1 Role of Accommodation in Clinical Measures of Proximal Vergence

Role of Accommodation in Clinical Measures of Proximal Vergence

Thesis

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in

the Graduate School of The Ohio State University

Rachel Fenton

Graduate Program in Vision Science

The Ohio State University

2019

Thesis Committee

Nicklaus Fogt, O.D., M.S., PhD, Advisor

Catherine McDaniel, O.D., M.S.

Donald Mutti, O.D., PhD

Copyrighted by

Rachel Fenton

2019

Abstract

Proximal vergence is the subtype of vergence that is stimulated by visual cues other than blur and disparity. There are two major clinical methods to assess proximal vergence. In one of these methods, termed the AC/A differencing method, proximal vergence is determined by calculating the difference in vergence change from the far-near

AC/A method and the vergence change from the gradient AC/A method (equated for the accommodative demand). In the other method, termed the +2.50D method, the change in vergence posture between distance viewing and near viewing through a +2.50D lens is calculated. In assessing these values, it is typically assumed that response accommodation matched the change in accommodative demand from distance to near, which would be 2.50D for a 40cm near viewing distance. However, individuals often do not alter their accommodation by the amount of the accommodative demand. Therefore, proximal values calculated using accommodative responses might vary from proximal values that are calculated using the accommodative demand. The purpose of the present research is to determine the extent to which response accommodation could influence these methods of assessing proximal vergence, in order to better understand how proximal vergence is measured and therefore to better understand the relationship between proximal vergence and the other vergence subtypes in future studies. Thirteen subjects were recruited, ages 22-37, who underwent a battery of measurements consisting

ii of interpupillary distance, visual acuity, stereoacuity, accommodative amplitudes, step vergence ranges, distance heterophoria, and near heterophoria using various refractive lenses. A Grand Seiko WR5100K autorefractor measured accommodation.

Accommodative data revealed high accommodative lags in many subjects, which influenced response AC/A ratios and response proximal vergence results. Proximal vergence was then calculated in four distinct ways, two based on stimulus measurements and two taking response accommodation into consideration. Statistical analysis using t- tests showed no statistically significant difference between any of these proximal vergence calculations after using the Bonferonni correction (p>0.0083 for all comparisons). Additionally, no statistically significant relationship between measures of fusional vergence and measures for proximal vergence were found (p>0.05) using linear regression analysis. In conclusion, this study found that all four clinical methods, using stimulus and response measurements, yielded similar values.

iii

Dedication

I would like to dedicate this to my parents, brother, and fiancé for their continued love, support, and encouragement.

Acknowledgments

I would like to thank my thesis advisor for his assistance and feedback throughout this project, as well as those who served on my thesis defense committee for their thoughtful critiques of this research and thesis. I additionally would like to thank all of my loved ones for their encouragement throughout this project. The project described was supported by Award Number Grant UL1TR002733 from the National Center For

Advancing Translational Sciences. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Center For

Advancing Translational Sciences or the National Institutes of Health.

Vita

Denison University (2010-2014): Bachelor of Arts in Psychology

The Ohio State University (2015-present): Seeking O.D. degree

The Ohio State University (2016-present): Seeking M.S. degree

Publications

Matthews, N., Welch, L., Achtman, R., Fenton, R., & FitzGerald, B. (2016).

Simultaneity and temporal order judgments exhibit distinct reaction times and training effects. PLoS ONE, 11(1). doi: 10.1371/journal.pone.0145926

Fields of Study

Major Field: Vision Science

Table of Contents

Abstract ...... ii Dedication ...... iv Acknowledgments ...... v Vita ...... vi List of Tables ...... ix List of Figures ...... x Chapter 1. Introduction and Literature Review ...... 1 Chapter 2. Methods ...... 13 Participants: ...... 13 Procedure: ...... 14 Chapter 3. Results ...... 20 General Data Interpretation: ...... 20 Stimulus Proximal Values: AC/A Differencing Method and +2.50D Method ...... 21 Proximal Vergence Calculations for Stimulus Values ...... 23 Far-Near Differencing Method with Stimulus AC/A ...... 23 The +2.50D Method ...... 24 Statistical Analysis of Stimulus AC/A Differencing and +2.50D Proximal Vergence ...... 25 Refractive and Accommodative Measures ...... 26 Response Far-Near AC/A Ratio and Response Gradient AC/A Ratio ...... 31 Proximal Vergence Calculations for Response Values ...... 32 AC/A Differencing Method with Response AC/A ...... 32 +2.50D Method Corrected for Remaining Accommodation ...... 33 Statistical Comparisons for Proximal Vergence Values ...... 35 Statistical Analysis: Vergence Ranges versus Proximal Values ...... 37 vii

Bibliography ...... 42

viii

List of Tables

Table 1. The accommodative amplitudes, vergence ranges, and heterophoria values ...... 21 Table 2. Stimulus far-near AC/A values and stimulus gradient AC/A values ...... 23 Table 3. Proximal vergence values using the stimulus AC/A far-near differencing method and the stimulus +2.50D method ...... 25 Table 4. Expected and measured (actual) change in accommodation from distance to near ...... 28 Table 5. Change in accommodation induced by the +1.00D lens at near, and the accommodation remaining when viewing through the +2.50D lens at near ...... 31 Table 6. Response far-near AC/A values and response gradient AC/A values ...... 32 Table 7. Response AC/A differencing proximal values and +2.50D (corrected for accommodation) proximal values ...... 34 Table 8. Results of paired t-tests for proximal values obtained by the four clinical methods applied in this experiment ...... 36

List of Figures

Figure 1. The static accommodative stimulus-response curve ...... 5 Figure 2. Distance Modified Thorington card with incandescent lamp ...... 15 Figure 3. Half-eye trial frame with refractive lenses and Maddox lens ...... 16 Figure 4. Autorefractor with near Modified Thorington card attached to near point rod . 17 Figure 5. Schematic of the experimental protocol ...... 19 Figure 6. Scatter plot with best fit line between Stimulus AC/A Differencing proximal vergence values and +2.50 Method Uncorrected proximal vergence values ...... 26 Figure 7. Scatter plot with best fit line between Response AC/A Differencing proximal vergence values and +2.50 Method Corrected proximal vergence values ...... 34 Figure 8. Proximal values obtained from nine subjects ...... 36

Chapter 1. Introduction and Literature Review

Vergence eye movements consist of disjunctive movements where both eyes move in opposite directions, or in other words both eyes move inward or outward (Ono,

1983). While Hering’s law of equal innervation is typically thought of in relation to conjugate eye movements, this law is applicable and valid when applied to vergence eye movements and states that both eyes receive equal innervation when conducting an eye movement (Ono, 1983). The vergence system is comprised of four distinct components, as originally described by Maddox (1893). Maddox termed these vergence subtypes tonic vergence, fusional vergence, accommodative vergence, and voluntary (proximal) vergence (Maddox, 1893; Morgan, 1980; Morgan, 1983; Leigh & Zee, 2006; Goss,

1995). These components will be discussed in detail throughout the following paragraphs.

Maddox (1893) described tonic vergence as baseline vergence that brings the eyes from their anatomic resting position to a slightly more converged position in the absence of a visual stimulus. In other words, tonic vergence is thought to be caused by the baseline tone of the extraocular muscles in order to hold our eyes in the physiologic position of rest or heterophoria position (Wick, 1985). The average normative value for tonic vergence is equivalent to the distance heterophoria, which is between two prism

1 diopters of divergence or exophoria and 1 prism diopters of convergence or esophoria

(Owens, et al., 1983; Scheiman & Wick, 2008; Goss, 1995).

