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Optometry & Vision Science:
doi: 10.1097/OPX.0b013e3181e19ec2
Original Article

Effect of Vergence Adaptation and Positive Fusional Vergence Training on Oculomotor Parameters

Thiagarajan, Preethi*; Lakshminarayanan, Vasudevan; Bobier, William R.

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*BSOptom, MS



School of Optometry, University of Waterloo, Waterloo, Ontario, Canada.

Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal's Web site (

Received January 1, 2010; accepted March 10, 2010.

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Purpose. Clinical studies have shown that positive fusional vergence (PFV) can be trained through a program of orthoptic exercises. Models of accommodation and vergence predict that training PFV would require a reduction in the convergence accommodation (CA) cross-link. Recent investigations have found that the CA/C ratio is not changed in a clinical population after orthoptics. We hypothesized that such orthoptic programs may instead act to reduce CA through changes in the relationship between fast and slow vergence components.

Methods. Eleven visually normal subjects were tested. Phoria adaptation to a 12-Δ base-out (BO) wedge prism and the resulting CA responses were monitored every 3 min for 15 min to a DoG target at 0.4 m. These measures were repeated after 2 weeks of orthoptics. Phorias, stimulus accommodative convergence (AC)/A and CA/C ratios, and PFV amplitudes at near were also determined. Before the orthoptics program, these measures were repeated under “adapted” conditions.

Results. Phoria adaptation following prolonged viewing through the 12-Δ BO wedge prism was associated with a concomitant reduction in the CA. These changes were asymptotic over time with 95% of the change occurring within the first 3 to 6 min. After 2 week of orthoptics, the rates and magnitudes of both phoria adaptation and CA reduction increased significantly (p < 0.01). PFV at 40-cm limits showed increases with orthoptics and under vergence adaptation. CA/C and AC/A ratios were unchanged after orthoptics, but the former was reduced, and the latter increased under the vergence adapted condition.

Conclusions. Orthoptics acts to change the time constant and magnitude of vergence adaptation to BO prisms, which leads to a concomitant reduction of CA over a similar time course. This process appears to underlie the increase in positive fusion limits. Although reductions in CA/C ratio occur under the vergence adapted state, this ratio is not directly changed with orthoptics.

The two reciprocal cross linkages between accommodation and vergence are now well established. Accommodative convergence (AC), defined as a reflexive change in convergence, which was driven by changes in accommodation, was discovered in the late 1800s.1,2 Much later, the reciprocal link of convergence accommodation (CA) was identified where a change in vergence drove a concomitant change in accommodation.3,4 Both these cross-links can be quantified as ratios. The AC/A ratio defines the measured amount of AC per unit change of accommodation and the CA/C ratio the amount of CA per unit change in vergence.

The capacity to view through a range of prisms has long served as a diagnostic procedure in clinical vergence testing.5,6 These “fusional” limits are typically defined by the prism magnitude that can be tolerated before a change in accommodation is evoked.5 By tradition, the measurement is extended beyond this blur point to define the prism magnitudes at which diplopia results, followed by where single vision is restored.1,5,6 The convergence stimulated by that of a prism is quite unlike the normal changes in fixation found in response to an object changing in depth, which invoke concomitant and symmetrical changes in both vergence and accommodation. In the case of viewing through a base-out (BO) prism, only the stimulus to convergence is increased, while the stimulus to accommodation remains the same as that before prism viewing. Thus, the oculomotor system must adjust to a lack of synchrony between accommodation and vergence. Clinical investigations for over a century5 have shown that subjects vary in the degree to which they can view through BO and base-in(BI) prisms before they experience blur and then diplopia. These responses would be expected because of the stress that prism viewing would place on the cross linkages of AC and CA. During such a “fusional vergence measure,” blur is typically reported before diplopia. Initially, the AC link was thought to cause the resulting blur arising in fusional vergence measures, where it was proposed that an increase in accommodation arose, which was associated with the recruitment of AC to aid in the fusion.7 However, subsequent empirical investigations8,9 were more consistent with a model wherein forced convergence drove the reciprocal CA cross-link as opposed to AC. This model is conceptually more attractive where prisms introduce disparities, which then lead to vergence changes that stimulate vergence accommodation.10–12

