comparisons of proximal vergence measures ac/a

Vision Development & Rehabilitation Volume 6, Issue 3 • September 2020

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gradient (+1.00) stimulus AC/A ratios (stimulus AC/A differencing method), the difference in calculated and gradient response AC/A ratios (response AC/A differencing method), and the change in vergence from distance to near with the +2.50D lenses (uncorrected +2.50D method). This latter value was also corrected for any active accommodation with +2.50D lenses (corrected +2.50D method).

ResultsThe mean proximal vergence values (∆) were 7.82 ± 5.98 (stimulus AC/A differencing method), 8.29 ± 3.30 (response AC/A differencing method), 6.23 ± 3.52 (uncorrected +2.50D method), and 5.13 ± 2.98 (corrected +2.50D method). The only comparison that showed both a significant correlation (p<0.05) and a non-significant difference from the paired t-test (p>0.05) was that between the stimulus AC/A differencing method and the uncorrected +2.50D method.

ConclusionsWhen response accommodation was account-ed for, differences occurred in the mean proximal values obtained with the various methods. The means of the methods most likely to be used clinically (stimulus AC/A differencing method and uncorrected +2.50D method) were similar, although some individuals demonstrated significant differences between these methods.

intRoduCtionIn 1893, Maddox published his seminal

manuscript in which he sub-divided vergence eye movements into four components that he termed tonic vergence, fusional vergence, accommodative vergence, and voluntary vergence.1-3 Tonic vergence represents the position of the eyes in the absence of disparity, blur, and proximal stimuli. The amplitude of tonic vergence can be assessed using the distance heterophoria, although this value does not necessarily match the vergence

Correspondence regarding this article should be emailed to Nick Fogt, OD, PhD, at [email protected]. All statements are the author’s personal opinions and may not reflect the opinions of the College of Optometrists in Vision Development, Vision Development & Rehabilitation or any institu tion or organization to which the authors may be affiliated. Permission to use reprints of this article must be obtained from the editor. Copyright 2020 College of Optometrists in Vision Development. VDR is indexed in the Directory of Open Access Journals. Online access is available at covd.org. https://doi.org/10.31707/VDR2020.6.3.p252.

Fogt N. Comparisons of proximal vergence measures. Vision Dev & Rehab 2020;6(3):252-63.

Keywords: Eye movements; proximal; vergence

Comparisons of Proximal Vergence MeasuresNick Fogt, OD, PhD, FAAO

The Ohio State University College of Optometry

ABStRACtBackgroundProximal vergence is defined as a vergence eye movement subtype driven by an “awareness of nearness”. The purpose of this experiment was to compare values of proximal vergence calculated with and without measures of accommodation to assess the clinical utility of each measurement method.

MethodsThirteen participants between the ages of 22 and 37 (mean = 28.5 ± 4.5 years) were enrolled. The distance and near heterophoria were measured using the Modified Thorington technique. The near heterophoria was measured under three randomized viewing conditions (no lenses, +1.00D lenses, +2.50D lenses). Refractive error was measured with an autorefractor. Proximal vergence was calculated as the difference in calculated (far-near) and

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253Vision Development & Rehabilitation Volume 6, Issue 3 • September 2020

posture in the dark because of accommodation.4 The average distance heterophoria has been reported to be between 2∆ exophoria and 1∆ esophoria.4-5 Fusional vergence, also referred to as disparity vergence or reflex vergence, is driven by retinal disparity and results in bifoveal fixation.1-3,6-8 Fusional vergence may be assessed by measuring the heterophoria at distance and near. The heterophoria reflects the amount of fusional vergence that is utilized under binocular conditions to attain fusion. Accommodative vergence occurs as a result of an accommodative response to blur. The magnitude of accommodative vergence for each diopter of accommodation is termed the accommodative convergence to accommodation (AC/A) ratio.8-10 Two common clinical methods to determine the AC/A ratio are the calculated or far-near method, and the gradient method.5,8-10 An important difference between these two AC/A measurements is that proximal vergence, defined below, influences the calculated AC/A but not the gradient AC/A. This may underlie the lower than expected correlation between these two measurement methods.5,11-13 The last subtype in the Maddox1 vergence classification is what Maddox termed voluntary vergence. Maddox described this vergence subtype as resulting from the “awareness of nearness” of a target.1,13-15 This subtype will hereafter be referred to as proximal vergence. Tait16 appears to be one of the earliest adopters of the term proximal, as evidenced by a statement from Hofstetter17 in which he credited Tait with the phrase “proximal sense” to describe vergence brought about by the proximity of a target. The perceived nearness of a target is potentially influenced by many stimuli, some of which include memory of a target’s location, proprioception, overlay, motion parallax, relative size, and size constancy.14-15,18 Proximal vergence could be responsible for the initiation of large vergence movements, particularly when the magnitude of the required vergence change is outside the range of disparity detection.14-15,18-19

