

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TABLE OF CONTENTS

Abstract...... ii Dedication...... iv Acknowledgments...... v Vita...... vi List of Tables ...... x List of Figures...... xi

Chapters

1. Introduction...... 1 1.1 Control system models...... 2 1.2 Components of vergence movement...... 4 1.3 Vergence Adaptation ...... 8 1.4 Background...... 11 1.5 Overview of experiments...... 13

2. Preliminary Studies...... 15 2.1 Experiment I: Brock string experiment...... 15 2.1.1 Introduction...... 15 2.1.2 Methodology...... 16 2.1.3 Data analysis ...... 18 2.1.4 Results...... 19 2.1.5 Conclusion ...... 21

2.2 Experiment II - Effect of accommodative vergence on vergence adaptation...... 21 2.2.1 Introduction...... 21 vii 2.2.3 Methods...... 22 2.2.4 Results...... 24 2.2.5 Conclusions...... 25

2.3 Experiment III: vergence dynamics after vergence adaptation studied in an anaglyphic setup...... 26 2.3.1 Introduction...... 26 2.3.2 Methods...... 26 2.3.3 Results...... 29 2.3.4 Conclusion ...... 33

3. Introduction - Main Study...... 34

4. Methods...... 36 4.1 Subjects...... 36 4.2 Baseline measurements...... 36 4.3 Experimental set up...... 37 4.3.1 Haploscope arrangement...... 37 4.3.2 Stimulus target ...... 39 4.4 Accommodative measurements ...... 39 4.5 Eye tracking instrument ...... 41 4.6 Test Trial...... 41

5. Results...... 45 5.1 Data analysis ...... 45 5.2 Accommodation – Baseline measure...... 45 5.3 Calculation of phoria and vergence adaptation...... 46 5.4 Calculation of vergence dynamics...... 48 5.5 Effect of vergence adaptation on vergence dynamics...... 51 5.6 Comparison between positive trials and negative trials...... 52 5.9 Vergence anomalous subjects...... 54

6. Discussion...... 56 6.1 Accommodation...... 56 viii 6.2 Vergence Adaptation ...... 56 6.3 Vergence parameters...... 57 6.4 Interpretation...... 58

7. Conclusion ...... 63

References...... 65

ix

LIST OF TABLES

Table Page

Table 2.1: Comparison of the vergence parameters in no adaptation and adaptation conditions for both convergence and divergence...... 30

Table 5.1: overall average values of vergence parameters (vergence latency, vergence amplitude and vergence peak velocity) before and after viewing the vergence adaptation target is shown along with the standard deviation for both convergence and divergence eye movements...... 51

Table 5.2: Comparison of average vergence parameters for negative and positive trials identified for convergence trials ...... 54

Table 5.3: Comparison of average vergence parameters for negative and positive trials identified for divergence trials...... 54

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LIST OF FIGURES

Figure Page

Figure 1.1: Simplified control system model for vergence eye movements...... 4

Figure 1.2: (A) illustration supporting Schor and Jiang’s model (B) illustration supporting Rosenfield et al.’s model ...... 6

Figure 1.3 Control system model of Saladin (2005)...... 7

Figure 1.4: Modified from the computer simulation model of Schor (1979) showing the decay of FVC (fast vergence controller) with the simultaneous increase in innervation of SVC (slow vergence controller). The net vergence position is the additive sum of FVC and SVC ...... 8

Figure 2.1: Illustration of the near condition (NC) trials 1 and 2 and far condition (FC) trials 3 and 4 ...... 18

Figure 2.2: Vergence position and velocity trace plotted for a given trial when both convergence and divergence movements were made ...... 19

Figure 2.3: Comparison of average velocity of both convergence and divergence eye movements made on all four trials...... 20

Figure 2.4: Illustration of vergence adaptation shown for both accommodative stimulus and disparity vergence stimulus for all the twenty six subjects ...... 25

Figure 2.5: Illustration of the target presentation in a given experimental trial ...... 28

Figure 2.6: Illustration of average vergence amplitude for the no adaptation (NA) and adaptation (A) trials for both convergence and divergence ...... 31

Figure 2.7: Illustration of average vergence amplitude for the no adaptation (NA) and adaptation (A) trials for both convergence and divergence ...... 32

Figure 2.8: Illustration of average vergence velocity for the no adaptation (NA) and adaptation (A) trials for both convergence and divergence...... 32

xi Figure 4.1: Block diagram showing the experimental set up...... 38

Figure 4.2: Illustration of target sequence presented in a given experimental trial.. 44

Figure 5.1: Box plots showing the magnitude of vergence adaptation calculated from the differences in phoria position measured at three instances in time for both convergence and divergence trials...... 47

Figure 5.2: Time series plot of vergence position data measured along with the target onset data from the Analog signal from the A/D board for a given trial...... 49

Figure 5.3: Time series plot showing the Target position, vergence position and vergence velocity. The vergence paramete rs measured (latency, peak velocity and amplitude) are marked ...... 50

Figure 5.4: Box plots showing the magnitude of vergence adaptation for all subjects on all the 20 trials...... 53

Figure 5.5: Time series plots showing absence of convergence response to the transient stimulus (a) and presence of convergence response after vergence adaptation (b) for three subjects who showed vergence anomaly ...... 55

Figure 6.1: Illustration of the four possible (A, B, C, D) interactions among the disparity detectors for vergence disparity and vergence burst neurons ...... 59

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CHAPTER 1

INTRODUCTION

Objects located at different depths are primarily viewed by moving the eyes in opposite directions to produce a disjunctive movement called vergence (Howard and Rogers 2002). When looking from far to near the eyes come together to converge. They move away from each other or diverge when looking from near to far. These fixational eye movements permit one to see a ‘single fused’ object by ensuring the fovea in each eye is used for fixation.

Vergence eye movements are the last to develop in human infants but they are often the first to fatigue and to become disrupted (Carpenter 1988). In patients reporting symptoms with visual tasks, vergence eye movements are often shown to be abnormal in optometric and ophthalmologic eye examinations (Carpenter 1988). Improper functioning of vergence eye movements leads to eyestrain, headaches and discomfort in performing prolonged near work. In comparison to other eye movements relatively little is known about the neurology of vergence eye movements (Gamlin 2002; Büttner-Ennever 2006). However, eye movement studies and theoretical control system engineering models have been applied to understand the dynamics of vergence eye movements (Schor and Ciuffreda 1983; Ciuffreda and Tannen 1995; Hung and Ciuffreda 2002).

1 Objects falling on non-corresponding points on the retina in each eye create disparity that serves as a stimulus for vergence eye movement (Westheimer and Mitchell 1956). Since it is the retinal disparity that drives the vergence eye movement rather than diplopia itself, it is preferable to call these eye movements “disparity” vergence movements rather than the more conventional “fusional” vergence movement (Stark, Kenyon et al. 1980).

1.1 Control system models

According to all vergence control system models, the output of the vergence system is continuously monitored so as to compare the eye position with the target position. Any difference between the eye vergence and target vergence is fed back into the vergence controller resulting in a negative feedback system. Vergence eye movement is stopped when the retinal disparity is minimized within Panum’s fusional area.

The first control system analysis of vergence eye movement was produced by Rashbass and Westheimer (Rashbass and Westheimer 1961). They found that disparity vergence was continuously sampled, making it a continuous feedback system. Further, it was found that there were two components to the disparity vergence eye movement; a transient vergence initiating component and a vergence sustaining component (Westheimer and Mitchell 1969; Jones and Kerr 1972).

Jones and Kerr (Jones and Kerr 1972) observed the vergence initiating component to be a coarse system elicited only by retinal disparity and having no preference to the shape of targets while the more fine tuned sustained component required similar targets to hold vergence. This was demonstrated by having subjects attempt to make vergence movements to either similar or dissimilar targets presented transiently for about 200 ms.

A model of the vergence eye movement control system was proposed by Krishnan and Stark (Krishnan and Stark 1977) that had two components; a fast vergence controller

2 and a slow vergence controller. Computer simulations were used in their model to demonstrate a fast controller that initiated the vergence movement (derivative controller). The neural impulse from the fast vergence controller was followed by a slow controller (integral controller) that reduced the disparity and maintained steady state. Neurological studies that followed later identified two types of vergence-related neurons in the midbrain, the burst and tonic neurons, that seemed to correlate with the functions of the fast and slow vergence controller (Mays, Porter et al. 1986). The firing rate of the burst neurons correlated well with vergence velocity while the vergence position correlated with the activity of the tonic cells.

The control system model proposed by Krishnan and Stark (Krishnan and Stark 1977) could not explain the presence of fixation disparity. This is a small vergence error that is commonly found while fixating on a target. According to Krishnan and Stark’s model (Krishnan and Stark 1977) the controller would reduce any vergence error such that fixation disparity would eventually be zero. Schor (Schor 1979 a; Schor 1979(b)) refined Krishnan and Stark’s model by describing the fast controller as a leaky neural integrator and the slow vergence controller as a system with a longer time constant to maintain vergence posture. The slow vergence controller described in Schor’s model explains the phenomenon of vergence adaptation explained in section 1.3 of this dissertation, and it is different from the slow vergence controller described in Krishnan and Stark’s model.

Schor (Schor 1979(b)) showed a bi-phasic decay of the vergence posture), characterized by a rapid decay in about the first 10 seconds when disparity vergence was prevented by monocular occlusion (open loop). This occurred due to dissipation of innervation from the fast vergence controller. This was followed by a gradual decay of the vergence posture contributed by the dissipation of innervation from the slow vergence controller. Figure 1.1 shows a simplified control system model for vergence eye movement.

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Negative feedback

Input: Fast fusional Output: Target disparity vergence Vergence eye Slow fusional (transient and movement vergence sustained)

Figure 1.1: Simplified control system model for vergence eye movements

Even though disparity vergence is described as a feedback system the initial 200 ms of the vergence movement occurs with no feedback (open-loop condition) (Hung, Semmlow et al. 1986; Semmlow, Hung et al. 1986; Semmlow, Hung et al. 1993) from the oculomotor system. Thus, the transient portion of the fast vergence controller is open loop while the sustained portion of the fast vergence controller gets feedback and is therefore closed loop.