Fusional vergence, also referred to as disparity vergence or reflex vergence, is driven by retinal disparity, and allows for both eyes to fixate on a target (Maddox, 1893;

Stark, et al., 1980; Morgan, 1983; Jiang, et al., 2002; Goss, 1995). Retinal disparity is defined as the difference in binocular angle between the target and the position of bifixation (Ciuffreda, et al., 2002). At a given fixation distance, there exists a collection of points in space that correspond to a binocular retinal disparity of zero, called the horopter (Tyler, 1983). Panum’s fusional area spans the line of the horopter to allow for small errors in fusional vergence posture without perceiving diplopia, while fixation disparity is the error in fusional vergence that exists within Panum’s area and is thought to act as a feedback mechanism to the fusional vergence system in order to maintain fusion (Ciuffreda, et al., 2002; Tyler, 1983; Scheiman & Wick, 2008; Leigh & Zee, 2006;

Panum, 1858; Fogt and Jones, 1998; Jaschinski, 2018).

Crossed diplopia exists when the object of regard exists outside the horopter as well as outside of the inner limit of Panum’s area, while uncrossed diplopia exists when the object of regard exists outside the horopter as well as beyond the outer limit of

Panum’s area (Fogt & Jones, 1998; Ciuffreda, et al., 2002). Positive fusional vergence is the convergence that occurs in response to crossed diplopia, while negative fusional vergence is the divergence response that occurs in response to uncrossed diplopia (Tyler,

1983; Ciuffreda, et al., 2002).

Additionally, fusional vergence can be broken down into fast and slow fusional vergence, both of which play a role in prism adaptation (Owens, et al., 1983). When a prism is initially introduced, the fast fusional vergence system reacts to decrease disparity but then decays leaving a large fixation disparity; the slow fusional vergence system then responds next to alleviate the fast fusional vergence system while also stimulating the tonic vergence system to change its tone to compensate for the added prism (Sreenivasan, et al., 2009; Schor, 1980).

Accommodative vergence occurs as a result of an accommodative response to blur, where stimulating accommodation leads to a convergence response and relaxing accommodation leads to a divergence response (Ciuffreda, et al., 1983). Maddox (1893) believed that accommodative vergence was the main contributor to the vergence response, while the other vergence components played a minor role in correcting for any inaccuracies in the accommodative vergence response (Maddox, 1983; Schor, 1992). It is now believed that the other vergence components may play a larger role in the overall vergence response than Maddox had originally believed (Ciuffreda, et al., 1983). The near triad is the synkinesis between accommodation, vergence, and pupillary response, meaning that these responses are linked when one is stimulated (Leigh & Zee, 2006;

Goss, 1995). In order to fully understand accommodative vergence, an overview of the accommodative system is warranted.

Just as there are thought to be four subsets of vergence, there are also thought to be four subsets of accommodation: blur, vergence, proximal, and tonic (Charman, 2008;

Heath, 1956). The stimulation of accommodation occurs when the ciliary muscle receives

3 parasympathetic innervation and contracts, leading to zonular relaxation and subsequently the crystalline lens returning to a more convex shape. These changes lead to an increase in the converging optical power within the eye; this is what allows for clear vision at near in pre-presbyopic patients (Rabbetts, 1998; Charman, 2008).

The typical accommodative response can be discussed through the static accommodative stimulus-response curve as shown in Figure 1, which consists of four distinct regions (Morgan, 1944). The first portion of this curve shows a flat line from zero to between approximately 0.50 and 1.50 diopters (average of 0.75D), which some researchers believe corresponds to a steady accommodative response, or tonic accommodation (Morgan, 1944; Ciuffreda, et al., 1983; Wick, 1985). The second portion is linear in nature and demonstrates a proportional change in accommodative response that is slightly less than the accommodative stimulus due potentially to lag of accommodation or to depth of focus (Ciuffreda, et al., 1983). Depth of focus allows for small errors in accommodation, such as a lead or lag of accommodation, to exist without perceiving blur (Morgan, 1944; Charman, 2008). Depth of focus in regard to our eyes would be the distance that the target image can exist away from the retina while still being interpreted as clear instead of blurred (Rabbetts, 1998). The third portion of the curve is non-linear in nature and corresponds to a significantly smaller accommodative response to an increasing accommodative stimulus (Morgan, 1944). Lastly, the fourth portion of the curve can be termed the saturation zone which graphically demonstrates the amplitude of accommodation, or the point at which no additional accommodative

4 response would occur in response to an increasing stimulus to accommodation (Morgan,

1944).

Figure 1. The static accommodative stimulus-response curve is shown. Used with permission from Wick B. (1985), Clinical factors in proximal vergence, Volume 62, Issue 1, pages 1-18, www.optvissci.com.

As previously mentioned, accommodative vergence occurs following a given accommodative response (Schor, 1992). The magnitude of accommodative vergence that occurs per one-diopter of stimulus to accommodation is termed the AC/A ratio, which informs much of our clinical decision-making regarding binocular vision disorders

(Horwood & Riddell, 2014). The AC/A ratio can be determined multiple ways, most commonly through the calculated method or through the gradient method (Scheiman &

Wick, 2008; Goss, 1995; Horwood & Riddell, 2013). The calculated, or far-near, method of determining the AC/A ratio takes into account the convergence demand of moving the eyes from a distance to a near target, the distance and near heterophorias, and the stimulus to accommodation while viewing a near target at a standard 40cm distance

(Scheiman & Wick, 2008; Goss 1995). The gradient method of determining AC/A holds the testing distance constant, while the stimulus to accommodation is altered using various magnitudes of refractive lenses and measuring the heterophoria response

(Bhoola, et al., 1995; Horwood & Riddell, 2013; Scheiman & Wick, 2008; Goss, 1995).

Both of these equations are listed below, where PD is the interpupillary distance in centimeters, D is the near working distance in meters (therefore 1/D is the accommodative demand at that given near distance), h is the near heterophoria, H is the distance heterophoria, esophoria is represented by a negative value, and exophoria is represented by a positive value.

(1) Calculated AC/A = [(PD/D) – h + H]/(1/D)

(2) Gradient AC/A = [(phoria)–(phoria with lens)]/(dioptric value of lens)

A notable difference between these two AC/A measurements is that proximal vergence, which will be defined below, is thought to play a role in the calculated AC/A, while it is absent in the gradient AC/A; this is due to the change in the physical stimulus location in

6 the calculated AC/A, while the gradient AC/A holds the testing distance constant. This difference likely leads to a poor correlation between these two measurement methods

(Bhoola, et al., 1995; Scheiman & Wick, 2008; Ciuffreda, et al.,1983).

The last subtype in the Maddox (1893) vergence classification is voluntary vergence, also termed proximal vergence throughout this thesis, which is the vergence response that results from the “awareness of nearness” of a target (Maddox, 1893; Fogt, et al., 2016). The perceived nearness of a target is potentially influenced by many stimuli, including previous knowledge of a target’s location, proprioception, overlay, motion parallax, texture gradient, and size constancy in relation to relative size (Schor, et al.,

1992; Fogt, et al., 2016). It is thought by some investigators that proximal vergence could explain how large distance to near or near to distance vergence movements are initiated, specifically when the magnitude of the vergence requirement is outside of the range of disparity detection (Fogt et al., 2016; Schor, et al., 1992; Wick & Bedell, 1989). The extent to which proximal vergence is thought to be involved in the total vergence response varies vastly between studies, likely due to varying testing conditions.