The literature largely suggests that in binocularly normal individuals under natural viewing conditions, fusional vergence is the greatest contributor to the overall static vergence response. Accommodative vergence is said to be the second largest contributor.9-10,15 However, this does not necessarily mean that proximal vergence makes no contribution to vergence. Hung and colleagues15 have suggested that proximal cues and proximal vergence may play a role in the overall static vergence response by supporting blur and disparity depth cues. Further, these investigators suggested that in vision therapy for binocular anomalies, proximal responses may direct binocular responses until accommodation and vergence ”normalize”. Whether proximal vergence significantly impacts on the overall vergence response under natural conditions,15,20 and whether it is correlated with symptoms of binocular dysfunction is not clear however and requires further study.

A better understanding of the relationships between the vergence subtypes could help guide approaches to therapy for vergence anomalies. For example, there is no consensus regarding the correlation between measures of proximal vergence and fusional vergence ranges. Mannen and colleagues21 concluded that following vergence therapy, proximal vergence measures declined while vergence ranges improved. This suggests that these two vergence measures may be inversely correlated. On the other hand, Hofstetter22 concluded that proximal vergence positively influences fusional vergence ranges. If proximal vergence enhances vergence ranges under natural seeing conditions or reduces the frequency or severity of symptoms related to binocular dysfunction, then vergence therapy procedures that increase a patient’s use of proximal vergence for near vergence responses would be appropriate. For example, procedures could be used to train proximal vergence in isolation. One such procedure


clinical measures of proximal vergence are found to be independent of other vergence measures such as fusional vergence ranges, then this suggests that proximal vergence and should be measured clinically and therapies should be directed at improving low proximal vergence values.

MethodS

The study protocol and consent form were approved by the Biomedical Sciences Institutional Review Board at The Ohio State University. Written informed consent was obtained from all participants prior to the study. Subjects were recruited using the Study Search study repository administered through The Ohio State University Center for Clinical and Translational Science, as well as through an e-mail to The Ohio State University College of Optometry staff, faculty, and students.

To be eligible for the study participants were required to be free of amblyopia and strabismus, to have adequate accommodation, and to be between 18 and 37 years of age. Specific eligibility criteria were Snellen visual acuities of 20/20 in both eyes uncorrected or while wearing contact lenses, local stereoacuity of 40 seconds of arc or better as measured with the Randot stereotest, and accommodative amplitudes (measured with the push-up method) that were above the minimum expected amplitude of accommodation calculated using the equation [15 - (0.25 x age)].5

Individuals who wore only spectacles for correction of their refractive error were excluded in order to avoid potential artifacts in the autorefractor measurements, and only contact lens correction could be worn during the experiment.

ProcedureAt the study visit the experimental pro-

cedures were reviewed and participants signed the informed consent form. The eligibility criteria were then assessed. In addition to the

could require that patients alternately fixate monocularly between difference of Gaussian (DOG) targets at two different depths.23

In order to address these questions about the potential importance of proximal vergence, clinicians and researchers have at least two methods available to assess proximal vergence.8,12,16,24 The results of these methods have, to our knowledge, never been directly compared on the same individuals. Given the many available cues for perceived distance, it seems likely that different testing methods may yield different results.