1.2 Components of vergence movement

Besides the disparity vergence eliciting vergence eye movements, accommodative vergence and to some extent proximal vergence also contribute to vergence eye movements (Carpenter 1991). While it is well established that innervation to the slow vergence controller of the vergence eye movement comes from the fast vergence controller (Schor 1979(b); Schor and Kotulak 1986), the contribution of accommodative convergence to slow vergence controller is less clear. Accommodative vergence is brought about by a change in accommodation through the cross-link gain controller. The amount of accommodative convergence brought about per diopter of accommodation is termed the AC/A ratio. Conflicting opinions are presented in the literature about the

4 placement of this AC/A cross-link and its contribution toward vergence adaptation through the slow vergence controller.

Studies by Schor and Kotulak (Schor and Kotulak 1986) and later by Schor (Schor 1992) demonstrated that both accommodation and vergence can be adapted through vergence accommodation and accommodative vergence respectively. Jiang (Jiang 1996) confirmed this finding by demonstrating a mean exophoric shift when accommodation was adapted. Because the slow accommodative output (accommodative adaptation) was increased, the fast accommodative output declined. This in turn produced a lower AC/A with the exophoric shift as a result. Hence, Jiang (Jiang 1996) concluded that the AC/A cross-link must be after the fast vergence controller but before the slow vergence controller.

However, studies by Rosenfield et al. (Rosenfield, Rappon et al. 2000) and Brautaset and Jennings (Brautaset and Jennings 2006) argue that the AC/A controller come after the slow vergence controller. Rosenfield et al. (Rosenfield, Rappon et al. 2000) found no change in AC/A ratio before and after prolonged monocular occlusion to create slow vergence controller decay. A decline in the output of the slow vergence controller should have caused an increase in the fast vergence controller, which should have decreased the AC/A ratio according to Schor (Schor 1992) and Jiang (Jiang 1996). Since no such change was observed it was concluded that the AC/A cross-link controller must be after both the fast and slow vergence controllers in the control system model. Figures 1.2 (A) and (B) illustrates the placement of cross-link gains for each model.

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(A)

(B)

Figure 1.2: (A) illustration supporting Schor and Jiang’s model (B) illustration supporting Rosenfield et al.’s model

The control system model proposed by Saladin (Saladin 2005) was meant to be clinician friendly (Figure 1.3), naming anatomical structures involved in the vergence dynamics. In this model the AC/A cross-link goes before the slow vergence controller and voluntary or proximal contribution from both accommodation and vergence feeds into the accommodative controller. Also, his model contains separate pathways for convergence and divergence. This dichotomy was not included explicitly in the earlier

6 control system models but experimental evidence has been accumulated for it ((Jones 1980; Hung, Zhu et al. 1997; Patel, Jiang et al. 1999).

Figure 1.3 Control system model of Saladin (2005). From J, Saladin. Stereopsis from a performance perspective. Optometry and Vision Science, Vol.82,(3), p.186-205, © The American Academy of Optometry, 2005. Reprinted with permission from the publisher

Under binocular viewing condition (closed loop) the output of the slow and fast controllers additively maintain the vergence posture as shown by Schor’s (Schor 1979(b)) computer simulated model (Figure 1.4).It is known that the slow vergence controller has a higher time constant. Therefore, it takes longer for the neural innervation to build up in this controller and also a longer time to dissipate the innervation when the disparity is removed (open loop) (Krishnan and Stark 1977). The fast vergence controller on the other hand has a lower time constant demonstrated by the initial faster decay of vergence

7 posture in open loop (Schor 1979(b); Sethi 1986). The neural innervation of the slow vergence controller causes vergence adaptation.

Figure 1.4: Modified from the computer simulation model of Schor (1979) showing the decay of FVC (fast vergence controller) with the simultaneous increase in innervation of SVC (slow vergence controller). The net vergence position is the additive sum of FVC and SVC

1.3 Vergence Adaptation

Vergence adaptation is used synonymously with terms like phoria adaptation and prism adaptation. Clinically, vergence adaptation is said to occur when the eyes tend to be more convergent i.e. less exophoric or more esophoric after viewing through base out prisms (Carter 1965) or after sustained viewing of a binocular stimulus (Patel, Jiang et al. 1999). Experimentally vergence adaptation has been demonstrated by incomplete relaxation of vergence posture when one eye is occluded after binocularly stimulating disparity vergence (Schor 1979 a). Neurologically, it is said to be an adjustment of tonic vergence innervation in response to sustained vergence disparity input (Ogle and Prangen 1953; McCormack and Fisher 1996). Vergence adaptation is a useful mechanism for the eye to cope with near work stress. Studies have established a correlation between poor vergence adaptation and patients with oculomotor symptoms (North and Henson 1981; Schor and Horner 1989).

8 Applying the control system model may seem to neatly explain how poor vergence adaptation can cause the visual symptoms presented in vergence anomalies. According to the control system model, the fast vergence controller initiates the vergence movement to a target reducing the retinal disparity. However, there is a residual retinal disparity because of the inexactness in binocular fixation (Schor and Ciuffreda 1983) termed fixation disparity. It is this fixation disparity that becomes the input for the slow vergence controller employed for sustained viewing. In addition to maintaining the vergence posture the slow vergence controller is said to relieve or supplement the easily fatigued fast controller of its stress (Carter 1965; Schor 1979(b); McCormack and Fisher 1996). It can be speculated that in cases of vergence anomaly the slow vergence controller is unable to maintain sustained vergence posture resulting in poor vergence adaptation. The onus of maintaining the posture then falls on the fast vergence controller. This is stressful to the vergence system and leads to oculomotor symptoms.

The above reasoning is based on an underlying assumption that the slow vergence controller relieves the fast vergence controller. Schor’s simulated model (Figure 1.4) shows that the output from the fast controller decrease as the output from the slow vergence controller increases. Further, it is proposed that the fast vergence controller after being relieved is ready to act on a novel stimulus (Schor 1979(b); Ciuffreda and Tannen 1995).

Implicit in the Schor model (Schor 1979(b)) is the idea that once slow vergence innervation is built up, this innervation has no influence on subsequent fast vergence movements. In order for this lack of interaction one would have to assume a kind of gating mechanism, whereby the slow vergence innervation is gated while the fast vergence innervation produces an eye movement. Alternatively, the fast and slow vergence pathways could function independently, such that there is no interaction either neurally or at the level of the extra ocular muscles because the two controllers could innervate different extra-ocular muscle fiber types.

9 From a neural point of view, the nature of the interaction between the fast and the slow vergence controllers is not well understood. The following are some known facts concerning the neurophysiology of vergence.

In order to produce a vergence movement, the disparity of the target object must be detected and a sensorimotor transformation must occur to convert the disparity signal to a vergence motor response. Richards (Richards 1970; Richards 1971) and Jones (Jones 1977) studied the detection of coarse disparities (0.5 to 4.6 degrees) psychophysically by flashing dichoptic targets. Both investigators reported individuals with stereoanomalies. That is, some subjects could not detect one class of disparities (convergent or divergent). Richards termed these individuals stereoanomalous, and argued that there are three pools of disparity detectors; convergence, divergence and zero disparity. Jones extended Richards work showing that individuals with stereoanomalies could also show vergence anomalies.

Later neurophysiological studies (Poggio and Talbot 1981; Poggio 1995) found neurons sensitive to the plane of fixation (tuned-zero neurons), closer targets (near cells) and beyond the plane of fixation (far cells), thus confirming Richards previous assertion. It is still not clear whether these disparity signals are used in generating the vergence eye movement (Werner and Chalupa 2004).

Once the disparity is detected the vergence signals eventually reach the brainstem where the vergence burst cells and tonic cells are responsible for the vergence movement. The burst cells code for vergence velocity while the tonic cells are responsible for vergence position. Both convergence and divergence cells have been found in an area of the mesencephalic reticular formation just dorsal and lateral to the oculomotor nucleus (Mays 1984; Mays, Porter et al. 1986).

The goal of this dissertation is to better understand the interaction between the slow and fast vergence controller. To do this, we will examine the influence of slow

10 vergence innervation on the dynamics of vergence eye movement after vergence adaptation. The term dynamics is used to refer to the parameters that are commonly used to characterize a vergence movement. These include vergence latency, vergence amplitude and vergence velocity. Latency is the reaction time and it is commonly measured by finding the difference between the target onset time and the time taken by the oculomotor system to make the vergence eye movement. The commonly reported vergence latency values ranges between 160-200 milliseconds (Rashbass and Westheimer 1961; Semmlow and Wetzel 1979; Ciuffreda and Tannen 1995). Latency reflects both the processing time for sensory information in the brain and the motor time taken to make the ocular movement. While the latency represents the sensory-motor transformation time, vergence velocity represents the motor firing action of the burst neurons that respond to the target disparity. The velocity signal is integrated into a position signal by the neural integrator. The difference between the initial and final vergence position gives the amplitude of vergence. Because of the tight relation between the position and vergence velocity a linear main sequence relation has been shown both in eye movement studies (Rashbass and Westheimer 1961) and in neurological studies (Mays, Porter et al. 1986).

1.4 Background

So far, only one study has looked at the question of whether sustained vergence influences the dynamics of vergence eye movements. In a study by Patel et al. (Patel, Jiang et al. 1999), vergence dynamics were compared between pre- and post- short term adapting conditions. The study had 6 subjects who were shown a 6-degree convergence demand for durations of 5, 30, 60 and 90 seconds, after which vergence demand toggled for three cycles between 4 degree and 6 degree. The target at each vergence demand was shown for 5 seconds. The study aimed to see if the fast vergence component (called the transient component in their study) could be adapted. Any change in vergence dynamics between the pre- and post condition was classified as an adaptation effect. They found that only the divergence dynamics changed, with the divergence peak velocity being lower after adaptation.