Clinical studies have shown that positive fusional limits can be increased with training when a battery of tasks requiring increased convergence is performed while accommodation is kept constant.13–18 However, the underlying mechanism for this improvement is not well understood. Typical CA/C ratios and positive fusion limits would predict that excessive accommodation arising from CA would be invoked well before fusional vergence limits were achieved. The lack of blurring could be explained if vergence adaptation were elicited during this measurement. This hypothesis would be consistent with the finding that such limits are dependent on the rate of prism introduction and the observation that phoria changes are often noted after fusion limits.19 Symptomatic subjects with deficient fusion limits, either in absolute magnitude or with respect to the magnitude of their phoria, show reduced vergence (prism) adaptation,20,21 and this capacity can be improved with vergence training.16–18,22

When fixation of a near object is prolonged, tonic levels of vergence are increased toward the stimulus level created by the near object.23 This response is viewed as adaptive and is modeled10,24,25 as a two-step process where, with prolonged fixation, a slow fusional vergence response replaces the initial output of the reflex (fast) vergence response. Furthermore, it appears that the output of CA is dependent on the fast vergence response and declines with adaptation.10,12,26

Early studies involving oculomotor training (orthoptics) looked at only the AC/A ratio, which was found to increase with positive fusional vergence (PFV) training27,28; however, these increases were transient. Subsequent studies providing orthoptic exercises for symptomatic groups have not been able to induce significant changes in the AC/A ratio nor the CA/C ratio.18 Specifically, as fusion limits were increased by orthoptics, neither the CA/C nor the AC/A ratios were changed. Changes in these ratios require different stimuli conditions. One successful strategy has been the use of periscopic lenses, which optically increased the interpupillary distances (IPD). Prolonged viewing through these devices resulted in increased AC/A and decreased CA/C ratios. However, when the periscopes were set to optically reduce the subject's IPD, the reverse effect was not reliably induced.26 Possibly, this bias in adjustment reflected the normal increase in IPD that accompanies growth of the cranium. What then allows the increased capacity to view through higher magnitudes of prism if this is not a result of changes in either the AC/A or the CA/C ratios? It is known that vergence adaptability improves with training17,18 as do parameters that indirectly measure this function.29 Vergence adaptation would in turn allow the necessary reduction in the CA cross-link output.10 Perhaps, the increased PFV limits after orthoptics follow from long-term changes in the speed and degree of vergence adaptation and concomitant reduction in the CA output. This study investigates this hypothesis.

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Eleven healthy emmetropes aged between 19 and 30 years (mean 24.6 ± 3 years) were recruited from the student/staff population at the School of Optometry at the University of Waterloo. The study was approved and received full ethics clearance from the Office of Research Ethics, University of Waterloo. Experiments were performed with the understanding and written consent of the participants.

The following visual criteria were required for all subjects: 20/20 visual acuity with ophthalmic correction; phorias taken using the modified Thorington technique (MTT)30 fell within Morgan's criteria31 for distance and near, as did other binocular motor findings of PFV and negative fusional vergence limits (taken using a prism bar), near point of accommodation (both monocular and binocular); negative relative accommodation (NRA) and positive relative accommodation (PRA) and near point of convergence (NPC).

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Experimental Procedures Pretraining Experimental Measures

The following baseline measures (before PFV training) were recorded on the same day of the screening visit.