Proximal vergence can be measured under closed loop or more commonly open loop conditions, where the loop refers to the negative feedback loop associated with blur accommodation or fusional vergence (Fogt, et al., 2016). In other words, blur accommodation is eliminated in an accommodative open loop scenario, disparity vergence is eliminated in a disparity open loop scenario, or both blur accommodation and fusional vergence are eliminated in a dual open loop scenario (Fogt, et al., 2016). Blur accommodation is eliminated through the use of pinhole apertures to increase depth of

7 focus or the use of a Difference of Gaussian (DOG) target, which is a blur free grating pattern (Hokoda, et al.,1983; Fogt, et al., 2016). Fusional vergence is eliminated through the use of prism or by covering one eye to create dissociated ocular conditions (Hokoda, et al., 1983; Fogt, et al., 2016).

The amount of proximal vergence that contributes to the overall vergence response can be discussed in terms of the proximal convergence to testing distance ratio, or PCT ratio, which is a value that describes the change in convergence that occurs secondary to a change in test distance or proximity (Fogt, et al., 2016). Conceptually, the

PCT ratio is analogous to the AC/A ratio, but describes the relationship between proximal cues and convergence instead of the relationship between accommodative cues and convergence as the AC/A ratio does. The PCT ratio is typically measured under open loop conditions, and is found to be 1.29 prism diopters per diopter on average, with a range from 0.5 to 2.0 prism diopters per diopter (Hokoda, et al., 1983). In addition to the

PCT ratio, proximal vergence can also be quantified as a percentage of the total vergence response. In general, studies show that proximal vergence plays a small role in the overall vergence response under closed loop conditions, whereas proximal vergence tends to play a large role under open loop conditions (Fogt, et al., 2016). Wick (1985) in his study measured the contribution of proximal vergence to the total vergence response at near by utilizing open vergence loop conditions during his measurements. He concluded that proximal vergence contributes approximately 22% to the total near target vergence response (Wick, 1985; Fogt, et al., 2016). North and colleagues found a 45% contribution of proximal vergence to the overall vergence response using an uncommon cue

8 disharmony methodology, which places two vergence cues correctly at one distance while the third vergence cue is set for a different distance (North et al., 1993, Fogt, et al.,

2016). Hung and colleagues (1996) developed a mathematical dual closed loop model, from which they calculated that proximal vergence contributes less than 1% to the total vergence response at near (Hung, et al., 1996; Fogt, et al., 2016). Additionally, various textbooks reference proximal vergence contributions of 50% or even up to 70% of the overall vergence response (Hokoda, et al., 1983; Scheiman & Wick, 2008).

While large variability exists in estimates of proximal vergence contributions in the laboratory setting, a valid question would be how large of a role proximal vergence plays under normal viewing conditions, or in other words is it worth assessing clinically.

Comparing proximal vergence measurements to the other vergence types may provide insight into this question, where an inverse correlation may indicate that proximal vergence is more significant when the magnitude of other vergence inputs are low, and a positive correlation may indicate a shared neural origin where the vergence components supplement each other. These questions have been addressed in the literature, with conflicting results. Morgan (1950) found an inverse correlation between clinical measures of accommodative vergence and proximal vergence, while Hofstetter (1951) found no such relationship. Regarding fusional vergence, Hofstetter (1951) found that proximal vergence supplemented fusional vergence (albeit the two were not correlated) during fusional vergence range testing, while Mannen and colleagues (1981) found a negative relationship between the two. Therefore, it is still unclear the extent to which proximal vergence plays a role in the total vergence response, as well as whether

9 proximal vergence has a positive, negative, or no relationship with the other vergence subtypes. A deeper understanding of these relationships could inform clinicians on different approaches to take with vision therapy. For instance, if a positive relationship exists between proximal vergence and the other vergence subtypes, then when patients undergo vergence training in vision therapy, extra exercises that focus on increasing the patient’s use of proximal cues to elicit near vergence responses could be introduced.

There exist two main clinical methods to determine proximal vergence values

(Morgan, 1950; Wick, 1985; Tait, 1933). The first method, which will be called the

+2.50D method throughout this thesis, requires the patient to view a distance target while the distance heterophoria is measured, then the patient views a near target through a lens that would reduce the accommodative demand of the near target to zero (+2.50D for a

40cm near distance) while the near heterophoria is measured; this way the change in vergence posture would be solely driven by proximal vergence, as accommodative vergence would have theoretically been eliminated (Wick, 1985; Tait, 1933). The equation Wick (1985) used to calculate the proximal vergence value in prism diopters is listed below:

(3) +2.50D method of proximal vergence = (PD/D) – (h) + (H)

where PD is the interpupillary distance in centimeters, D is the near working distance of the target in meters, h is the near heterophoria through the +2.50D lens, H is the distance heterophoria, esophoria is represented by a negative value, and exophoria is represented

10 by a positive value. This method, however, assumes that patients will relax their accommodation by the amount of the lens that the patient views through during near testing. If patients do not truly relax their accommodation fully, then accommodative vergence would still be contributing to this calculation in addition to proximal vergence.

This problem will be discussed and addressed in this thesis.

The second method of calculating proximal vergence, which will be termed the

AC/A differencing method, takes the difference between the far-near AC/A and the gradient AC/A, the equation for which is listed below (Bhoola, et al., 1995; Scheiman &

Wick, 2008):

(4) AC/A differencing proximal vergence = (far-near AC/A) – (gradient AC/A)

The stimulus AC/A ratio calculations will utilize the theoretical change in accommodative demand between the two test conditions, while the response AC/A ratio calculations will utilize the true accommodative response of the patient between the two test conditions. Taking the difference between the far-near and gradient AC/A ratios is thought to reflect the proximal vergence value, as the far-near AC/A reflects both accommodative vergence and proximal vergence while the gradient AC/A reflects accommodative vergence only (Bhoola, et al., 1995; Scheiman & Wick, 2008).

These two aforementioned clinical measurements for determining proximal vergence were compared in a previous study, where heterophorias were measured by the alternating cover test (Owusu, et al., 2016). Owusu and colleagues (2016) found that the

AC/A differencing method and the +2.50D method were correlated, but the +2.50D method produced a ratio that was larger than that of the AC/A differencing method

(Owusu, et al., 2016). As accommodative responses were not measured in this study, it is plausible that if participants had a less than expected accommodative response, that this may account for part of the differences in these measurements; however, this has yet to be tested (Owusu, et al., 2016).

The purpose of this study is to compare the two methods of assessing proximal vergence and to determine the role that accommodation plays in these two measures, specifically by comparing both the stimulus proximal vergence values and response proximal vergence values where response accommodation is measured. Heterophoria measurements in the present research will utilize the Modified Thorington technique

(Sanker, et al., 2012).

Chapter 2. Methods

Participants:

This research was approved by the Institutional Review Board at The Ohio State

University and follows the principles of the Declaration of Helsinki, including obtaining informed consent of all subjects. Subjects were recruited using the Study Search website through The Ohio State University Center for Clinical and Translational Science, as well as through an e-mailed study advertisement to The Ohio State University College of

Optometry staff, faculty, and students.

The nature of this study required that only participants with normal binocular vision and accommodation be tested. Therefore, specific inclusion criteria were used.