11 Patel et al.(Patel, Jiang et al. 1999) concluded that the transient or fast vergence component is adaptable but that the adaptation is direction specific, suggesting separate pathways for convergence and divergence sensorimotor control. Such a result could mean two things. First, the adaptation effect in their study must involve a suppression or reduction in the divergence disparity detectors or the divergence burst cells. Second, since the convergence velocity did not change, it seems that the change in divergence related cells was not accompanied by a concomitant change in the convergence cells. If the convergence velocity had increased, for example, there may have been a transformation of non-directional burst cells to convergence burst cells. Alternatively or in addition there might have been an increase in the tonic innervation level of the convergence burst cells, making it easier for these cells to reach their firing threshold.

A final explanation for the results of Patel et al. (Patel, Jiang et al. 1999) is as follows. It could be argued that after a period of sustained convergence, tonic innervation to the extraocular muscles (medial recti) is maintained. Such an increase in tonicity could alter the vergence dynamics of the vergence movement made to a new target. Specifically, the increased tonicity of the extraocular muscles could decrease the velocity (and possibly the amplitude) of convergence and divergence movements. The only way in which the tonic innervation would not influence a burst-driven vergence movement is if the tonic innervation were gated during the vergence movement. In Patel et al.’s (Patel, Jiang et al. 1999) study only the divergence velocity decreased. Therefore, one would have to hypothesize the presence of a non-linear gating mechanism, such that the tonic innervation to the extraocular muscles is gated for the convergence movement (so the burst and tonic innervation to the medial recti do not interact) but is not gated for the divergence movement.

The relationship between fast and slow vergence could not be fully assessed in Patel et al.’s (Patel, Jiang et al. 1999) study. This is because the vergence adaptation in their study was not likely to have been complete. Vergence adaptation begins almost after about 10 s of viewing the vergence target (Sethi 1986), but the adaptation is not complete

12 for about 4.5 to 5 minutes (Brautaset and Jennings 2005) for at least a 6 prism diopter target disparity at 40 cm. In Patel et al’s (Patel, Jiang et al. 1999) study the maximum duration for the convergence demand was 90 sec. Also, the vergence adaptation effect was not measured in their study and hence it is not clear if complete vergence adaptation occurred. This is important because it can be seen from Schor’s (Schor 1979(b)) simulated model (Figure 1.4) that the fast vergence output goes down as the slow vergence output increases. Hence, to study the interaction between the fast and slow vergence controllers, it must be established that vergence adaptation has taken effect.

As previously discussed, the fast vergence controller has a coarse and a fine component. The coarse component initiates the vergence movement without any feedback from the oculomotor system (open loop condition). The initial 200 ms of the vergence response is known to be contributed by the open loop component (Horng, Semmlow et al. 1998). In Patel et al’s (Patel, Jiang et al. 1999) study target duration of 5s included the open loop and the closed loop component of the vergence controller. In such a case it is possible that there could be an interaction in vergence dynamics between the open loop and the closed loop component.

For the reasons cited above, we performed the study described here to fully assess the interaction between slow and fast vergence controller. The specific question asked in the current study is that, does the innervation for slow vergence interact with the innervation for fast vergence, or is the slow vergence innervation gated when fast vergence movement occur.

1.5 Overview of experiments

Three preliminary studies were conducted to refine and shape the methodology for the main study. These experiments are described in chapter 2. The main study is described in the later chapters.

13 In the first experiment we studied the vergence dynamics for a real world target. In the second experiment we looked at the interaction between accommodation and vergence. The third experiment studied the vergence adaptation effect on vergence dynamics in an anaglyphic target set up.

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CHAPTER 2

PRELIMINARY STUDIES

2.1 Experiment I: Brock string experiment

2.1.1 Introduction

As a first step to study vergence dynamics, a real target under natural conditions was used. Natural conditions here refer to a visually rich environment that contains objects and visual frames that provide effective cues to relative depth to the observer (Erkelens, Steinman et al. 1989). The Brock string, a commonly employed therapeutic device in optometric vision therapy practice was selected for this purpose. The Brock string consists of a long string usually 6 meters in length with three wooden color beads (red, yellow and green). In vergence therapy a patient is asked to fixate between the color beads trying to keep the fixated bead clear and single. The non-fixated beads fall outside the limits of Panum’s fusional area and are seen double, a phenomenon called physiological diplopia. This helps the patients to appreciate the difference between diplopia (double vision) and haplopia (single vision). As the beads in the string can be easily aligned with the midline it serves as a convenient target to stimulate symmetrical vergence.

The current experiment was done to study the effect of short term vergence adaptation on vergence dynamics for a real world target. The study also aimed to ensure

15 that the custom made ISCAN (ISCAN, inc., Woburn, MA) infrared eye tracker goggle would be adequate to track vergence eye movements.

2.1.2 Methodology

Subjects

Five subjects with no binocular vision anomalies were enrolled. All subjects signed a consent form approved by the Biomedical Sciences Institutional Review Board of The Ohio State University prior to participation. The age range was 23-28 years. All subjects had corrected or uncorrected 20/20 vision for both distance and near. There were 3 emmetropes and 2 myopes with contact lens correction. The near phoria for the subjects were less than 4 ∆ (exophoria or esophoria) and the vergence facility with 12 ∆ BO/3 ∆ BI was greater than 15 cycles per minute.

Experimental setup

A Brock string was mounted on a black board that was at eye level for the subject. Two sets of target conditions, a far condition and a near condition were shown. For the far conditions the Brock string beads were positioned such that the vergence disparity was 4/8/12 degrees. For the near condition the beads had a disparity of 12/16/20 degrees. The chosen disparity levels were comparable to an earlier study (Alvarez, Semmlow et al. 2005). For each subject the inter-pupillary distance (IPD) was measured and entered into an Excel (Microsoft Corporation, Redmond, WA) worksheet program to calculate the distance at which the beads needed to be positioned to give the above target disparities.

Subjects were seated with a chin rest to minimize head movements. Subjects wore an ISCAN (ISCAN, Inc., Woburn, MA) infrared eye tracker goggle that monitored the eye movements. The eye tracker had a temporal resolution of 60Hz. This temporal

16 resolution was adequate to track vergence eye movement (Patel, Jiang et al. 1999). The spatial resolution of the instrument was 10-15 arc minutes .

A calibration run was recorded before the start of every test trial. In this calibration run, subjects were asked to look at colored pegs placed 4 degrees to the right and left of the central bead. After the calibration procedure, the pegs were removed and subjects were asked to look at the central bead for 40 seconds and were instructed to look back and forth between the central bead and either the closer or farther bead. Each bead was fixated for about 1 second while keeping it clear and single. Four trial conditions were measured in random order. In trial 1, subjects were asked to look between the center bead and the bead farther away in the near condition. In trial 2, subjects were asked to look between the center and the closer bead in the near condition. In trial 3, subjects were asked to look between the center bead and the bead farther away in the far condition and in trial 4, subjects looked between the center and closer bead in the far condition. Figure 2.1 illustrates the four trial conditions. It must be noted that both convergence and divergence velocities were obtained in each of these trials as the subjects looked back and forth between the beads. Two cycles of convergence and divergence eye movements were measured for each trial.

17

Figure 2.1: Illustration of the near condition (NC) trials 1 and 2 and far condition (FC) trials 3 and 4

2.1.3 Data analysis

A linear regression was plotted between the eye position during the calibration procedure and the angle of fixation to calculate the gain of the eye-tracker. The calibrated eye position data for the trial runs was calculated by subtracting the zero position (eye position while fixating on the center bead) and dividing the gain obtained from the linear regression equation in the calibration run. A time series of the calibrated eye position was plotted.

Vergence position was calculated by subtracting the difference in calibrated eye position between the left and right eye. In order to calculate the vergence velocity the traces were inspected for blink artifacts and saccades and such trials were discarded. The vergence position was low pass filtered at 5 Hz using a computer program and vergence velocity was calculated by differentiating the position data against time. Figure 2.2 shows both the vergence position and the vergence velocity plot. 18

Vergence velocity

Vergence position

Figure 2.2: Vergence position and velocity trace plotted for a given trial when both convergence and divergence movements were made

2.1.4 Results

The overall means for the five subjects along with the standard error of means for both convergence and divergence velocity on all four trials is shown in Figure 2.3

19

Figure 2.3: Comparison of average velocity of both convergence and divergence eye movements made on all four trials

Assumptions for equal variance and normality distribution of the residuals were checked and were found satisfactory. Repeated measures ANOVA was performed with vergence velocity as the response variable and subject as a random variable. The independent variable was trial condition. Repeated measures ANOVA was performed for both convergence velocity and divergence velocity separately.

Significant differences (p<0.001) among the trial conditions were found for both convergence and divergence velocities. Tukey post-hoc analysis showed a significant difference between the far condition and the near condition except between trials 1 and 3 for the convergence velocity. However, for divergence velocity there was a significant difference between far and near condition trials. That is, both trials 1 and 2 (near condition) were significantly different from trials 3 and 4 (far condition).

20 2.1.5 Conclusion

In this experiment velocities for divergence and convergence under a short adaptation period (40 seconds) for two different initial positions of the target were compared. There were two different initial positions for the real target used in this study; they were 8 degrees (trials 3 and 4) and 16 degrees (trials 1 and 2).

The ISCAN (ISCAN, Inc., Woburn, MA) instrument used was adequate in tracking the vergence eye movements (Figure 2.2). Vergence velocity for both convergence and divergence varied based on the initial target position after a short adaptation time. The vergence velocity recorded in this study (convergence =33.85 deg/s; divergence=31.04 deg/sec) was higher than that reported in a previous study (convergence=17.53 deg/s; divergence=16.9 deg/s). (Alvarez, Semmlow et al. 2005). Erkelens et al.(Erkelens, Steinman et al. 1989) have reported higher vergence velocities under natural conditions. Also, with change in target distances accommodation could have influenced the vergence eye movement.

2.2 Experiment II - Effect of accommodative vergence on vergence adaptation

2.2.1 Introduction

The aim of this experiment was to study the effect of accommodative vergence on the slow vergence controller (vergence adaptation). The information from this study helps in determining whether it was necessary to use targets at a constant accommodative demand rather than real world targets to exclude accommodative vergence.