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Stimulus AC/A Ratio and Stimulus CA/C Ratio

The stimulus AC/A (sAC/A) ratio was measured using the gradient method where ophthalmic lenses ranging from +2.00 diopters (D) to −2.00 D in 1-D steps were introduced in front of the eyes, and the corresponding near phoria was recorded using the MTT. The slope of the linear fit plotted with induced lenses (in D) along the x axis and the resultant phoria (in Δ) along the y axis defined the sAC/A ratio. The stimulus CA/C (sCA/C) ratio was then measured with the accommodation feedback loop opened by asking the participants to fixate difference of Gaussian pattern (DoG) of 0.2 cpd placed at 0.4 m. This design of DoG does not stimulate blur-driven accommodation, and it has a narrow band of frequencies with well-defined edges to stimulate motor fusion.32,33 BO prisms of magnitudes 0, 3, 6, 9, and 12Δ were introduced in front of the left eye, and the concomitant change in the accommodative response was recorded. Measures from the subject's right eye were taken once the subject reported fusion through the prism. The sCA/C ratio was calculated from the slope of the linear fit plotted using the convergence stimulus (in meter angles) along tx axis and the resultant accommodative response (in D) along y axis.

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Pretraining Measurement of Phoria and Convergence Accommodation during 15 min of Prism Adaptation

This experiment was conducted under conditions of open-loop accommodation. Participants binocularly fixated the DoG target at 0.4 m through 12-Δ BO placed in front of the left eye for 15 min. Any change in the open-loop accommodative response would indicate a change in the CA response (because proximal and tonic accommodation responses would be constant). Hence, in the current investigation, the change in the open-loop accommodative response was realized as a change in the CA response. The DoG target was generated on a laptop and imaged onto a miniature 1.77-in LCD. The subject viewed the image through a semisilvered mirror placed 0.28 m from the target. This provided an optical path of 0.4 m from the subject's eye. Phoria and open-loop accommodative responses were recorded immediately after the prism insertion. These measures were repeated in 3-min intervals up to 15 min while the subject held binocular fixation at 0.4 m.

Accommodative responses were measured at 25 Hz and averaged over 5-s intervals using a PowerRefractor (MultiChannel Systems, Reutlingen, Germany) following individual calibrations. Although the binocular accommodative responses were measured, only those from the right eye alone were averaged in the analysis. Heterophoria measures were taken using custom-designed MTT scale at 6 m and 0.4 m.30

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Measurement of BO to Blur, and sAC/A and sCA/C Ratios under Induced Vergence Adapted State

The testing sequence repeated the fusion limits and cross-link ratio measures under open-loop conditions for both accommodation and vergence, after 15 min of binocular viewing through the 12-Δ wedge prism placed before the left eye. This experiment was conducted at a separate session (with at least 24 h of interval from the screening visit) but before the training sessions, to avoid the influence of vergence adaptation that had taken place during the baseline measures. A cartoon image was projected onto the 1.77-in monitor providing a high contrast image and luminance of 31.5 cd/m2. The subject viewed the monitor as above through the semisilvered mirror. The cartoon image was preferred over text to enhance subject attention given the lengthy viewing time. A baseline phoria measure was obtained. Then, the phoria immediately after prism insertion was recorded. Participants were asked to binocularly fixate the high contrast cartoon target with the prism in place for 15 min. The following measurements were taken with the adapting stimulus remaining in place: near BO range, sAC/A ratio, and sCA/C ratio. The cross-link ratios were measured with the same procedure described earlier in the pretraining measures. The vergence amplitudes were measured in a stepwise manner using a prism bar. Finally, a postadaptation phoria measure was taken through the adapting prism.

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PFV Training Sessions

Following the induced vergence adaptation experiment, participants underwent a vergence training program for a 2-week period, which comprised a total of 6 sessions (3 sessions per week). The training was designed from clinical protocols that served to increase PFV limits. The basis of the training was much like having a subject view through a series of BO prisms of increasing magnitudes. The tasks provided a steady increase in convergence demand while holding accommodation fixed.31 Each session lasted for 25 to 30 min, and each participant had a total of ∼180 min of training. During each session, PFV was trained conventionally31 using variable tranaglyphs and an aperture rule. At the end of each training session, participants' PFV amplitudes were recorded using a synoptophore. The synoptophore targets were slides with second (flat fusion), and third (stereopsis) degree fusion targets with suppression checks. All training was limited to these “in office” visits. Details of the training methods are captured in the Appendix (

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Post-Training Measurements

Post-training measurements were made during the week following the completion of the training. This short time interval was introduced in order that residual effects arising from the training could be differentiated from short-term effects arising immediately after a convergence training session. Changes in the experimental variables including the sAC/A and the sCA/C ratios as well as the phoria and the CA responses during 15 min of prism adaptation under open-looped accommodation were measured after the training. In addition, clinical parameters such as NPC, distance and near heterophoria, distance and near positive and negative fusional amplitudes lag of accommodation, NRA, and PRA measures were repeated.