The first method of calculating proximal vergence will be referred to as the AC/A differencing method. In this method the difference between the calculated AC/A ratio and the gradient AC/A ratio is determined. As mentioned above, the idea behind this approach is that the calculated AC/A ratio reflects contributions from both proximal vergence and accommodative vergence while the gradient AC/A ratio reflects only the accommodative vergence contribution.5,11-12

The second method, termed the +2.50D method, 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 reduces the accommodative demand of the near target to zero (e.g. +2.50D for a 40cm near distance) and the near heterophoria is measured. In this way, the change in vergence posture from distance to near viewing is theoretically driven only by proximal vergence, as accommodative vergence should not be produced if as expected accommodation does not change.8,16,24

The purpose of this study is to compare the two methods of assessing proximal vergence described above and to determine the role that accommodation plays in these two measures. The results can inform clinicians as to what the range of measurements for these different methods is likely to be, and whether these measurement methods can be substituted for one another. Ultimately, if


During this rest period, participants removed the trial frame and spoke with the examiner who was approximately 2m away.

For each of these three near heterophoria conditions, a near Modified Thorington card (Bernell Corporation, Mishawaka, IN) was viewed at a distance of 40cm. The card was attached to a near point rod that was affixed to the autorefractor. A penlight was attached to the card and shone through the central hole on the card. Participants were instructed to keep the details on the card clear throughout testing and to mentally note the position of the vertical red line image seen by the right eye relative to the horizontal scale on the card. As participants viewed the target, the investigator took 10 autorefractor measurements of accommodation from the left eye. The participants were then asked for the location of the red line on the card which represented the near heterophoria measurement for each condition.

Finally, step fusional vergence ranges were measured using a prism bar. Vergence ranges were measured at distance and then at near, and base-in prism ranges were measured before base-out prism ranges. The purpose of these vergence range measures was to determine if there was any correlation between proximal vergence measures and fusional vergence ranges.22

data AnalysesStimulus AC/A Differencing Method

The stimulus calculated or far-near AC/A ratio was determined using equation 1 below (symbols from Wick8).5,8-10

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

In this equation, IPD is the interpupillary distance in centimeters, D is the distance of the near fixation target in meters, h is the near heterophoria, and H is the distance heterophoria. Esophorias are negative while exophorias are positive.

visual acuity, stereoacuity, and accommodative amplitudes, the interpupillary distance was also measured.

Next, the proximal vergence measures were initiated. Participants wore a trial frame throughout the experiment to allow use of various lenses for each testing condition. Participants were positioned in the Grand Seiko WR5100K autorefractor (Grand Seiko Co., Japan) with their chin in the chinrest and forehead against the forehead rest. In addition to providing an open view, the Grand Seiko WR5100K autorefractor has been shown to have good repeatablity.25-26 The Grand Seiko provided a measurement of refractive error, which was then converted to the accommodative response for each testing condition.

Participants then viewed a distance Modified Thorington card (created for this study) with a Maddox lens in front of the right eye. The distance Modified Thorington card was placed at a distance of four meters. A light was placed behind the card and shone through a hole in the center of the card. 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 scale on the card. As participants viewed the target, the investigator took 10 autorefractor measurements of accommodation from the left eye. Participants were then asked for the location of the red line on the Modified Thorington card, which represented the distance heterophoria measurement.

All participants completed three trials in which the near heterophoria was measured. In addition to the Maddox lens in front of the right eye (worn in all 3 conditions), participants viewed binocularly through either no refractive lenses, +1.00D lenses, or +2.50D lenses. The presentation order of these three viewing conditions was randomized. A five-minute waiting period occurred between trials to allow any residual vergence adaptation or accommodative adaptation to dissipate.


The denominator used in these calculations was initially 2.25D, which represented the change in accommodative demand from far (4m) to near. The mean stimulus calculated AC/A ratio using this denominator was 5.44 ± 1.67 ∆/D. Some of the participants were found to have uncorrected refractive error at distance with the autorefractor (mean spherical equivalent = 0.11 ± 0.64D). In those cases, the required change in accommodation from distance to near was not 2.25D. The denominator of the calculated AC/A ratio was corrected for the distance refractive error and the mean calculated AC/A ratio was re-calculated. This value was 5.83 ± 3.13 ∆/D. Because the mean uncorrected and corrected calculated stimulus AC/A ratios were similar, the uncorrected value was used for all calculations that follow.

The stimulus gradient AC/A ratio was calculated by determining the change in heterophoria position between the 40cm with no lens viewing condition and the 40cm with +1.00D lens viewing condition (equation 2 below).5,9,11 This difference was considered the stimulus gradient AC/A since the denominator (the power of the lens) was +1.00D.