21 2.2.3 Methods

Subjects

26 subjects, 21 to 39 yrs of age (mean=26 + 4), were enrolled in the study. All subjects signed a consent form approved by the Biomedical Sciences Institutional Review Board of The Ohio State University prior to participation. Subjects had 20/20 vision and normal binocular vision. 18 were exophoric (0.5 Δ to 10 Δ), 5 were esophoric (0.5 Δ to 5 Δ) and 3 were orthophoric.

Experimental set up

Dissociated phoria was measured using the modified Thorington technique. The modified Thorington technique uses a Muscle Imbalance Measure (MIM) card (Bernell ® 1980) that was mounted at 40 cm on a white board to cut off peripheral distractions. The card has a center aperture that was illuminated with a reading lamp. Subjects were made to wear a trial frame with a red Maddox rod trial lens that was mounted horizontally in front of the right eye. A vertical streak was seen through the right eye and the center light was seen through the left eye. The MIM card (Bernell ® 1980) has calibrated vertical and horizontal circular marks each representing 1 prism diopter at 40cm. Every 2 prism diopter is numerically marked on the card. Subjects were asked to call out the number and the position of the red line with respect to the center light. If the line was to the right, the eye position is esophoric. If the line is to the left the eye position is exophoric, and orthophoria is the result if the line crosses the center light.

Procedure

The subject’s head was stabilized with a chin rest and their phoria was measured before (pre-phoria) and after (post-phoria) adapting to either a 6 Δ BO or a negative lens for 5 minutes, on different days in a random order. Vergence adaptation is found to be

22 maximal around 3 minutes (Henson and North 1980) and in a recent study (Brautaset and Jennings 2005) it was found that vergence adaptation was complete by 5 minutes to a 6 prism base-out given at 6 m and 40 cm. Hence, 5 minutes was chosen as the adapting time for this task.

The negative lens power was calculated based on the individual’s stimulus AC/A ratio in order to equate the amount of convergence to 6 Δ. This was done by asking the subjects to report the phoria while viewing binocularly through +1.00, + 2.00, plano, - 1.00 and -2.00 diopter lenses after maintaining a clear image of the Thorington (MIM) numbers. The order of the lenses was randomized to prevent any carry over adaptation effect. A regression line was plotted between the lens power and the measured phoria value. The slope of this regression was taken as the stimulus AC/A ratio (Rainey 2000; Rosenfield, Rappon et al. 2000). The required negative lens power to give the needed 6 Δ diopter of convergence was calculated based on this AC/A ratio. The average calculated AC/A ratio was 2.56 Δ/D. This calculated AC/A ratio seems lower than the normal value reported in the literature of 4 Δ/D. This was because of the asymmetry observed between negative lens and positive lens used in younger subjects. Hence, for the purpose of calculating the negative lens power required to bring about 6 Δ of convergence, the AC/A was calculated only from the plano and negative lens powers for each subject.

Subjects fixated on a 2° word target (“CLEAR”) at 40cm during the adaptation time. For the disparity vergence condition the subjects remained binocular (closed loop condition for vergence) and the 6 Δ BO lens was placed in front of the left eye. For the accommodative condition, the subject’s left eye was patched in order to elicit only accommodative vergence (open loop condition for vergence) while adapting through the negative lens mounted in front of the right eye. Thus, any change in phoria position would have resulted only from the change in accommodation and the resultant accommodative convergence produced. The prism and the lens in the above conditions were removed and the Maddox rod was mounted quickly in front of the right eye before

23 measuring the post-phoria. Subjects were asked to close their left eye while the lenses were changed.

2.2.4 Results

Vergence adaptation was calculated by subtracting the pre-phoria from the post- phoria measurement. Positive values indicated more esophoria or less exophoria, while negative values represented the opposite result. Mean adaptation to the 6 Δ BO stimulus was 2.18 ± 1.27 Δ, and mean adaptation to the negative lens was 1.65 ± 1.6 Δ. Figure 2.4 shows the magnitude of vergence adaptation measured on each of the 26 subjects.

From Figure 2.4 it can be seen that 24 subjects showed vergence adaptation to the 6 Δ BO. Two subjects (subject 4 and 23) showed neither a positive nor a negative vergence adaptation to the prism. For the accommodation stimulus 22 subjects showed vergence adaptation in the esophoric direction. One subject (subject 5) showed neither a positive nor a negative vergence adaptation to the negative lens. Three subjects (subjects 3, 11 and 15) showed an increase in exophoria viewing the accommodative stimulus.

24

Figure 2.4: Illustration of vergence adaptation shown for both accommodative stimulus and disparity vergence stimulus for all the twenty six subjects

A one sample t-test was used for data analysis. Vergence adaptation with prism and with the lens was significantly different from 0 (p<0.0001). There was no significant difference in the magnitude of adaptation observed between the prism and negative lens (p=0.204).

2.2.5 Conclusions

Vergence adaptation was induced with both the vergence disparity target and the accommodative target. The mean amplitude of vergence adaptation found in this study was similar in the two conditions. This suggests that the slow vergence controller for vergence adaptation receives input from both disparity and accommodative vergence. Hence, this study is in agreement with those of Schor and Kotulak (Schor and Kotulak 1986) and Jiang (Jiang 1996) in that the AC/A cross-link is before the slow vergence controller in the control system model. Therefore, accommodative convergence can

25 induce vergence adaptation and accommodation must be held constant to study the interaction between the fast vergence controller and slow vergence controller.

2.3 Experiment III: vergence dynamics after vergence adaptation studied in an anaglyphic setup

2.3.1 Introduction

The purpose of this study was originally to study the interaction between the slow vergence controller and the fast vergence controller using anaglyphic targets. Data collected on five subjects showed higher vergence latency than that reported in the literature. Such a result could have been due to the lower luminance of the anaglyphic targets. Also, an order effect for phoria and vergence adaptation was found when more than one trial was performed on the same day. The methods and results are discussed below.

2.3.2 Methods

Subjects

5 subjects between the ages of 24 and 34, with no known binocular vision problems and 20/20 vision were enrolled. All subjects signed a consent form approved by the Biomedical Sciences Institutional Review Board of The Ohio State University prior to participation.

Experimental setup

Computer generated anaglyphic targets (blue and red) were displayed at 65 cm on a black screen. The target at this distance subtended 1.5º of visual angle. The target luminance of the red and blue targets was measured with a LITEMATE III Photometer

26 (Model 504, Photoresearch, Burbank, CA) and was found to be 1.2 cd/m2. The blue and red filters used in this study had complete cancellation with the computer generated blue and red targets. The edges of the computer screen were masked using a black screen and the entire testing procedure took place in a dark room to avoid fusional artifacts.

Procedure

The subject’s head movements were minimized using a chin and headrest. Eye movements were recorded using the IOTA Orbit Eyetrace (IOTA AB, ver 1.71, Sweden) infrared eye tracker goggle. The eye tracker had a sampling rate of 500 Hz. Red and blue filters were mounted on the trial lens holder of the eye tracker in front of the right and left eye respectively.

Two conditions, no adaptation (NA) and adaptation (A) were performed on different days in random order. Ten trials for each of the conditions were recorded. A calibration run preceded each experimental run. In a calibration run a set of three white horizontal crosses at eccentricities –5, 0 and +5 degrees were shown. Subjects were asked to fixate at each of the crosses for about a second. The recorded eye position was linearly regressed against the target eccentricity angle to calculate the gain of the instrument from the sum of the least squares linear regression equation. This gain was used to calibrate the eye data collected in the subsequent experimental run.

In an experimental run, subjects viewed a central white fixation cross for 2s, followed by a 6º convergence target. The convergence target was displayed for 5 seconds for the no adaptation (NA) condition and was displayed for 3 minutes for the adaptation (A) condition. From the 6º convergence position, subjects then made either a divergence or a convergence movement to a 4º target that was displayed for 10seconds. The target sequence in an experimental trial is shown in Figure 2.5. In the ten trials, 5 trials used a 4º convergence targets and 5 had 4º divergence targets for both NA and A conditions. For one subject only four trials were measured for the adaptation condition. The data

27 collected from the IOTA Orbit Eyetrace (IOTA AB, ver 1.71, Sweden) software was analyzed offline. Three trials were measured for the adaptation condition in a given day and ten trials were measured for the NA condition in one day. A 3-5 minute break was given between trials. During the break time, the room was dimly illuminated with an incandescent bulb and subjects were encouraged to look away from the computer screen and to look elsewhere in the room.

Figure 2.5: Illustration of the target presentation in a given experimental trial

The anaglyphic targets were generated using a Visual Basic 6 program. The program generated the target disparity based on every subject’s Inter-Pupillary Distance (IPD). A digital voltage was sent out of a Digital-to-Analog (D/A) channel of an Analog- to-Digital (A/D) board miniLAB 1008 (Measurement Computing corporation, Norton, MA) to indicate the onset of a target presentation. The data from this board was sampled at 500 Hz to match the sampling rate of the eye tracker. The IOTA Orbit Eyetrace (IOTA 28 AB, ver 1.71, Sweden) software does not allow an external synchronization of the recorded eye position. Hence, a computer mouse was wired to take the voltage signal out from the mouse’s left click button. This signal was fed into the same A/D board that was used for the targets. Thus, when the record button of the IOTA Orbit Eyetrace (IOTA AB, ver 1.71, Sweden) was clicked with the mouse, a voltage signal was sent to the recording board allowing synchronization of the recorded eye movement trace with the target onset time. The end of a trial was recorded by clicking the stop button of the IOTA Orbit Eyetrace (IOTA AB, ver 1.71, Sweden) with the specially wired computer mouse.

2.3.3 Results

Data analysis

The vergence eye movement position data was low pass filtered at 5Hz to eliminate high frequency noise in the signal. The filtered position was then differentiated to calculate the vergence velocity. This procedure was comparable to an earlier study on vergence dynamics (Patel, Jiang et al. 1999). Vergence latency and vergence amplitude were calculated by visual inspection of the plotted vergence eye trace and by going through the vergence position data column to note the change in vergence position. All the vergence dynamics parameters were calculated for both the 4º convergence and divergence movements made from the 6º convergence target. Data showing blink artifacts were eliminated. In the vergence adaptation trials the comparison of phoria values before and after 3 minutes of sustained vergence showed vergence adaptation in 76% of the trials.