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Data Analysis

Changes in clinical measures of NPC, distance and near phoria, PRA and NRA, negative fusional amplitudes at distance and near, lag of accommodation and positive fusional amplitude at distance were analyzed using a paired t-test before and after the training. Phoria and CA responses measured during the 15-min adaptation period as part of the pretraining and post-training and induced adaptation conditions were fitted with exponential decay functions with GraphPad Prism 4 software (GraphPad Software, San Diego, CA) to determine the rates and magnitudes of phoria adaptation and CA response reduction. The resulting exponential decay functions for phoria adaptation and CA reduction for each of the three conditions could then be compared. The AC/A ratio, CA/C ratio, and BO to blur value at 0.4 m taken during the three conditions were analyzed using repeated-measures ANOVA. Detailed descriptions of the orthoptic exercises and changes are found in the Appendix (

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Clinical Parameters Altered with Training

The PFV training showed the expected changes in a number of clinical measures. Importantly, the BO to blur value at 0.4 m was significantly increased from the pretraining measure both under the vergence adapted state (p < 0.001) and after training (p < 0.001). Also, the post-training value was significantly greater than the value obtained under vergence adapted state (p < 0.001) as shown in Fig. 1. BO to break value could not be analyzed before and after training because, for the majority of the participants after the training, since the value lay beyond the testing range of the prism bar (45 Δ; Table 1).

Figure 1
Figure 1
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Table 1
Table 1
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The near point of convergence reduced significantly (t = 6.127, p < 0.01). Near heterophoria was found to be significantly less exophoric (t = 4.132, p < 0.01) from the pretraining value by an averaged value of 1.4 Δ.

PFV training did not significantly change the distance heterophoria (t = 1.312, p = 0.219), where the mean change in its magnitude was <1 Δ. No changes were found for lag of accommodation, NRA and PRA, negative fusional amplitudes at distance and near, and positive fusional amplitude at distance (p ≥ 0.05) before and after PFV training. A nonsignificant increase in the BO to blur (PFV) value at distance was further noted.

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Experimental Results

After training, the magnitude and speed of both the phoria adaptation (Fig. 2) and concomitant reduction in the CA (Fig. 3) increased when measured every 3 min during a 20-min period of fixation through a 15-Δ BO prism. The time constant (time to reach 63% of phoria adaptation), plateau (the saturation of phoria adaptation), and magnitude of phoria adaptation were significantly different (p < 0.001), indicating a faster and a greater degree of phoria adaptation after training as shown in Fig. 2 (Table 2).

Figure 2
Figure 2
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Figure 3
Figure 3
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Table 2
Table 2
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Similarly, for CA, there was a significant difference in the time constant (time to reach 63% of CA response reduction; p = 0.014), plateau (the point at which the CA response saturates; p < 0.01), and the amount of reduction (p = 0.016) before and after training. Thus, prism adaptation induced a faster and a greater amount of CA response reduction after training These values are given in Table 3.

Table 3
Table 3
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There was no significant difference between pretraining and post-training AC/A ratios (p = 0.999) or the CA/C ratios (p = 0.146). However, the AC/A ratio measured under the vergence adapted state was found to be small but significantly increased from the pretraining (p = 0.023) and post-training (p = 0.025) values as shown in Fig. 4. Also, the CA/C ratio that was measured under vergence adapted state was found to be significantly reduced from the pretraining (p < 0.01) and post-training (p < 0.01) values as shown in Fig. 5.