Specifically, participants were required to be between ages 18 to 37 years in order to account for the normal age-related decline in accommodation, to have a Snellen visual acuity of 20/20 in both eyes when uncorrected or while wearing contact lenses, and to have local stereoacuity of 40 seconds of arc or better using the Randot stereotest.

Additionally, participants were required to have accommodative amplitudes as measured with the push-up method that fell within the subject’s normal age range, defined as an accommodative amplitude above their minimum amplitude of (Scheiman & Wick, 2008):

(5) Minimum accommodative amplitude = 15-(0.25 x age) 13

Additionally, individuals wearing spectacle correction only were excluded in order to avoid potential artifacts in the autorefractor measurements due to the presence of additional lenses.

All participants met the inclusion criteria, with only one participant having a monocular accommodative amplitude value which was on the borderline for eligibility; this participant’s data was excluded for other reasons, as will be discussed in the results section.

Procedure:

As participants arrived, the experimental procedures and informed consent were reviewed, and then the subject signed the informed consent form. After this, the participants’ age, contact lens prescription (if known), interpupillary distance, visual acuity, stereoacuity, and accommodative amplitudes were obtained.

Throughout the experiment, participants wore a half-eye trial frame where various lenses could be placed for each testing condition. Participants were then instructed to place their chin in the chinrest and forehead touching the forehead rest of a Grand Seiko

WR5100K autorefractor (Grand Seiko Co., Japan). In addition to providing an open view to allow for distant target viewing, the Grand Seiko WR5100K autorefractor has also been shown to take reliable and repeatable measurements (Davies, et al., 2003; Win-Hall, et al., 2007). The Grand Seiko provides a measurement of refractive error, which in turn was converted to the accommodative response for each testing condition in this

14 experiment. The examiner recorded the autorefractor output for each condition in this experiment (vertex distance setting = 0). See Figures 2 and 3 for photographs of the distance Modified Thorington card and trial frame set up, respectively.

Subjects then viewed a distance Modified Thorington card through the autorefractor beam splitter while wearing the half-eye trial frame with a Maddox lens in front of the right eye. The distance Modified Thorington card was placed at the end of the examination room, at a distance of four meters. The examiners created this card by using measurements from the near Modified Thorington card that were then scaled for the proper distance of four meters. An incandescent light was then placed behind the card and shone through a hole that was drilled in the center of the card.

Figure 2. Distance Modified Thorington card with incandescent lamp.

Figure 3. Half-eye trial frame with refractive lenses and Maddox lens.

Participants were instructed to keep the details on the card clear throughout testing and to mentally take note of the position of the vertical red line image seen by the right eye relative to the horizontal target position on the card, as they would be asked for that information after the autorefractor measurement was taken. As participants viewed the target, the autorefractor button was held down in order to capture 10 measurements of accommodation from the left eye. The participants were then asked for the location of the red line, which was the distance heterophoria measurement.

Next, three distinct trials were completed with all participants to determine various near heterophoria measures. In addition to the Maddox lens in front of the right eye, participants had +1.00D lenses, +2.50D lenses, or no refractive lenses placed in front of both eyes. The presentation order of these three viewing conditions was randomized and a five-minute waiting period between trials was completed for each participant to allow any residual vergence or accommodative adaptation to dissipate. During this five- 16 minute rest period, participants removed the trial frame and lenses, and conversed with the examiner who was seated approximately half way across the room.

For each of these three conditions, a near Modified Thorington card (Bernell

Corporation, Mishawaka, IN) was viewed at a distance of 40cm from the subject. The card was maintained at this 40cm distance by firmly attaching the card to a near point rod that was affixed to the autorefractor. See Figure 4 for a photograph of this autorefractor set up. A penlight was attached behind the card so that the light would shine through the central hole.

Figure 4. Autorefractor with near Modified Thorington card attached to near point rod.

Once again, participants were instructed to keep the details on the card clear throughout testing and to mentally take note of the position of the vertical red line image seen by the right eye relative to the horizontal target position on the card, as they would be asked for that information after the autorefractor measurement was taken. As participants viewed the target, the autorefractor button was held down in order to capture

10 measurements of accommodation from the left eye. The participants were then asked for the location of the red line, which was the near heterophoria measurement for each of the three aforementioned near testing conditions.

Finally, step fusional vergence ranges were measured using a prism bar and either a Snellen chart for distance measurements, or a near acuity chart at 40cm for near measurements. Vergence ranges were measured at distance and then at near, as well as base-in before base-out. A visual schematic of the protocol is shown in Figure 5.

Figure 5. Schematic of the experimental protocol.

Chapter 3. Results

General Data Interpretation:

Data were initially gathered from 13 participants (age range 22-37). The accommodative amplitudes, vergence ranges, and heterophoria values for each participant in each viewing condition are shown in Table 1.

Binocular Distance Near Distance Near Near Near Accommodative Vergence Vergence Phoria Phoria Phoria Phoria Amplitude (D) Ranges BI, Ranges BI, (prism (prism through through BO (prism BO (prism diopters) diopters) +1.00D +2.50D diopters) diopters) (prism (prism diopters) diopters) 11.0 6/14/12, 6/12/10, -3.0 -2.0 1.0 4.0 8/12/10 6/12/10 11.0 x/6/4, 6/30/18, -1.0 0.0 3.0 5.0 14/18/16 16/30/20 8.0 2/4/2, 8/16/14, 2.0 13.0 15.0 16.0 1/4/2 12/14/12 7.5 4/6/4, x/8/6, -1.0 3.0 7.0 9.0 2/14/6 8/14/8 8.0 x/4/2, x/4/2, -0.5 -1.0 1.0 3.0 x/2/1 x/18/16 11.0 x/10/8, 8/30/25, 0.0 1.0 2.0 10.0 35/45+/45+ 35/45+/45+ 11.0 x/4/2, 4/12/10, -4.0 1.0 1.0 4.0 12/25/14 10/40/20 11.0 x/6/4, 6/8/6, -4.0 -4.0 -1.0 0.0 35/45+/45+ 45+/45+/45+ 10.0 4/6/4, x/8/6, -0.5 5.0 2.0 6.0 12/16/8 x/30/12 11.0 x/6/4, 12/18/14, -2.0 0.0 2.0 6.0 12/16/10 10/25/16 9.0 x/8/6, 10/20/16, 1.5 9.0 10.0 14.0 4/20/18 10/35/30 10.5 6/8/6, x/10/8, -0.5 -1.0 4.0 10.0 x/10/8 x/25/20 8.0 x/8/2, 6/18/14, 0.0 2.0 9.0 9.0 4/12/10 x/20/18 9.77 ± N/A N/A -1.00 ± 2.00 ± 4.31 ± 7.38 ± 1.44 1.85 4.65 4.61 4.50 Table 1. The accommodative amplitudes, vergence ranges, and heterophoria values are shown for each individual participant (esophoria is negative, exophoria is positive). Mean values with standard deviations are shown at the bottom of the table.

Stimulus Proximal Values: AC/A Differencing Method and +2.50D Method

The change in vergence posture from far to near viewing was calculated using the numerator of equation 1 which was described in the introduction. As a stand-alone equation, that is:

(5) Vergence from far to near = [(PD/D) – h + H]

PD is the interpupillary distance in centimeters, h is the near heterophoria at 40cm

(esophoria is negative), and H is the distance heterophoria. Dividing this vergence value by 2.50D, which is the accommodative demand of the near Modified Thorington card, results in the stimulus far-near AC/A ratio.