(2) Gradient AC/A = [(near phoria)–(near phoria with +1.00D lens)]/(+1.00D)

The mean gradient AC/A ratio was 2.31 ± 2.43 prism diopters.

Stimulus proximal vergence values in prism diopters were calculated using the AC/A differencing method by taking the difference in the stimulus calculated AC/A ratio and the stimulus gradient AC/A ratio (equation 3 below) and then multiplying this difference by 2.50D (the accommodative demand at 40cm).

(3) AC/A differencing method of proximal vergence = (calculated AC/A) – (gradient AC/A)

The +2.50D Method (Uncorrected)Proximal vergence values (uncorrected for

any remaining accommodation and accommo-dative vergence) were also calculated using the +2.50D method. Since the distance heterophoria in this experiment was measured at 4m, to apply equation 4 below it was necessary to determine the expected heterophoria at 6m. To do this, a graph of ocular vergence (x-axis) versus accommodative demand (y-axis) was made.27 A line that included convergence demands (based on the interpupillary distance) at numerous accommodative demands was made, as was a line that included heterophoria values at these accommodative demands. From this graph, it was then possible to determine the expected heterophoria at 6m. The mean proximal vergence value was then calculated using equation (4) below (symbols from Wick8).8,24,28

(4) +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, and H is the distance heterophoria. In this equation, esophoria is represented by a negative value and exophoria is represented by a positive value.

Proximal Values incorporating Response AccommodationRefractive and Accommodative Measures

Examination of those refractive data obtained from the autorefractor demonstrated that the distance autorefraction for one participant showed 2.00 diopters of cylinder. Much smaller cylinder values for this participant were found at 40cm in all viewing conditions. A second participant 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. Finally, a third participant showed relatively low levels of cylinder (under 0.75D) in all viewing conditions except the +2.50D lens condition. In this latter condition, the cylinder was 5.87D for this participant. Because of these varying cylinder values, these three participants were excluded in the following analyses.

The average spherocylindrical autorefractor values for each participant in each testing condition were first converted into spherical equivalent values.

Next, the change in accommodation for the 10 remaining participants was assessed from the distance and near autorefractor recordings. The mean change in accommodation was 1.45 ± 0.48D for these 10 subjects. As described below, ultimately 9 subjects were included in the response proximal calculations. The mean change in accommodation from distance to near for these 9 subjects was 1.52 ± 0.46D.

Following that, the change in accommo-dation induced when viewing through the +1.00D lenses at near was determined. This value was needed to calculate the response gradient AC/A ratio. The fact that the autorefractor reads -1.00D when a +1.00D lens is inserted was accounted for. The mean change in accommodation induced by the +1.00D lens was 0.68 ± 0.30D. One participant demonstrated no change in accommodation with the +1.00D lens in place. Because the denominator of the response gradient AC/A ratio is the change in accommodation induced by a lens, the response gradient AC/A could not be calculated for this participant. Therefore, 9 participants are included in the remaining analyses.

Once the change in accommodation with the +1.00D lens at 40cm was determined, the total accommodation remaining with the +2.50D lenses in place at 40cm was calculated. These values indicated the extent to which accommodation was still active and therefore the extent to which accommodative

vergence was still in effect with the +2.50D lens in place. If all accommodation was relaxed when the +2.50D lenses were in place, then the value for refractive error measured when participants viewed through the +2.50D lenses was expected to be equal to the distance autorefractor measurement (compensated by +0.25D because the original distance measurement was taken at 4m) plus -2.50 (to account for the power of the +2.50D lens placed in front of the eyes).The mean accommodation remaining with the +2.50D lenses in place was 0.26 ± 0.50D.

The response calculated AC/A ratio was determined for each participant using the following equation:

(5) Response calculated AC/A ratio = [(PD/D) - h + H]/(Change in accommodation from distance to 40cm)

The mean response calculated AC/A ratio was 9.49 ± 4.33 prism diopters/diopter. The response gradient AC/A was also calculated. This was done by taking the change in heterophoria between the 40cm (no lenses) viewing condition and the 40cm (+1.00D lenses in place) condition, and dividing this difference by the change in (response) accommodation induced by the +1.00D lens (equation 6). The mean response gradient AC/A was 3.13 ± 1.77 prism diopters per diopter.