Vergence Dynamics

The average values and the standard deviation for the vergence parameters (vergence latency, vergence amplitude and peak vergence velocity) are shown in Table 2.1. The parameters were compared between the two conditions (NA and A) for both

29 convergence and divergence trials. The comparison of means with standard error of mean is plotted for latency (Figure 2.6), amplitude (Figure 2.7) and peak velocity (Figure 2.8) and is shown below.

Vergence Convergence Divergence Parameters No Adaptation Adaptation No Adaptation Adaptation Latency 370.2 ± 91.3 496.3 ± 264.6 451.1 ± 119.3 496.8 ± 94.8 (ms) Amplitude 3.6 ± 1.1 4.4 ± 2.1 5.2 ± 1.3 5.6 ± 0.8 (degrees) Peak Velocity 16.4 ± 7.5 26 ± 25.6 22.3 ± 6.6 24.1 ± 8.3 (degrees/s)

Table 2.1: Comparison of the vergence parameters in no adaptation and adaptation conditions for both convergence and divergence

It can be seen from Table 2.1 that the recorded vergence latency in this experiment is much higher than that reported in earlier studies (150 -250 ms (Rashbass and Westheimer 1961; Ciuffreda and Tannen 1995; Alvarez, Semmlow et al. 2005). This could have resulted for two reasons. The luminance of the targets (1.2 cd/m2) used in this experiment is lower and this could have increased the latency. It has been shown that a decrease in luminance increases the latency of disparity vergence (Stephens 1982). Second, accommodative vergence is known to have a longer latency of about 280-380 ms (Krishnan, Shirachi et al. 1977; Ciuffreda and Tannen 1995). It is unclear if subjects employed accommodative vergence in this experiment, although one might not have expected this since the targets were held at a constant distance.

The measured average differences between the convergence latency, amplitude and peak velocity for adaptation and no adaptation trials were 126ms, 0.8º and 9.6º/s. For

30 divergence the differences were 45.7ms, 0.4º and 2º/s. Non-parametric Wilcoxon rank sum test was performed on vergence dynamic parameters between the no adaptation and adaptation trials. No statistically significant (p>0.1) differences were found between the two trials for any of the parameters.

Figure 2.6: Illustration of average vergence amplitude for the no adaptation (NA) and adaptation (A) trials for both convergence and divergence

31

Figure 2.7: Illustration of average vergence amplitude for the no adaptation (NA) and adaptation (A) trials for both convergence and divergence

Figure 2.8: Illustration of average vergence velocity for the no adaptation (NA) and adaptation (A) trials for both convergence and divergence

32 Phoria measures

In the NA trial, ten runs were made with breaks in between. For the “A” condition, three trials were made. The order effect was plotted for phoria measures in these conditions. Interestingly, it was found that the phoria values fluctuated up and down randomly. The vergence adaptation measured by the difference in pre-phoria and post- phoria also seem to show some positive correlation with the phoria measure (i.e) when a greater phoria was measured the magnitude of phoria adapatation was greater and vice- versa for lower measured values of phoria in a given trial. These data show that even though the adapting target was shown only for 5 seconds some vergence adaptation effect was found that could be carried over to the subsequent trial and could influence the phoria measured in a subsequent trial.

2.3.4 Conclusion

For both convergence and divergence, there were no statistically significant differences observed in the NA condition and A condition dynamics for any of the vergence parameters. Greater variability in measured, particularly for convergence latency and velocity, was observed. Also, the vergence latency found in this study was longer than that reported in the literature. Decreased target luminance could be the factor responsible for this observation.

33

CHAPTER 3

INTRODUCTION - MAIN STUDY

Experiments I to III described in the earlier chapter lead to a more refined experiment to address the primary goal of this dissertation. The primary goal is to investigate the influence of the slow vergence controller on the fast vergence controller. In brief, the following were learned from experiments I to III that facilitated the design of the current experiment:

A. Experiment I (Brock string experiment): Two different target distances were chosen to elicit different disparity vergence. From the graph plotted in Figure 2.4 it can be seen that trial 1 (12-16 degrees) and trial 4 (8-12 degrees) showed significant difference for both convergence and divergence velocity. In the current experiment the magnitude of disparity vergence was chosen to be 8, 12 and 16 degrees based on the result from Experiment I. B. Experiment II (Effect of accommodative vergence on vergence adaptation): It is well established that vergence and accommodation act in synergy through the cross-link gain controllers when looking at near targets. However, it was unclear if the accommodative gain controller would contribute to the slow vergence controller. In experiment II we showed that accommodative vergence contributes to the slow vergence controller, by demonstrating vergence adaptation after accommodative vergence was elicited under open loop vergence conditions. Thus

34 it is important to maintain a constant target distance to avoid changes in accommodation demand while the target disparity is being changed. For the current experiment the target distance was held constant. C. Experiment III (vergence dynamics in an anaglyphic set up): In this experiment longer latencies were observed for both convergence and divergence movements. This could have been either a result of the low target luminance used in the study or because of accommodative vergence. Also, the phoria measures and the magnitude of vergence adaptation were observed to vary over the ten trials measured in the “NA” condition. This shows that vergence adaptation of one trial interacts with the phoria measure of the subsequent trial, in spite of the breaks given in between the trials when subjects were asked to fixate elsewhere. Importantly, this implies that measuring vergence dynamics in more than one trial at a time would show some interaction on measurements made on the subsequent trials. Hence, the current study restricted data collection to only one trial in a given day for each subject. The time between two trial runs was at least 24 hours. Also, a haploscope arrangement with targets of higher luminance was used for the current study. The targets in the current study had adequate contours and detail to hold accommodation and provided for easy blur detection.

35

CHAPTER 4

METHODS

4.1 Subjects

Twenty subjects (8 males and 12 females) with visual acuities of 20/25 or better and with no known ocular or systemic problems were enrolled, after signing a consent form approved by the Ohio State University Biomedical Sciences Review Board. The age of the subjects varied between 21 and 32 years of age (mean = 24.3 ± 2.7).

Subjects were either emmetropic or corrected for their refractive error with contact lenses. Spectacle wearers were excluded from the study to avoid erroneous noise that could be produced in the eye tracker from spectacle reflection. 9 emmetropes and 11 myopic subjects (refractive error ranged from -1.25 D to -6.25 D) were enrolled.

4.2 Baseline measurements

On the first study visit, baseline measures of monocular near point of accommodation (NPA) with a 20/40 near card target and near point of convergence (NPC) with pencil push up method were measured on all subjects. The average NPA for the right eye was 8 cm and that for the left eye was 9 cm. The average NPC was found to

36 be 6cm. These measurements were within the accepted normal range (Scheiman, Wick et al. 2002).

4.3 Experimental set up

4.3.1 Haploscope arrangement

Two front surface mirrors were mounted at right angles to one another and at 45 degrees to the facial plane. The mirrors were placed at a distance of 12 cm from the subject’s lateral canthus. Targets were presented on two identical CRT monitors (CTX, VL 501 and CTX, VL 510) that were positioned at 28cm from each of the front surface mirrors (Figure 4.1). Thus, the total optical distance from the target to the subject was 40 cm. The targets were held at this constant distance thus minimizing the accommodative and proximal cues associated with target distance (Rosenfield, Chun et al. 1997; Semmlow, Alvarez et al. 2007). The edges of the two front surface mirrors were obscured with a rhombus shaped black aperture on one and a rectangular black aperture on the other. This was done to prevent peripheral fusional cues.

The two monitors were programmed from one computer using Visual Basic6. VGA and DVI monitor splitter cables were used to split the display so that the left half of the display was seen on one computer monitor and the right half was seen on the other. Thus simultaneous display of targets with no or minimal lag time between the monitors was achieved. The screen resolution of both monitors was 1024 x 768. The monitors were physically aligned to each other and the center of the target (fixation cross) was aligned to the center of the mirror using a Visual Basic program that allowed alignment of the target independently on each monitor. From this centered position target disparity was presented using computer software that accounted for each subjects’ inter-pupillary distance. The monitors were closely matched in luminance using a handheld light meter (LITEMATE, III, Model # 502, Burbank, CA) and by perceptually adjusting the brightness for a simultaneous luminance match for identical targets presented on each

37 monitor. Both the luminance measurement and the simultaneous luminance match were made for the target reflected from the front surface mirrors. A white target on a black background was used for this study and the Michelson luminance contrast [(Lmax-Lmin) / (Lmax + Lmin)] measured on the right and left monitors for these targets were 98.1 % and 98.3%. The average luminance value of the targets measured on the monitors was about 92 cd/m2. This luminance value was much higher than that used for the anaglyphic targets (1.2 cd/m2) in experiment III.

Figure 4.1: Block diagram showing the experimental set up. TC 1 and TC 2 are target monitors 1 and 2 respectively where the target stimulus is displayed. M1 and M2 are the mirrors mounted at 45 degrees angle to the subject’s face plane. E1 and E2 are the eye- tracking units consisting of the infrared source and cameras before the left and right eyes

38 4.3.2 Stimulus target

The target used in this study consisted of two squares (1 deg and 1.6 deg) concentrically placed with a central fixation cross (0.4 deg). This target was effective in holding foveal fusion and had sufficient details to hold the accommodative response. This target was presented binocularly to generate the disparity targets, and monocularly to the right eye for phoria measurements.

Although the target distance was not changed in this experiment, the accommodative response could have changed for the different target disparities presented. The accommodative response could not be estimated simultaneously with eye position measurements because the infrared source from our autorefractor interacted with that of the eye tracker producing spurious noise in the eye movement data. Hence the accommodative response was measured prior to the study. The measurement of accommodation is discussed below.

4.4 Accommodative measurements

Accommodative measurements were made on the first study visit. The target stimulus with the same dimensions and closely matched luminance as that used in the haploscope presentation was presented on a Compaq computer monitor (Michelson luminance contrast = 98.2%). The edges of the monitor were masked with a black board. The monitor was placed behind a Grand Seiko binocular autorefractor/keratometer (WR- 5100K) at a distance of 40 cm from the subject’s lateral canthus. Subjects’ heads were stabilized with the autorefractor’s head and chin rest.