The stimulus gradient change in vergence was calculated by determining the change in heterophoria position between the 40cm with no lens and the 40cm with

+1.00D lens viewing conditions. The stimulus gradient AC/A ratio was calculated by dividing this change in vergence by the power of the lens used to produce a change in accommodation; the accommodative stimulus in the case of this research was 1.00D, therefore the stimulus gradient change in vergence is equal to the stimulus gradient AC/A ratio value. The stimulus far-near and stimulus gradient AC/A ratios are shown in Table

2. It can be seen in the data that the stimulus far-near AC/A values often exceeded the stimulus gradient AC/A values.

Stimulus Far-Near AC/A Ratio Stimulus Gradient AC/A Ratio (prism diopters per diopter) (prism diopters per diopter) 5.7 3.0 6.0 3.0 1.7 2.0 4.8 4.0 6.1 2.0 6.8 1.0 3.4 0.0 6.1 3.0 4.0 -3.0 5.0 2.0 2.8 1.0 5.7 5.0 5.5 7.0 4.89 ± 1.50 2.31 ± 2.43 Table 2. Stimulus far-near AC/A values and stimulus gradient AC/A values for each participant are shown. Mean values with standard deviations are shown in the last row for all participants.

Proximal Vergence Calculations for Stimulus Values

Stimulus proximal vergence values were referenced to 2.50D (40cm test distance) of accommodative demand and were calculated for all subjects. This calculation was completed irrespective of the autorefractor measurements. The examiners felt that including all subjects in this portion of the analysis was appropriate, as clinically it is assumed that patients accommodate in the expected manner when calculating stimulus values.

Far-Near Differencing Method with Stimulus AC/A

Stimulus proximal vergence values using the far-near differencing method were calculated using the following method. Since proximal vergence values are typically 23 referenced to the near working distance at which they are measured (40cm in the case of this research), the stimulus far-near AC/A ratio was multiplied by 2.50D in order to determine the amplitude of accommodative convergence at 2.50D. Similarly, the stimulus gradient AC/A ratio was also multiplied by 2.50D. Finally, the proximal vergence was calculated by determining the difference between the accommodative vergence values from the far-near and gradient AC/A ratios. Algebraically, the proximal vergence value calculated in the manner above is equivalent to simply taking the difference in the stimulus far-near AC/A ratio and the stimulus gradient AC/A ratio. These results are detailed in Table 3. Additionally, the proximal convergence to test distance (PCT) ratios for each participant were obtained by dividing the proximal vergence values by 2.50D, the results of which are also displayed in Table 3.

The +2.50D Method

Stimulus proximal vergence values (uncorrected for any remaining accommodation and accommodative vergence) were also calculated using the +2.50D method. The following equation was applied:

(6) Proximal Vergence = (PD/D) - h + H

PD is the interpupillary distance, h in this case is the near heterophoria while viewing through the +2.50D lens, and H is the distance heterophoria. These values are also shown

24 in Table 3. PCT ratios for each participant were calculated by dividing these proximal vergence values by 2.50D, the results of which are also displayed in Table 3.

Stimulus AC/A Differencing Method: Stimulus +2.50D Method: Proximal vergence (prism diopters) and Proximal vergence (prism diopters) associated PCT ratio (prism and associated PCT ratio (prism diopters/diopter) diopters/diopter) 6.75 (2.7) 8.25 (3.3) 7.50 (3.0) 10.00 (4.0) -0.75 (-0.3) 1.25 (0.5) 2.00 (0.8) 6.00 (2.4) 10.25 (4.1) 11.25 (4.5) 14.50 (5.8) 8.00 (3.2) 8.50 (3.4) 5.50 (2.2) 7.75 (3.1) 11.25 (4.5) 17.50 (7.0) 9.00 (3.6) 7.50 (3.0) 6.50 (2.6) 4.50 (1.8) 2.00 (0.8) 1.75 (0.7) 3.25 (1.3) -3.75 (-1.5) 6.75 (2.7) 6.46 ± 5.85 (2.58 ± 2.34) 6.85 ± 3.25 (2.74 ± 1.30) Table 3. Proximal vergence values using the stimulus AC/A far-near differencing method and the stimulus +2.50D method are shown. PCT ratios are shown in parentheses. Mean values with standard deviations for all participants are listed in the last row.

Statistical Analysis of Stimulus AC/A Differencing and +2.50D Proximal Vergence

A paired t-test was used to compare the proximal vergence values for the stimulus far-near differencing method and the stimulus +2.50D method. No statistically significant difference between these values was found (t = 0.29, p = 0.78). Statistically significant agreement was found between these two proximal vergence methods using Pearson correlation (R=0.56, p=0.05), as shown in Figure 6.

Figure 6. Scatter plot with best fit line between Stimulus AC/A Differencing proximal vergence values and +2.50 Method Uncorrected proximal vergence values for all participants.

Refractive and Accommodative Measures

Examination of these refractive data demonstrated that the distance autorefraction for one subject showed 2.00 diopters of cylinder. Much smaller cylinder values for this subject were found at 40cm in all viewing conditions. A second subject showed 1.37D of cylinder at distance, 1.00D of cylinder at 40cm with no lenses, 0.50D of cylinder at 40cm through the +1.00D lenses, and 0.37 diopters of cylinder at 40cm through the +2.50D lenses. Lastly, a third subject showed relatively low levels of cylinder (under 0.75D) in all viewing conditions except the 40cm with +2.50D lenses condition. In this latter condition, the cylinder was 5.87D for this subject. Because of these inconsistent cylinder values, these three participants were not included in the following analyses.

The first step in analyzing the accommodative data was to convert the average spherocylindrical autorefractor values for each participant into spherical equivalent values for each testing condition.

In order to understand what these spherical equivalent values represent, we must first understand specifically what the autorefractor is measuring. When an individual shifts their fixation from distance to near, the following is measured:

(7) Autorefractor reading at 40cm without lenses = Accommodation + Autorefractor

reading at distance

As an example, a patient for whom the distance autorefraction shows -0.50DS would need 2.00D of accommodation (ignoring any lag of accommodation) in order to accurately accommodate on a target at 40cm (2.50D demand). If the patient does accommodate by 2.00D, then the autorefractor will read -2.00D. Therefore, by equation

(7) above, the reading on the autorefractor at 40cm with no lenses in front of the eyes will equal -2.50D. If less than -2.50D of minus power is read by the autorefractor at 40cm, this indicates that the patient is under-accommodating, or showing an accommodative lag. Wick (1985) used similar logic to calculate the expected change in accommodation from distance to near in the population. Wick based his calculations on Morgan’s (1944) data, which demonstrated a lead of accommodation at distance equal to 0.75D on average. Wick (1985) attributed this accommodative lead to tonic accommodation.

Further, at a 2.50D accommodative demand, Morgan’s data demonstrated on average a

0.50D lag of accommodation (Wick, 1985). Wick (1985) therefore calculated that the expected change in accommodation from distance to near was 1.25D.

The expected change in accommodation between distance and near (40cm) with no lens in place was calculated using equation (7), where the accommodation value was set at 2.50D (for the 40cm accommodative demand); this analysis did not factor in a lag of accommodation at 40cm. The actual change in accommodation from distance to near

(40cm) was also calculated, by taking the absolute value of the difference between the distance and near (40cm) autorefractor outputs. The expected and actual response changes in accommodation for the ten participants are shown in Table 4.