(6) Response gradient AC/A = [(near phoria)–(near phoria with +1.00D lens)]/(Change in accommodation at 40cm with +1.00D lens)

Response AC/A Differencing MethodResponse proximal vergence values using

the AC/A differencing method were calculated in the same manner as the stimulus proximal values with one exception. The response calculated 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.

+2.50D Method Corrected for Remaining Accommodation

The stimulus proximal vergence values were 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 (described above) by the response gradient AC/A ratio (as this is the AC/A ratio most likely to be unaffected by proximal influences). The accommodative vergence value obtained in this way was then subtracted (or added in cases where accommodation was relaxed more than expected) from the proximal vergence value to obtain the corrected proximal vergence value.

ReSultSThirteen participants with a mean age of

28.5 ± 4.5 years (age range 22-37 years) were enrolled in the study. The mean heterophoria values (exophoria positive) were -1.00 ± 1.85 prism diopters at the 4m distance, 2.00 ± 4.65 prism diopters at near with no lenses, 4.31 ± 4.61 prism diopters at near with +1.00D lenses, and 7.38 ± 4.50 prism diopters at near with +2.50D lenses.

Stimulus Proximal ValuesThe stimulus proximal values are summar-

ized in Table 1. Included in this table are the mean PCT ratios (proximal convergence/test distance (PC/T) ratios) for comparison to

previous studies.13,28 For the ACA stimulus and response differencing methods, the PC/T ratio was taken to be the difference between the calculated and gradient AC/A ratios. For the +2.50D uncorrected and corrected methods, the calculated proximal vergence value was divided by 2.50D.

Comparisons of Proximal Vergence ValuesAccommodative Influences

Before describing comparisons of the proximal vergence values between the AC/A differencing method and +2.50D method, it should be noted that a comparison of the proximal values obtained with the stimulus AC/A differencing method and the response AC/A differencing method showed no significant difference (mean difference = 0.16 ± 2.47 prism diopters, paired t-test: p = 0.846). Similarly, there was no significant difference between the proximal values obtained with the +2.50D method uncorrected for accommodation and the +2.50D method corrected for accommodation (mean difference = 1.03 ± 1.84 prism diopters, paired t-test: p =0.132).

The results of the following comparisons are summarized in Table 2.

Stimulus AC/A differencing Method versus uncorrected +2.50d Method

The proximal values obtained with the stimulus AC/A differencing method and the +2.50D method (uncorrected for any accom-mo dation remaining with the +2.50D lens in place) were compared using the Bland Altman

table 1. Proximal vergence values and PCt (proximal convergence/test distance) ratios calculated with each method. For the stimulus methods, those values in parentheses were determined from 9 participants in order to compare stimulus and response values.

Condition Mean proximal value ± standard deviation (prism diopters)

Mean PCt ratio ± standard deviation (prism

diopters/diopter)

Stimulus ACA differencing method 7.82 ± 5.98 (8.46 ± 4.17) 3.12 ± 2.39

+2.50D method uncorrected 6.23 ± 3.52 (6.16 ± 3.08) 2.49 ± 1.41

Response ACA differencing method 8.29 ± 3.30 3.32 ± 1.32

+2.50D method corrected 5.13 ± 2.98 2.05 ± 1.19


method (Figure 1).29 All 13 participants were used in this comparison. The differences followed a normal distribution (Anderson-Darling statistic, p = 0.54). The mean of the differences (bias) between the two methods (AC/A differencing method - +.2.50D method) was 1.59 prism diopters and the standard deviation of this mean was 4.84 prism diopters. The 95% confidence interval ranged from -7.90 to 11.08 prism diopters. Linear regression between these variables yielded a coefficient of determination (R2) of 34.4% (p = 0.035).

The stimulus proximal values obtained with the AC/A differencing method and the uncorrected +2.50D method were also compared using a paired t-test. The difference between the values was not statistically significant (t = 1.19, p = 0.258).

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Mean of Stimulus AC/A differencing method and Uncorrected +2.50D method

Figure 1: Bland Altman difference versus mean response for the stimulus AC/A differencing method and the uncorrected +2.50D method. The solid line is the mean difference (bias) and the dashed lines are the 95% limits of agreement.