Subjects wore an empty trial frame and were instructed to keep the square target clear and single. Ten measurements of the refractive status were then made from the right eye with the Grand Seiko binocular autorefractor/keratometer WR-5100K. Next, subjects wore an 8 base in prism or an 8 prism base out in front of the left eye or trial lenses of power +1.25D or –1.25D lenses in front of both eyes. The order of the prisms or lenses

39 was randomized for each subject. Instructions to maintain the square target clear and single were given in all conditions. Ten measurements were made for each condition from the right eye. Since the left eye saw through the prism and measurements were made only in the right eye, off-axis refraction resulting from prism was avoided.

The 8 prism diopter vergence demand closely approximated the change in vergence demand created in the experimental task (4 degree vergence change). Similarly the 1.25D of accommodative change is expected had the target been seen in real depth. The calculations for these values are shown below.

The viewing target distance is at 40 cm or 0.4 m (d)

Convergence demand = PD (cm) / d (m)

For an average PD of 6 cm, the convergence demand at this distance is = 6/0.4 = 15 prism diopters = 8.18 deg (1 prism diopter = 0.5454 deg)

In the main experimental task, a 4 degree change in vergence demand was made from a 12 degree convergent position. Thus a convergence movement was made to a 16 deg target or a divergence movement was made to an 8 deg target. Thus, the accommodative response was measured for a 4 degree vergence change by giving an 8 prism BI (divergence demand) and 8 prism BO (convergence demand) in front of one eye.

For 12 deg or 22 prism diopters of convergence, the corresponding target distance would be about 27.27 cm. This creates an accommodative demand of 3.6 D. For 16 deg or 29 prism diopters the target distance would be about 20.68 cm, producing an accommodative demand of 4.83 D. For 8 deg or 15 prism diopters the viewing distance would be 40 cm with an accommodative demand of 2.5 D. Thus the change in accommodative demand along the three vergence postures is about 1.2 D. Hence, a +

40 1.25 D and a -1.25 D lenses were used to measure the accommodative response for the subjects.

4.5 Eye tracking instrument

The ISCAN (ISCAN, Inc., Woburn, MA) infrared eye tracker goggle was used to measure the eye movements. This device allows for binocular eye movement measurement. The instrument has an infrared light source that illuminates the eye after reflected from a beam-splitter. The reflected eye image from the beam splitter travels back to an infrared camera that captures the video image of the eye. The dark pupil is brightly illuminated by the infrared light source and and tracked by the software. The software allows the user to change the threshold settings. This was adjusted for each subject such that the pupil was accurately tracked with minimum or no noise. The temporal sampling rate of the instrument was 60 Hz for 132 trial runs and 120 Hz for 268 trials. Both of these sampling rates were adequate for collecting vergence data (Patel, Jiang et al. 1999). The spatial resolution of the instrument is 10-15 arc minutes.

Onset of the target was signaled by a change in the digital voltage output signal. This signal was taken from an Analog-Digital (A/D) miniLAB 1008 (Measurement Computing corporation, Norton, MA) board and was fed into the Analog-in channel of the ISCAN (ISCAN, Inc., Woburn, MA) board. Such a set up permitted the synchronization of target presentation with the eye movement recording.

4.6 Test Trial

The following steps describe the sequence of target presentation for a given test trial. The sequence is also shown in Figure 4.2:

41 1. Calibration: A calibration preceded the trial run. The calibration was performed for each eye separately. A set of horizontal and vertical crosses were shown and subjects were instructed to look at the center cross, then to look to the cross on the left and then the cross on the right, fixating at each cross for about a second. When the crosses were presented on one monitor the other monitor had a black screen. Only horizontal eye movements were of interest in this study so the calibration was performed in the horizontal meridian. 2. Fixation: After the calibration procedure subjects were asked to blink and were then alerted before starting the trial. The trial began with a fixation cross presented on both monitors for 2 seconds. The target had a convergence demand of 8 degrees. The position of the eye while fixating at this cross was taken as the zero position. 3. Phoria measure 1 (pre-phoria): The fixation cross was extinguished and then the concentric square target was presented to the right eye for 20 seconds. A black screen (0.3 FL luminance) was displayed for the left monitor and the left eye in the dark room saw no visible targets. 4. Fixation: After the pre-phoria measurement the fixation cross (8 degrees) was again shown for 2 seconds 5. 12 degree disparity target (non-adapting condition): The 12 degree vergence disparity target was shown for 5 seconds. This required a 4 degree convergence movement to be made from the fixation cross. 6. 16 degree or 8 degree disparity target: Either a 16 degree (convergence trial) or an 8 degree (divergence trial) vergence disparity target was randomly selected to be displayed for 0.2 seconds (200 milliseconds). The short duration of the target was to elicit the open-loop or reflexive fast vergence eye movement. 7. Phoria measure 2 (phoria):

42 The short duration disparity target described in the previous step was followed by another phoria measurement for 20 seconds. Any change in phoria posture would indicate the presence of phoria adaptation resulting from the prior vergence eye movements made to the targets shown above. 8. Fixation: The fixation cross was viewed for 2 seconds after the phoria measurement 9. 12 degree disparity target (adaptation condition): The 12 degree vergence disparity target was shown for 300 seconds (5 minutes). 5 minutes was found to be sufficient to have produce prism adaptation (Brautasett & Jennings 2005). At the end of the 2.5 minutes the computer beeped twice to indicate the remaining 2.5 minutes. The computer beeped again to indicate that 3 seconds remained prior to the next target presentation. 10. 16 degree or 8 degree target – 0.2 seconds Either a 16 degree (convergence trial) or an 8 degree (divergence trial) vergence disparity target that was presented in the non-adapting trial was displayed for 0.2 seconds (200 milliseconds) at the end of the adaptation condition. 11. Phoria measure 3 (post-phoria): The phoria was measured for 20 seconds at the end of the target presentations described above to measure the vergence adaptation effect 12. Fixation cross: The trial terminated with the subject viewing the fixation cross.

Prior to the test trial a subjective phoria measurement was made with the Muscle Imbalance Measure (MIM) card (Bernell ® 1980) and the Maddox rod held in front of the right eye. After the test trial the phoria value was measured again. As stated earlier, in a given day only one test trial data was performed. Subjects were asked to come on 20 different days. 10 trials were given for the convergence direction and 10 trials were measured for the divergence direction. The order of the trials was randomized for each

43 direction (convergence and divergence). The randomization was done in Microsoft Excel (Microsoft Corporation, Redmond, WA) for each subject.

Figure 4.2: Illustration of target sequence presented in a given experimental trial

44

CHAPTER 5

RESULTS

5.1 Data analysis

Eye movement and target signal data collected by the ISCAN (ISCAN, Inc., Woburn, MA) software were analyzed offline using MATLAB® R2007a (The MathWorks Inc., Natick, MA) software. Eye movement data were calibrated from the calibration procedure performed prior to the trial. Vergence eye position was calculated from the difference between the calibrated right eye and left eye position. Time series plots of calibrated vergence eye position were made for further analysis.

5.2 Accommodation – Baseline measure

As discussed in the methods, accommodation measures were taken on all subjects on the first day of the trial while viewing the target stimulus on a computer with and without lenses (1.25 DS) and prisms (8 prism diopters). Average values were calculated from the 10 readings taken for each of the viewing condition on every subject. With the 8 BI prism, there was modest relaxation of accommodation of about 0.13 D ± 0.27. With the 8 BO prism, the average increase in accommodation was about 0.22 D ± 0.22. With

45 +1.25 DS, accommodation relaxed by about 1.00 D ± 0.2 and for the –1.00 DS lens the eyes accommodated by 1.00 D ± 0.4.

5.3 Calculation of phoria and vergence adaptation

Objective phoria position was measured for 20 seconds. The first 10-15 s of phoria measure is contributed by the fast vergence component decay (Krishnan and Stark 1977; Schor 1979 a) and the remaining phoria measure indicates the slow vergence component decay. It is the last 5s that is of interest in this study. Average position for the last 5s is calculated as the measure of phoria. Three phoria measures were made in a given trial at three different instances in time as described in the methods. First, it was measured after the calibration procedure and was called pre-phoria (phoria 1). Next it was measured before the presentation of the 12 degree convergent vergence adaptation target and was called phoria (phoria 2) and finally it was measured at the end of the vergence adaptation period and after the brief presentation of the transient divergent or convergent stimuli. This latter phoria measure was called the post-phoria (phoria 3). Differences between the pre-phoria measure, phoria measure and post-phoria measure were calculated. On average, the differences between the above phoria measures were found to be significantly different from zero (p <0.05) for both the convergence and divergence trials (Figure 5.1). The difference between the post-phoria and pre-phoria measure showed the greatest change (Box plots on the right in Figure 5.1). This shows that the vergence adaptation target (12 degree convergent target) was often effective in eliciting vergence adaptation effect.

46

7.5

5.0

2.5

0.0

Vergence adaptation (degrees) adaptation Vergence -2.5

-5.0 Convergence Divergence Convergence Divergence Convergence Divergence phoria-prephoria postphoria-phoria postphoria-prephoria

Figure 5.1: Box plots showing the magnitude of vergence adaptation calculated from the differences in phoria position measured at three instances in time for both convergence and divergence trials. Measures shown on the left were made at the beginning of the trial prior to vergence adaptation and that on the right were made at the end of the trial after viewing the vergence adaptation target

A positive value for the differences between each of the phoria measures demonstrates positive vergence adaptation (positive trials). A negative value or zero indicates a lack of vergence adaptation (negative trials). It can be seen from Figure 5.1 that there is variability observed in the magnitude of vergence adaptation measured. That is, both positive trials and negative trials were found in the data. As the primary aim of this experiment is to study the interaction of vergence adaptation on the fast vergence controller it becomes important to separate out the positive and negative trials. This is discussed further in section 5.5

47 5.4 Calculation of vergence dynamics

Twenty subjects completed all the 20 trials. Two vergence measurements to a transient target (either a convergent 16 degrees or a divergent 8 degrees target) were made in a given trial at different time intervals as described in the methods. The first measure was made after viewing the 12 degree convergent target for 5 seconds (pre- adaptation) and the second measure was made after viewing the 12 degree convergent target for five minutes to induce vergence adaptation (post-adaptation). The analysis for both these measures and for the convergence and divergence eye movements is identical.