Actual change in accommodation from Expected change in accommodation distance to near (diopters) from distance to near (diopters) 1.19 2.13 1.94 2.75 1.25 2.75 1.63 2.82 2.07 3.07 1.75 2.44 1.12 2.50 0.87 2.75 0.74 2.31 2.00 3.82 1.45 ± 0.48 2.73 ± 0.47 Table 4. Expected and measured (actual) change in accommodation from distance to near. Mean values with standard deviations for these 10 subjects are shown in the last row.

As seen in Table 4, many of the participants demonstrated far less accommodation at 40cm than expected. A possible explanation for these large 28 accommodative lags is that participants may have altered their accommodation around the time that they gave the verbal response associated with the heterophoria measurement. It seems unlikely that participants who demonstrated these high accommodative lags maintained them throughout the heterophoria measurement. The response AC/A ratios (shown in Table 6) in which the actual response change in accommodation between distance and near served as the denominator for this ratio, are quite high in some of these cases due to calculating in these high lags. In fact, these values are perhaps too high to fully support the idea that accommodation was as low as that recorded when the participant reported their heterophoria measurement at 40cm.

These issues will be addressed in the discussion.

In order to understand the next group of calculations relevant to accommodation, an understanding of the influence of corrective lenses and changes in ocular accommodation on the refractive error outputs measured by the autorefractor is required.

First, the autorefractor reports the correction for refractive error. Therefore, if an autorefractor measurement is made through a +1.00D lens, the autorefractor will read

-1.00D. Further, if a participant relaxes accommodation, this will be read as an increase in positive or plus power.

The next calculation related to refractive error measurement involved determining the change in accommodation induced when looking through the +1.00D lens at 40cm. It was necessary to obtain this value in order to calculate the response gradient AC/A. This was determined using the following equation:

(8) [(40cm refractive error value with +1D lens) – (40cm refractive error value)] + 1

It was necessary to add 1.00 to the difference in refractive error values because the autorefractor reads -1.00D with the +1.00D lens in place. The results of this calculation are shown in Table 5.

Once the change in accommodation with the +1.00D lens at 40cm was determined, the total accommodation remaining with the +2.50D lens in place at 40cm was calculated. These values indicated the extent to which accommodation was still active, and therefore accommodative vergence was still in effect, with the +2.50D lens in place. The first step to making this calculation is to determine the change in refractive error values between distance and near (40cm with no lens in place), which was calculated as described previously. This value represents the amount of accommodation that must be relaxed with the +2.50D lens in place, in order for the accommodation at distance and the accommodation with the +2.50D lens to be equivalent. As mentioned in the introduction, the idea of measuring proximal vergence with the +2.50D lens in place is that the +2.50D lens eliminates blur accommodation (or at least eliminates the stimulus for blur accommodation) such that any change in vergence from distance to near is thought to be driven only by this change in distance (proximal cues). To calculate the accommodation that remains with the +2.50D lens in place, the change in accommodation from 40cm to 40cm through the +2.50 lens value will be subtracted from the change in accommodation from distance to 40cm value. These values are also shown in Table 5.

Change in Accommodation Induced by the Accommodation Remaining with the +1.00D Lens at Near (diopters) +2.50D Lens at Near (diopters) 1.01 0.01 0.51 -0.485 0.69 0.315 1.07 0.060 0.69 -0.555 0.88 0.380 -0.01 0.195 0.75 0.380 0.57 -0.815 0.69 0.63 0.68 ± 0.30 0.01 ± 0.48 Table 5. Change in accommodation induced by the +1.00D lens at near, and the accommodation remaining when viewing through the +2.50D lens at near (negative values indicate that accommodation was not fully relaxed). Mean values and standard deviations are listed in the last row.

Response Far-Near AC/A Ratio and Response Gradient AC/A Ratio

Regarding the response far-near AC/A ratios, these values were calculated using the following equation:

(9) Response far-near AC/A ratio = [(PD/D) - h + H]/Change in accommodation

from distance to 40cm with no lens in place

The response gradient AC/A was also calculated. This was done by taking the change in heterophoria between the 40cm (no lens) viewing condition and the 40cm

(+1.00D lens in place) condition, and dividing this difference by the change in (response) accommodation between these two conditions, as calculated earlier.

The response far-near AC/A ratios and response gradient AC/A ratios are shown in Table 6.

Response Far-Near AC/A Ratio (prism Response Gradient AC/A ratio (prism diopters/diopter) diopter/diopter) 4.39 0.00 10.04 3.96 4.31 1.45 6.90 4.69 8.17 4.38 13.39 3.43 4.89 - 16.22 5.33 7.63 3.54 14.35 1.46 9.03 ± 4.32 3.14 ± 1.78 Table 6. Response far-near AC/A values and response gradient AC/A values for each participant are listed. The missing value is due to the fact that the denominator for the response gradient AC/A calculation was nearly zero diopters. Mean values and standard deviation values are listed in the last row.

Proximal Vergence Calculations for Response Values

AC/A Differencing Method with Response AC/A

Response proximal vergence values using the far-near differencing method were calculated in the same manner as the stimulus proximal values with one exception. The response far-near AC/A ratios and response gradient AC/A ratios were each multiplied by the actual accommodative response from distance to 40cm, and then the difference between these products was taken to be the proximal vergence value. These values are shown in Table 7.

+2.50D Method Corrected for Remaining Accommodation

As discussed earlier, proximal vergence values (uncorrected for any remaining accommodation and accommodative vergence) were calculated using the +2.50D method. That is, the equation: Proximal vergence = (PD/D) - h + H, where PD is the interpupillary distance, h is the near phoria when viewing through the +2.50D lens, and H is the distance phoria.

The proximal vergence values calculated as just described were also corrected for any remaining accommodation, and therefore any remaining accommodative vergence.

This was accomplished by multiplying the remaining accommodation with the +2.50D lens in place (as described above) by the response gradient AC/A ratio (as this was deemed the most accurate, unencumbered by proximal influences, measure of the AC/A).

The accommodative vergence value obtained in this way was then subtracted from the proximal vergence value to obtain the corrected proximal vergence value. These values are also shown in Table 7.

Statistically significant agreement was found between these two response proximal vergence methods using Pearson correlation (R=0.93, p<0.01), as shown in

Figure 7.

Response AC/A Differencing Response +2.50D Base Out to Break Method: Proximal Vergence Method: Proximal Vergence Ranges at (prism diopters) Vergence (prism diopters) 40cm (prism diopters) 8.50 5.50 40 7.57 4.56 25 4.64 2.46 35 4.56 3.53 25 6.61 5.80 12 11.16 11.30 30 - - - 8.05 8.03 14 8.17 8.37 18 15.27 8.91 45+ 8.28 ± 3.31 6.49 ± 2.85 N/A Table 7. Response AC/A differencing proximal values and +2.50D (corrected for accommodation) proximal values for all participants are listed. The missing values occurred because the response gradient AC/A could not be calculated for this subject. Base out to break vergence range values for each subject are shown in the right column. Mean values and standard deviation values are listed in the last row.

Figure 7. Scatter plot with best fit line between Response AC/A Differencing proximal vergence values and +2.50 Method Corrected proximal vergence values for the 9 remaining participants.