Stimulus AC/A Differencing Method versus Corrected +2.50D Method

The proximal values obtained with the stimulus AC/A differencing method and the +2.50D method (corrected for any accommodation remaining with the +2.50D lens in place) were compared using the Bland Altman method (Figure 2). Nine participants were used in this comparison. The differences followed a normal distribution (Anderson-Darling statistic, p = 0.31). The mean of the differences (bias) between the two methods (AC/A differencing method - +.2.50D method) was 3.32 prism diopters and the standard deviation of this mean was 3.44 prism diopters. The 95% confidence interval ranged from -3.42 to 10.06 prism diopters. Linear regression between these variables yielded a coefficient of determination (R2) of 33.9% (p = 0.100).

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Mean of Stimulus AC/A differencing method and Corrected +2.50D method

Figure 2: Bland Altman difference versus mean response for the stimulus AC/A differencing method and the corrected +2.50D method. The solid line is the mean difference (bias) and the dashed lines are the 95% limits of agreement.

table 2. Results of comparisons of methods.

Comparison Mean difference (bias) (prism diopters)

limits of agreement (prism diopters)

Regression Paired t-test

Stimulus ACA differencing method – Uncorrected +2.50D method

1.59 ± 4.84 -7.90 - 11.08 R2 = 34.4%(p = 0.035)

p = 0.258

Stimulus ACA differencing method – Corrected +2.50D method

3.32 ± 3.44 -3.42 - 10.06 R2 = 33.9%(p = 0.100)

p = 0.020

Response ACA differencing method - Uncorrected +2.50D method

2.13 ± 2.79 -3.34 - 7.60 R2 = 38.4%(p = 0.075)

p = 0.051

Response ACA differencing method - Corrected +2.50D method

3.16 ± 1.78 -0.33 - 6.65 R2 = 71.4%(p = 0.004)

p = 0.001


The proximal values obtained with the stimulus AC/A differencing method and corrected +2.50D method were also compared using a paired t-test. The difference between the values was significant (t = 2.90, p = 0.020).

Response AC/A Differencing Method versus Uncorrected +2.50D Method

The proximal values obtained with the response AC/A differencing method and the +2.50D method (uncorrected for any accommodation remaining with the +2.50D lens in place) were compared using the Bland Altman method (Figure 3). Nine participants were used in this comparison. The differences followed a normal distribution (Anderson-Darling statistic, p = 0.51). The mean of the differences (bias) between the two methods (AC/A differencing method - +.2.50D method) was 2.13 prism diopters and the standard deviation of this mean was 2.79 prism diopters. The 95% confidence interval ranged from -3.34 to 7.60 prism diopters. Linear regression between these variables yielded a coefficient of determination (R2) of 38.4% (p = 0.075).

The proximal values obtained with the response AC/A differencing method and uncorrected +2.50D method were also compared using a paired t-test. The difference

Resp

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Mean of Response AC/A differencing method and Uncorrected +2.50D method

Figure 3: Bland Altman difference versus mean response for the response AC/A differencing method and the uncorrected +2.50D method. The solid line is the mean difference (bias) and the dashed lines are the 95% limits of agreement.

between the values approached significance (t = 2.29, p = 0.051).

Response AC/A Differencing Method versus Corrected +2.50D Method

The proximal values obtained with the response AC/A differencing method and the +2.50D method (corrected for any accom-modation remaining with the +2.50D lens in place) were compared using the Bland Altman method (Figure 4). Nine participants were used in this comparison. The differences followed a normal distribution (Anderson-Darling statistic, p = 0.392). The mean of the differences (bias) between the two methods (AC/A differencing method - +.2.50D method) was 3.16 prism diopters and the standard deviation of this mean was 1.78 prism diopters. The 95% confidence interval ranged from -0.33 to 6.65 prism diopters. Linear regression between these variables yielded a coefficient of determination (R2) of 71.4% (p = 0.004).

The proximal values obtained with the response AC/A differencing method and corrected +2.50D method were also compared using a paired t-test. The difference between the values was statistically significant (t = 5.33, p = 0.001).