Blink free vergence traces were selected for analysis. Of the total trials collected for convergence and divergence 153 trials for convergence and 167 trials for divergence were found to be free of blink artifacts in both pre-adaptation and post-adaptation condition. Therefore, these data were usable for further pair wise analysis. Figure 5.2 shows a sample vergence trace collected over the entire duration of the test trial with the components of the trial marked.

Vergence position data was low-pass filtered at a cut-off frequency of 10 Hz. This cut-off frequency was comparable to earlier studies (Patel, Jiang et al. 1999). A two point difference method was used to calculate the vergence velocity from the filtered vergence position. Filtered vergence position, vergence velocity and target analog signals were then plotted for further calculations (Figure 5.3).

48

Figure 5.2: Time series plot of vergence position data measured along with the target onset data from the Analog signal from the A/D board for a given trial

Peak velocity was calculated as the maximum velocity in a given velocity trace. Vergence amplitude was calculated as the difference between the start and end of a vergence movement. The start and end of the movement was identified as average of two points prior to the start of vergence eye movement. This point was easily located from the beginning of the velocity plot. The end of the vergence movement was identified as the vergence posture that corresponded with the deceleration of the vergence velocity to zero. A similar criterion has been used in earlier studies (Bahill, Clark et al. 1975). Vergence latency was calculated from the difference between target onset time (noted from the change in analog signal) and the change in vergence eye position noted by manually going over the data column. This difference was then divided by the time taken between each data point (1/120 = 0.008333 for 120 Hz sampling rate or 1/60 = 0.016667 for 60 HZ sampling rate) to give the value in milliseconds.

49

Vergence peak velocity

25

20 Target 15

10 Vergence poisition 5

Position (degrees) 0

-5

-10

-15 Vergence amplitude

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 Time (seconds)

Vergence latency

Figure 5.3: Time series plot showing the Target position, vergence position and vergence velocity. The vergence parameters measured (latency, peak velocity and amplitude) are marked

The overall average vergence latency, amplitude and peak velocity before and after sustained convergence is shown for both convergence and divergence in Table 5.1 below.

50 Condition Convergence Divergence Latency Amplitude Peak Latency Amplitude Peak (ms) (degrees) Velocity (ms) (degrees) Velocity (deg/s) (deg/s) Pre-adaptation 226.8 (± 57) 1.7 (± 0.9) 14.7 (± 7.5) 245.9(± 69) 3.2 (± 1.6) 16.2 (± 6.8) Post-adaptation 225.9 (± 44) 2.0 (± 0.9) 15.9 (± 8.3) 274.3 (± 86) 1.8 (± 1.0) 10.7 (± 3.8)

Table 5.1: overall average values of vergence parameters (vergence latency, vergence amplitude and vergence peak velocity) before and after viewing the vergence adaptation target is shown along with the standard deviation for both convergence and divergence eye movements

A one sample t-test was performed on the difference between the pre-vergence adaptation vergence parameters and post-vergence adaptation vergence parameter for both the convergence and divergence directions. No significant difference was found for convergence latency between the pre-vergence and post-vergence adaptation trials (p=0.484). Significant differences however were observed for both vergence amplitude and vergence velocity (p <0.05) in the convergence trials. For the divergence trials significant differences (p <0.05) were observed for all the vergence parameters (latency, amplitude and velocity).

On average, vergence amplitude and velocity increased for convergence by 17.7 % and 8.2 % respectively after vergence adaptation. For the divergence eye movement the latency increased by 11.6 %, whereas there was a decrease in vergence amplitude and velocity by 43.8 % and 34% respectively.

5.5 Effect of vergence adaptation on vergence dynamics

The post-phoria (phoria 3) minus the pre-phoria (phoria 1) values measured in this experiment are plotted in Figure 5.1. From this figure it can be seen that there is variability in vergence adaptation both for the convergence and divergence trials. Figure

51 5.4 below shows the vergence adaptation variability in individual subjects (20 trials). It can be seen that though many of the subjects (n=12) showed vergence adaptation on all trials, some subjects showed no vergence adaptation on some trials. However, no subject fell under the zero line in Figure 5.4, indicating that all subjects showed vergence adaptation on at least some trials.

To analyze the influence of vergence adaptation on the fast vergence controller the trials were divided into positive trials (vergence adaptation occurred) and negative trials (vergence adaptation did not occur) and were reanalyzed. Positive trials are those with a decrease in exophoria or increase in esophoria after sustained vergence to the 12 degree convergent target for 5 minutes. Negative trials are those where there was an increase in exophoria or a decrease in esophoria after sustained vergence to the 12 degree convergent target. A cut-off value of vergence adaptation greater than 0.8 degrees was used to identify the positive and negative trials. 0.8 degree was the mean adaptation effect found after viewing the 12 degree convergence target for 5 seconds and was thus used as the cut-off value. Values of 0.8 degrees or less were identified as negative trials.

5.6 Comparison between positive trials and negative trials

About 20% of the trials were identified as negative trials for both convergence (30 out of 153 trials) and divergence (34 out of 167) trials. The average vergence parameters (vergence latency, vergence amplitude and vergence peak velocity) are tabulated below for the negative and positive trials for both convergence (Table 5.2) and divergence trials (Table 5.3).

52

7.5

5.0

2.5

0.0

Vergence adaptation (degrees) adaptation Vergence -2.5

-5.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Subjects

Figure 5.4: Box plots showing the magnitude of vergence adaptation for all subjects on all the 20 trials

A one sample t-test was performed under each of these trial conditions. For convergence, no significant differences were found between pre-adaptation and post- adaptation trials under negative trials (p>0.4). Under positive trials however, significant differences were found for vergence amplitude and velocity (p<0.05) but not for latency (p=0.599)

53

Condition Convergence (negative trials) Convergence (positive trials) Latency Amplitude Peak Latency Amplitude Peak (ms) (degrees) Velocity (ms) (degrees) Velocity (deg/s) (deg/s) Pre-adaptation 220.6 (± 34) 2.0 (± 0.9) 16.9 (± 7.3) 228.4 (± 62) 1.6 (± 0.9) 14.1 (± 7.5) Post-adaptation 215.4 (± 39) 2.0 (± 0.8) 16.8 (± 6.5) 228.2 (± 44) 2.0 (± 0.9) 15.7 (± 8.7)

Table 5.2: Comparison of average vergence parameters for negative and positive trials identified for convergence trials

For divergence, significant differences were found for vergence velocity and amplitude but not for latency (p=0.655) in the negative trials. Significant difference (p<0.05) was found for all vergence parameters in the positive trials.

Condition Divergence (negative trials) Divergence (positive trials) Latency Amplitude Peak Latency Amplitude Peak (ms) (degrees) Velocity (ms) (degrees) Velocity (deg/s) (deg/s) Pre-adaptation 267.9 (± 75) 2.8 (± 1.2) 13.8 (± 4.4) 240.4 (± 66) 3.3 (± 1.6) 16.8 (± 7.2) Post-adaptation 271.4 (± 93) 1.6 (± 0.9) 9.71 (± 3.4) 275.1 (± 84) 1.9 (± 1.0) 11.0 (± 3.9)

Table 5.3: Comparison of average vergence parameters for negative and positive trials identified for divergence trials

5.9 Vergence anomalous subjects

It was found that on some trials (at least 4 out of 10 convergence trials), three subjects in this study showed no convergence response to the transient (200 ms) vergence

54 stimulus. Interestingly, a vergence response was elicited for the same transient target after vergence adaptation. Figure 5.5 shows a trial run from each of these three subjects.

12 12

10 10

8 Subject 1 (a) 8 Subject 1 (b)

6 6

4 vergence position (degrees)

Vergence position (degrees) 4 2

2 0

0 1.5 2 2.5 3 3.5 2 2.5 3 3.5 Time (seconds) Time (seconds)

11 11

10 10

9 9 8 Subject 2 (a) Subject 2 (b) 8 7 7 6 6 Position (degrees) Position (degrees) 5 5 4 4 3 3 2 2 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Time (seconds) Time (seconds)

11 11 10 10

9 Subject 3 (a) 9 Subject 3 (b) 8 8

7 7

Position (degrees) Position (degrees) 6 6 5 5

4 4 3

3 0.8 0.9 1 1.1 1.2 1.3 1.4 1 1.2 1.4 1.6 1.8 2 2.2 Time (seconds) Time (seconds)

Figure 5.5: Time series plots showing absence of convergence response to the transient stimulus (a) and presence of convergence response after vergence adaptation (b) for three subjects who showed vergence anomaly

55

CHAPTER 6

DISCUSSION

6.1 Accommodation

The baseline accommodation measured with the Grand Seiko autorefractor showed that vergence induced by prism disparity was primarily brought about by disparity vergence rather than accommodative vergence. There was only a minimal change in accommodation when the disparity was introduced (0.13D and 0.22D), and this may have originated from the CA/C cross-link interaction between accommodation and disparity convergence. Thus, when disparity is introduced and the accommodative demand is held constant, the primary source of vergence is disparity vergence.

6.2 Vergence Adaptation

The purpose of this experiment was to induce vergence adaptation, such that the dynamics of vergence eye movement could be measured before and after this adaptation. Vergence adaptation was brought about by viewing a 12 degree convergence target for five minutes. The adaptation effect was calculated by a change in phoria position. Hence, a more convergent posture after viewing the target would indicate positive vergence adaptation in the expected direction. In the current study, vergence adaptation was found

56 after viewing the target for 5 minutes as well as for 5 seconds (Figure 5.1). The adaptation effect, as expected, was greater for the 5 minute viewing time (about 2.3 deg more esophoric) when compared to the 5 seconds viewing time (about 0.8 deg change in vergence posture).