Statistical Comparisons for Proximal Vergence Values

The proximal vergence values obtained by the stimulus AC/A differencing method, the +2.50D method uncorrected for accommodation, the response AC/A differencing method, and the +2.50D method corrected for accommodation were each compared to each other using a paired t-test. For these statistical comparisons, the three participants that were originally removed only when calculating the proximal values by both the response AC/A method and the +2.50D method corrected for accommodation were removed from all proximal values regardless of the method by which these values were calculated. In addition, those data from one other participant were removed because it was not possible to calculate the proximal values for the response AC/A differencing method or for the +2.50D method corrected for accommodation, as the response gradient

AC/A calculation would have had a denominator that was nearly zero. This left nine subjects for these statistical comparisons. The means of the proximal values for each of the four clinical methods were 7.03 ± 4.01 prism diopters for the stimulus AC/A differencing method, 6.75 ± 2.99 prism diopters for the +2.50D method uncorrected for accommodation, 8.28 ± 3.31 for the response AC/A differencing method, and 6.50 ± 2.85 for the +2.50D method corrected for accommodation. These means are plotted in Figure

8 and the results of the statistical comparisons are shown in Table 8.

Figure 8. Proximal values obtained from nine subjects (mean ± SD).

Comparison of Proximal Vergence Values Result (paired t-test) Stimulus AC/A differencing method versus t=0.255, p=0.805 +2.50D method (uncorrected) Stimulus AC/A differencing method versus t=1.524, p = 0.166 Response AC/A differencing method Stimulus AC/A differencing method versus t=0.433, p = 0.677 +2.50D method (corrected) Response AC/A differencing method versus t=1.572, p = 0.155 +2.50D method (uncorrected) Response AC/A differencing method versus t=2.513, p = 0.036 +2.50D method (corrected) +2.50D method (uncorrected) versus +2.50D t=0.437, p = 0.674 method (corrected) Table 8. Results of paired t-tests for proximal values obtained by the four clinical methods applied in this experiment.

It can be seen that only the comparison of the response AC/A differencing method versus the +2.50D method corrected for accommodation method was statistically significantly different (p<0.05). However, when the error rate was corrected for multiple comparisons

(Bonferroni correction: α = 0.05/6 = 0.0083) then even this latter comparison was not significantly different.

Statistical Analysis: Vergence Ranges versus Proximal Values

As mentioned in the introduction, it is of interest to compare proximal vergence values to vergence ranges, which reflect fusional vergence. This was completed by comparing the base out to break vergence value at 40cm to the proximal vergence values obtained by all four clinical methods using linear regression. The base out to break vergence value was used instead of the base out to blur vergence value, as not all participants demonstrated a base out to blur value. The p-values for these regressions were all insignificant (p>0.05). The correlation coefficients (r) were 0.50 (p=0.17) for the stimulus AC/A differencing method, -0.25 (p=0.52) for the stimulus +2.50D method uncorrected, 0.48 (p=0.19) for the response AC/A differencing method, and -0.02

(p=0.97) for the +2.50D method corrected.

Chapter 4. Discussion

The purposes of this research project were to compare the results from two clinical measures of proximal vergence, the AC/A differencing method and the +2.50D method, and to assess the accommodative response while performing these measurements to determine whether differences in the proximal values obtained by these two methods could be accounted for by accommodation.

In regard to the proximal vergence values, all of the clinical methods applied in this study yielded similar results. The only comparison that approached, but did not reach, statistical significance was between the response AC/A differencing method and the +2.50D method corrected for accommodation. The response AC/A differencing method value was found to be larger than the +2.50D method value corrected for accommodation. One implication of these results is that the stimulus values are adequate to measure proximal vergence. A second implication of these results is that the +2.50D method likely does not require correction for any remaining accommodative vergence while viewing through the +2.50D lens.

It is of interest to note that the proximal values obtained here were generally larger than those reported previously in the literature. One way to interpret this result is that the stimulus conditions (dissociated viewing, potentially inconsistent or reduced contrast accommodative target) in this experiment induced greater reliance on proximal 38 stimuli (Schor et al., 1992, Hung et al., 1996). However, the values obtained in this experiment are similar to those reported by Owusu and Fogt (2016) for the stimulus

AC/A differencing method (mean PCT ratio = 1.87 ± 4.86), and these values obtained are lower than those obtained by these previous investigators with the +2.50D (uncorrected) method (mean PCT ratio = 4.18 ± 3.91).

Regarding the accommodative responses, the participants’ response in changing from distance viewing to near viewing at 40cm was significantly less than expected, leaving in some cases relatively large lags of accommodation. It is possible that the accommodation measures were in error due to malfunction of the autorefractor, however this is unlikely due to the established reliability of this instrument (Davies, et al., 2003;

Win-Hall, et al., 2007).

Large lags of accommodation were reported by Bhoola and colleagues (1995), who reported that the accommodative response to a refractive lens was on average 50% of the lens power when their subjects were asked to accommodate through lens powers of

-1.00D and -2.00D. The average change in accommodation from 40cm to 40cm through a

+1.00D lens for the 10 participants discussed earlier in the current experiment was 0.68D

± 0.30D, which is 68% of the stimulus, while the average change in accommodation from

40cm to 40cm through a +2.50D lens for these same ten participants was 1.46D ± 0.47D, which is 58% of the stimulus. While the present results are comparable to the results found in the Bhoola et al. (1995) paper, it seems possible that because the participants in the current study were viewing the stimulus with the two eyes dissociated (thereby eliminating convergence accommodation) and because the red line seen through the

Maddox rod may have served as an accommodative (albeit weak) stimulus, perhaps accommodation was poorly controlled. It is also the case that the room lights were dimmed in this study, so that participants could easily see the light projected from the center of the card. Under such lighting conditions, accommodation may be more variable and may even assume the tonic accommodative position (Rabbetts, 1998). Overall, it could be that participants allowed their accommodation to fluctuate in this experiment, such that when the participant verbalized the heterophoria measure the accommodation was in a more appropriate location compared to when the autorefractor measurements were taken.

Lastly, one source indicates that minus lenses may be more accurate for measuring a gradient AC/A, as minus lenses stimulate accommodation along the linear portion of the accommodative stimulus-response function (Scheiman & Wick, 2008).

However, the author did not indicate why plus lenses were less accurate (Scheiman &

Wick, 2008). A study by Majumder and Mutusamy (2016) additionally found that the gradient AC/A varies depending on whether it is measured with plus or with minus lenses. The present study utilized plus lenses to measure the gradient AC/A, so the use of minus lenses or the technique of combining the result of both a plus and minus lens could be considered in future studies.

Finally, there was little or no relationship between the proximal vergence values and the base out to break fusional vergence values. This suggests that proximal vergence and fusional vergence may be independent of one another as suggested by Hofstetter

(1951). This result suggests that methodologies aimed at targeting proximal vergence

(such as mental imagery) should likely be incorporated into orthoptic therapy for vergence disorders, as proximal vergence may not improve with therapies primarily aimed at improving fusional vergence.

In conclusion, this study found that all four clinical methods of determining proximal vergence result in similar values. Future studies can be directed toward understanding the relationship between proximal vergence and other vergence subtypes.