Resp

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Mean of Response AC/A differencing method and Corrected +2.50D method

Figure 4: Bland Altman difference versus mean response for the response AC/A differencing method and the corrected +2.50D method. The solid line is the mean difference (bias) and the dashed lines are the 95% limits of agreement.


Comparison of Proximal Vergence Measures and Fusional Vergence Ranges

All of the proximal vergence measures were compared to the base-out to blur vergence ranges at near using linear regression. Comparisons were made between the proximal vergence values and both the vergence ranges as measured from the demand and the vergence ranges as measured from the heterophoria. In cases where participants did not report blur, the break finding was used in the analysis. Two of the 13 participants (only one of these participants was included in comparisons with the response proximal values) reached the maximum value on the prism bar of 45 prism diopters and that is the value that was used in these regression analyses. While a number of the comparisons trended toward a positive correlation, only the comparison of the proximal values obtained from the response AC/A differencing method and the fusional vergence ranges measured from the heterophoria was significantly (positively) correlated (R2 = 45.4%, p = 0.048).

diSCuSSionThe objectives of this study 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 influence of the accommodative response on these measurements.

In regard to the mean proximal vergence values (Table 1), the largest value was found for the AC/A differencing methods, and the smallest value was found for the +2.50D method corrected for remaining residual accommodation. While these values are similar to the value of 6.4 prism diopters reported by Wick,8 they are larger than those values reported in some other studies.13 It could be that the stimulus conditions (dissociated viewing, reduced contrast target) in this experiment resulted in significant reliance on proximal stimuli.14,15

The mean of the differences (bias) between the various tests ranged from 1.59 prism diopters to 3.32 prism diopters. The two methods most likely to be used clinically (stimulus AC/A differencing method and +2.50D method uncorrected) did demonstrate a significant correlation (p = 0.035), and the paired t-test suggested that these two methods resulted in similar values (p = 0.258). While the overall results of these methods were similar, there were individuals for whom the differences were quite large (Figure 1).

On the other hand, when the accommo-dative response was factored in, the relationship between the various methods of measurement was reduced. The mean differences between methods in which accommodation was assessed in at least one of the methods under comparison ranged from 2.13 to 3.32 prism diopters. For all three of the comparisons in which the accommodative response was accounted for in at least one of the tests, there were no instances where both the p-value associated with the regression was less than 0.05 and the p-value associated with the paired t-test exceeded 0.05.

What conclusions can be drawn from these results? First, those tests in which accommodation was not accounted for (and those tests therefore most likely to be applied clinically) produced similar results overall. However, because there were differences between these tests for individual participants, when assessing proximal vergence for a clinical patient the practitioner should consider assessing proximal vergence with both the AC/A differencing method and the +2.50D method. Second, when accommodation is accounted for, it is clear that differences appear between the various clinical methods. Clinicians and researchers should be aware that methods of measurement of proximal vergence may not result in the same findings, and that differences between these measurement methods are likely larger when accommodation is accounted for in the testing.


Lastly, while the regression analyses com-paring proximal vergence values and near base-out vergence ranges trended in a positive direction, only one of the comparisons reached significance. This suggests that proximal vergence values are largely independent of base-out vergence ranges, and that consideration should be given to testing and training proximal vergence in isolation from other vergence subtypes. Future studies utilizing a larger sample with a wide range of heterophoria values will help to quantify the relationship between proximal and fusional vergence values.

AcknowledgmentsThis work formed the basis of Dr. Rachel

Fenton’s (2019) Master of Science thesis in Vision Science from the Ohio State University. Dr. Emmanuel Owusu performed a pilot study demonstrating the feasibility of this work. Funding for this work was provided by the Ohio State University College of Optometry. The project described was supported in part by Award Number Grant UL1TR002733 from the National Center for Advancing Translational Sciences. The content is solely the responsibility of the author and does not necessarily represent the official views of the National Center for Advancing Translational Sciences or the National Institutes of Health.

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AUTHOR BIOGRAPHY:Nick Fogt, OD, PhDColumbus, Ohio

Nick Fogt is a professor at the Ohio State University College of Optometry. He currently teaches the posterior segment and systemic disease courses at the College of Optometry, as well as a graduate course in eye movements.

His primary research interests are in the areas of binocular vision, head and eye movements, and sports vision.

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