6.3 Vergence parameters

Comparisons of the vergence parameters (vergence latency, vergence amplitude, vergence peak velocity) were made before and after sustained convergence for both the convergence and divergence trials. The analysis was first performed for all trials, regardless of whether vergence adaptation occurred (Table 5.1). For the convergence trials, vergence latency did not change significantly before and after vergence adaptation. However, vergence peak velocity and vergence amplitude increased after adaptation by 8.2% and 17.7% respectively. For the divergence trials, all three parameters showed significant changes after vergence adaptation. For divergence, vergence latency increased by 11.5% after adaptation while vergence amplitude and vergence peak velocity decreased by 43.8% and 34% respectively. Patel et al.(Patel, Jiang et al. 1999), who used shorter periods of sustained convergence, reported only a decrease in peak divergence velocity (25%) while the other parameters that were measured in their study (steady state vergence posture and latency to peak velocity) did not change.

In our experiment the trials were also divided into positive trials that showed vergence adaptation in the expected direction and negative trials that did not show vergence adaptation. In the negative trials, for convergence there were no significant differences in the vergence parameters before and after sustained convergence. However, in the positive trials, convergence peak velocity and convergence amplitude increased by 11.4 % and 25% respectively. These differences were found to be statistically significant (p<0.05). The convergence latency however was not found to be statistically significant (p=0.599).

57 For the divergence trials, vergence amplitude and peak velocity decreased for both the negative and positive trials. The peak velocity decreased by 34.5% for the positive trials and by 31.2% for the negative trials. The vergence amplitude decreased by 42.4% for the positive trials and by 42.8% for the negative trials. These decreases were found to be statistically significant (P <0.05). Divergence latency increased in both the positive and negative trials but the increase was found to be significant only for the positive trials (p<0.05).

6.4 Interpretation

In interpreting these results, we will first consider the peak velocity and amplitude parameters. Regardless of whether vergence adaptation occurred, vergence peak velocity and vergence amplitude declined for the divergence trials following a period of sustained convergence. These results can be interpreted to mean that only sustained convergence, and not vergence adaptation, is required to bring about decreases in divergence amplitude and divergence velocity. Referring to Figure 6.1 below, what is shown are the pools of convergent disparity detectors and divergent disparity detectors in the cortex, as well as the pools of convergent and divergent burst cells in the midbrain. The disparity detectors drive the vergence burst cells. The fact that sustained convergence results in a decrease in divergent peak velocity could mean that any of the possibilities (shown in Figure 6.1) might occur. These possibilities are:

(A) Sustained convergence leads to suppression of divergent disparity detectors (B) Sustained convergence leads to suppression of divergent burst cells (C) Sustained convergence leads to conversion of divergent disparity detectors to convergent disparity detectors (D) Sustained convergence leads to conversion of divergent burst cells to convergent burst cells

58 Of these possibilities, the most likely is that the divergent disparity detectors are suppressed or undergo conversion. These are the most likely possibilities because there was a concomitant change in vergence amplitude with changes in vergence peak velocity that matches the main sequence relationship (vergence peak velocity versus amplitude) previously described in the literature (Rashbass and Westheimer 1961; Hung, Ciuffreda et al. 1994). It has been reported for vergence that if the amplitude of a vergence movement changes by 1 deg, then the peak velocity of this vergence movement changes by 4 deg/s (Hung, Ciuffreda et al. 1994). In our experiment, the reduction in divergent response amplitude for trials that showed vergence adaptation was 1.4 deg with an accompanying decrease in peak divergence velocity of 5.8 deg/s. For the trials where vergence adaptation did not occur, the reduction in divergent response amplitude was 1.2 deg with a reduction in peak divergence velocity of 4.1 deg/s.

CORTEX

Convergent disparity Divergent disparity detectors C detectors A

MESENCEPHALON

Convergent Burst Divergent Burst neurons neurons D B

Figure 6.1: Illustration of the four possible (A, B, C, D) interactions among the disparity detectors for vergence disparity and vergence burst neurons

59 If the divergent disparity detectors are suppressed or reduced in number, then the target disparity may not be assessed accurately. This could lead to a larger undershoot such as that found after sustained convergence in this study. In addition, suppression or reduction in the number of divergent disparity detectors would reduce the number of burst cells driven by the disparity detectors. This in turn could reduce the vergence peak velocity, just as we found.

On the other hand, if the burst cells were suppressed or declined in number, then one would expect a drop in velocity, but any change in amplitude may not match the change expected from the main sequence. The critical test of the disparity detector hypothesis would be an experiment in which divergent stereoanomalies are tested for before and after a period of sustained convergence. In that case, our hypothesis would predict an increased incidence of divergent stereoanomalies following a period of sustained convergence.

Also, in our study we found three subjects (15% of the study population) who apparently showed vergence anomalies for the convergence direction on at least 4 out of the 10 trials. Earlier studies have reported an incidence of 20% for vergence anomaly with convergence anomaly being more common (Jones 1972; Jones 1977). Both vergence anomaly and stereoanomaly are said to be due to a lack of disparity detectors (Richards 1970; Richards 1971; Jones 1977). We observed that following the sustained period of convergence in the current experiment, the three subjects were subsequently able to respond to the transient convergent target. Such a finding could probably support the mechanism presented in (C) where greater convergent disparity detectors are recruited from the divergence disparity detector pool.

The convergence results, on the other hand, show that sustained convergence does not influence convergence amplitude and convergence peak velocity unless convergent vergence adaptation occurs. This, combined with the divergence results, implies that a strong sustained effort capable of driving vergence adaptation can result in one of the

60 following. Sustained convergence might lead to an increase in the number of convergence (disparity detection or burst) cells available to produce a vergence movement. Alternatively or in addition, sustained convergence might lead to a rise in the tonic innervational level of the convergence (disparity detection or burst) cells, making it easier for them to reach their firing threshold.

The final vergence parameter that was measured in this experiment is the vergence latency. Vergence latency encompasses the time taken for the sensory signals to reach the cortex, the processing of the information (disparity detection) necessary for an appropriate eye movement, and the motor signal (vergence burst neuron activity) to elicit a vergence response. For the vergence responses recorded before and after vergence adaptation we can safely assume that the sensory signal reaching the cortex via the optics of the eye and the visual pathway would essentially remain a constant. Thus, a change in vergence latency before and after vergence adaptation would reflect the disparity processing time (sensory processing) and the time taken to generate the vergence movement (motor output). It was found in this study that the divergence latency increased significantly after vergence adaptation. This could mean that there was an increase in sensory processing because of lower availability of divergent disparity detectors (process (C) in Figure 6.1) or alternately because of the suppressed activity due to sustained convergence (process (A) in Figure 6.1). It is also possible that the motor output is causing the delay by taking a longer time to reach the firing threshold due to process (B) or (D). Convergence latency showed an insignificant decrease in latency after vergence adaptation.

In addition to the explanations put forth so far, an alternate explanation for the results would involve the activity at the lower motor level. It is possible that increased neural innervation could increase the tonicity of the medial recti. Recent neurophysiological studies (Büttner-Ennever 2006) have identified a unique type of slow non-twitch, fatigue-resistant muscle fiber called the multiply innervated muscle fibers (MIFs) that are different and have independent topographic organization from the singly

61 innervated muscle fiber (SIF). The SIFs primarily drive eye movements while the MIFs participate in determining the tonic muscle activity as in gaze-holding, vergence and eye alignment (Buttner-Ennever, Horn et al. 2001; Buttner-Ennever, Horn et al. 2002; Büttner-Ennever 2006). Thus, the SIFs and its inputs may be associated with the transient response of the fast vergence controller while the MIFs may be associated with the sustained response of the fast vergence controller. The role of MIFs in vergence adaptation has not yet been examined.

If the tonicity of the MIFs were to increase as convergence is sustained, then the SIFs would have to operate against the sustaining forces of the MIFs in order to produce a vergence movement. This could result in a decline in vergence parameters (velocity and amplitude) when a vergence eye movement is made in the convergent or divergent direction. Instead, the results of the current study showed a decline in the vergence parameters for divergence but an increase in velocity and amplitude for convergence trials (when vergence adaptation occurred) after sustained convergence.

It is difficult to explain this result by proposing a gating mechanism, in which the MIFs are inhibited while the SIFs are innervated to produce a vergence movement. In that case, the MIFs would only be inhibited or gated when a convergence movement is made, allowing interaction between the MIFs and SIFs when a divergent movement is made. Further, it is difficult to explain how “peripheral” interactions such as those described here could account for the increase in convergent velocity and amplitude noted after sustained convergence or how such interactions could explain why the vergence main sequence relationships continued to be obeyed after sustained convergence. We therefore feel that the most parsimonious explanation for the results is a change in the properties of disparity detectors brought about by sustained convergence.

62

CHAPTER 7

CONCLUSION

In this experiment, we aimed to study the influence of the slow vergence controller, responsible for vergence adaptation, on the fast vergence controller that initiates a vergence eye movement in the presence of a target disparity. Specifically, the study was to examine the interaction of the slow vergence controller with the transient (open loop) part of the fast vergence controller (Westheimer and Mitchell 1969; Jones and Kerr 1972; Hung, Semmlow et al. 1986; Semmlow, Hung et al. 1993).

The results show that after a period of sustained convergence, divergence amplitude and peak velocity decline. The reduction in these parameters occurs regardless of whether sustained convergence brings about vergence adaptation. The concomitant change in amplitude and peak velocity seems to fit the main sequence. This suggests that changes in the divergent disparity detectors might be responsible for the decline in amplitude and peak velocity. Studies in which stereoanomalies are assessed prior to and after sustained convergence are necessary to solidify this theory.

On the other hand, after a period of sustained convergence, convergence amplitudes and peak velocities do not change unless vergence adaptation takes place. When these parameters change, they increase.

63 Finally, because vergence adaptation is correlated with declines in divergent peak velocity and amplitude but it is correlated with increases in convergent peak velocity and amplitude, we conclude that the slow fusional vergence innervation is gated during a vergence eye movement.

Previous literature suggests that vergence adaptation would release the fast vergence controller to quickly act on a novel target (Schor 1979(b); Ciuffreda and Tannen 1995). From our study we can conclude that while this may be true for eye movements made in the convergent direction, the divergence movements would be slower and less accurate after sustained convergence.

64

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