Bibliography

1. Bhoola H, Bruce AS, Atchison DA. (1995). Validity of clinical measures of the AC/A ratio. Clinical and Experimental Optometry; 78(1): 3-10. 2. Charman, W.N. (2008). The eye in focus: Accommodation and presbyopia. Clinical and Experimental Optometry; 91(3), 207-225. 3. Ciuffreda, K.J. and Hung, G.K. (2002). Model-based understanding of clinical vergence testing. In: Models of the visual system. New York, NY: Kluwer Academic/Plenum Publishers. 625-641. 4. Ciuffreda, K.J. and Kenyon, R.V. (1983). Accommodative vergence and accommodation in normal, amblyopes, and strabismics. In: Schor, C.M. and Ciuffreda, K.J. Vergence eye movements: Basic and clinical aspects. Woburn, MA: Butterworth Publishers. 101-173. 5. Davies, L.N., Mallen, E.A.H., Wolffsohn, J.S. and Gilmartin, B. (2003). Clinical evaluation of the Shin-Nippon NVision-K 5001/Grand Seiko WR-5100K autorefractor. Optometry and Vision Science; 80(4): 320-324. 6. Fogt, N. and Jones, R. (1998). Comparison of fixation disparities obtained by objective and subjective methods. Vision Research; 38(3), 411-421. 7. Fogt N, Toole AJ, Rogers DL. (2016). A review of proximal inputs to the near response. Clinical and Experimental Optometry; 99: 30-38. 8. Goss, D.A. (1995). Ocular accommodation, convergence, and fixation disparity. Newton, MA: Butterworth-Heinemann. 9. Heath, G.G. (1956). Components of accommodation. American Journal of Optometry and Archives of American Academy of Optometry; 33(11), 569-579. 10. Hofstetter, H.W. (1951). The relationship of proximal convergence to fusional and accommodative convergence. American Journal of Optometry and Archives of American Academy of Optometry; 28(6), 300-308. 11. Hokoda, S.C. and Ciuffreda, K.J. (1983). Theoretical and clinical importance of proximal vergence and accommodation. In: Schor, C.M. and Ciuffreda, K.J. Vergence eye movements: Basic and clinical aspects. Woburn, MA: Butterworth Publishers. 75-97. 12. Horwood, A.M. and Riddell, P.M. (2014). Disparity-driven vs blur-driven models of accommodation and convergence in binocular vision and intermittent strabismus. Journal of the American Association for Pediatric Ophthalmology and Strabismus; 18(6), 576-583. 13. Horwood, A.M. and Riddell, P.M. (2013). The clinical near gradient stimulus AC/A ratio correlates better with the response CA/C ratios than with the response AC/A ratio. Strabismus; 21(2), 140-144. 42

14. Hung, G.K., Ciuffreda, K.J., and Rosenfield, M. (1996). Proximal contribution to a linear static model of accommodation and vergence. Ophthalmic & Physiological Optics; 16(1), 31-41. 15. Jaschinski, W. (2018). Individual objective versus subjective fixation disparity as a function of forced vergence. PLoS ONE; 13(7), https://doi.org/10.1371/journal.pone.0199958. 16. Jiang, B., Hung, G.K. & Ciuffreda, K.J. (2002). Models of vergence and accommodation-vergence interactions. In: Models of the visual system. New York, NY: Kluwer Academic/Plenum Publishers. 341-384. 17. Leigh, R.J. & Zee, D.S. (2006). The neurology of eye movements. New York, NY: Oxford University Press, Inc. 18. Maddox EE. (1893). The Clinical Use of Prisms and the Decentering of Lenses. 2nd edition. Bristol: John Wright and Co. 19. Majumder, C. and Mutusamy, R. (2016). Variation in AC/A ratio using the gradient method with plus or minus lenses. Optometry & Visual Performance; 4(4), 152-155. 20. Mannen, D.L., Bannon, M.J., and Septon, R.D. (1981). Effects of base-out training on proximal convergence. American Journal of Optometry and Physiological Optics; 58(12), 1187-1193. 21. Morgan, M.W. (1950). A comparison of clinical methods of measuring accommodative-convergence. American Journal of Optometry and Archives of American Academy of Optometry; 27(8), 385-396. 22. Morgan, M.W. (1944). Accommodation and its relationship to convergence. American Journal of Optometry and Archives of American Academy of Optometry; 21(5), 183-195. 23. Morgan, M.W. (1983). The Maddox analysis of vergence. In: Schor, C.M. and Ciuffreda, K.J. Vergence eye movements: Basic and clinical aspects. Woburn, MA: Butterworth Publishers. 15-21. 24. Morgan, M.W. (1980). The Maddox classification of vergence eye movements. American Journal of Optometry & Physiological Optics; 57(9), 537-539. 25. North, R.V., Henson, D.B., and Smith, T.J. (1993). Influence of proximal, accommodative and disparity stimuli upon the vergence system. Ophthalmic and Physiological Optics; 13, 239-243. 26. Ono, H. (1983). The combination of version and vergence. In: Schor, C.M. and Ciuffreda, K.J. Vergence eye movements: Basic and clinical aspects. Woburn, MA: Butterworth Publishers. 373-400. 27. Owens, D.A. and Leibowitz, H.W. (1983). Perceptual and Motor consequences of tonic vergence. In: Schor, C.M. and Ciuffreda, K.J. Vergence eye movements: Basic and clinical aspects. Woburn, MA: Butterworth Publishers. 25-74. 28. Owusu E, Zimmerman A, Fogt N (2016). The relationship between clinical measures of proximal vergence. American Academy of Optometry Annual Meeting; program #165016. 29. Panum, P.L. (1858). Physiologische untersuchungen uber das sehen mit zwei augen. Schwerssche Buchhandlung: Kiel. 43

30. Rabbetts, R.B. (1998). Bennett and Rabbetts’ clinical visual optics. Jordan Hill, Oxford: Butterworth-Heinemann Ltd. 31. Sanker, N., Prabhu, A., and Ray, A. (2012). A comparison of near-dissociated heterophoria tests in free space. Clinical and Experimental Optometry; 95, 638- 642. 32. Scheiman, M. and Wick, B. (2008). Clinical management of binocular vision: Heterophoric, accommodative, and eye movement disorders. Philadelphia, PA: Lippincott Williams & Wilkins. 33. Schor, C.M. (1992). A dynamic model of cross-coupling between accommodation and convergence: Simulations of step and frequency responses. Optometry and Vision Science; 69(4), 258-269. 34. Schor, C.M. (1980). Fixation disparity: A steady state error of disparity-induced vergence. American Journal of Optometry & Physiological Optics; 57(9), 618- 631. 35. Schor, C.M., Alexander, J., Cormack, L., and Stevenson, S. (1992). Negative feedback control model of proximal convergence and accommodation. Ophthalmic and Physiologic Optics; 12(3), 307-318. 36. Sreenivasan, V., Bobier, W.R., Irving, E.L., and Lakshminarayanan, V. (2009). Effect of vergence adaptation on convergence-accommodation: Model simulations. IEEE Transactions on Biomedical Engineering; 56(10), 2389-2395. 37. Stark, L., Kenyon, R.V., Krischnan, V.V., and Ciuffreda, K.J. (1980). Disparity vergence: A proposed name for a dominant component of binocular vergence eye movements. American Journal of Optometry & Physiological Optics; 57(9), 606- 609. 38. Tyler, C.W. (1983). Sensory processing of binocular disparity. In: Schor, C.M. and Ciuffreda, K.J. Vergence eye movements: Basic and clinical aspects. Woburn, MA: Butterworth Publishers. 199-295. 39. Wick, B. (1985). Clinical factors in proximal vergence. American Journal of Optometry & Physiological Optics; 62(1), 1-18. 40. Wick, B. and Bedell, H.E. (1989). Magnitude and velocity of proximal vergence. Investigative Ophthalmology & Visual Science; 30(4), 755-760. 41. Win-Hall, D.M., Ostrin, L.A., Kasthurirangan, S., et al. (2007). Objective accommodation measurement with the Grand Seiko and Hartinger Coincidence Refractometer. Optometry and Vision Science; 84(9), 879-887.