Figure 4
Figure 4
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Figure 5
Figure 5
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The Impact of Vergence Adaptation on Clinical Findings

When subjects were adapted to 12-Δ BO prism viewing at 40 cm, a clear reduction in CA occurred. This reduction is consistent with oculomotor models of accommodative and vergence cross-links,10,23,24 which predict that vergence adaptation reduces CA output. In this adapted state, the reduced CA would lead to the finding of the reduced CA/C ratio. This is consistent with other studies that showed changes in the cross-link gains with BO prism adaptation.26 Similarly, the increased PFV limit (BO to blur) is best explained as a consequence of this reduction in CA. It is worthy of note that vergence (phoria) adaptation is often found following BO prism limits leading to a transiently more esophoria (less exophoria) position.19 Thus, it appears that fusion limits will be affected by the capacity of subjects to invoke vergence adaptation during the slow and smooth application of Risley prisms or by the step changes induced by prism bars as in this study. The invoking of prism adaptation would, in part, explain the variations reported for fusion limit testing and the improved reliability found when fusion limits are conducted in a more standardized method.34

The small increase in AC/A with adaptation is also consistent with earlier findings in which the AC cross-link gain was found to increase by a small (∼0.3 Δ) but significant amount, with phoria adaptation in humans26,35 and, also, in monkeys.36 This has been interpreted as a lack of specificity in the adaptation responses but also would be consistent with oculomotor models23,24,26 where the decreased CA would reduce the net accommodative response, thereby increasing reflex accommodation and accommodative-driven convergence. Alternatively, because only the stimulus AC/A ratio was measured, the accommodative response is unknown, and if it was reduced, it alone could explain a higher AC/A value. Further experimental measures of response AC/A could resolve this.

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The Impact of Orthoptics

When subjects in this study increased their PFV limits with orthoptics, their CA/C or AC/A ratios were not significantly altered. It is important to emphasize that this was post-training but not under an adapted state. Thus, the increased PFV cannot be attributed to a reduction in the CA/C ratio or changes in the AC/A ratio. This is consistent with the findings of Brautaset and Jennings18 who showed no change in the CA/C or AC/A ratios for patients with convergence insufficiency who had increased their PFV limits after orthoptic treatment. Instead, it appears that patients may increase their PFV limits through a more rapid onset of vergence adaptation resulting in reduced CA output. This is evident from the pretraining and post-training exponential decay functions of phoria adaptation and open-loop accommodative (CA) response reduction. Therefore, we propose that the well-documented increases in PFV amplitudes after orthoptics result from the increased speed of onset and magnitude of vergence adaptation. Thus, greater amounts of vergence adaption and the concomitant reduction in CA output allow a greater range of BO prisms to be overcome before blur results. This change in adaptation would not be expected to influence the measures of AC/A or CA/C.

An improved NPC demonstrates enhanced amplitude of convergence, and the result is consistent with the earlier studies.15,18 Results demonstrated post-training reduction in the near but not the far phoria. The reduced exophoria is small at 1.4 Δ statistically (p < 0.01) but not clinically significant. Whether this reflects small transient changes after orthoptics or small changes in the AC/A ratio, which could not be detected in this experiment, is not clear.

We note that the adaptation changes did not transfer to the PFV measures at 6 m in that no significant increases were found. Current models10,25 would predict that the increased rate of adaptation should carry forward to this distance as well. It is generally found that 6-m fusion limits are smaller than those found at near. Thus, in the case of visually normal subjects, it is not clear if there is ceiling effect imposed at 6 m on PFV or whether the transference of adaptation is affected by the viewing distance.

This study confirmed that vergence adaptation acts to reduce the CA response. When vergence adaptation is increased in its rate of onset through orthoptic exercise, then there is a concomitant increase in the speed and magnitude of the reduction in the excess CA, thereby allowing subjects to view through a larger range of prisms before experiencing blur. This is recognized clinically as an increase in the PFV limits. This research provides a link between studies which find vergence adaptation to be reduced in binocular motor problems (such as convergence insufficiency)20,21 and those where vergence adaptation is improved after orthoptic exercises. The results further support models that describe vergence adaptation as acting to reduce the fast vergence output such that cross-link output is also attenuated.10,24,26 Second, this study confirms previous findings13–18 showing that the ability to converge the eyes while keeping accommodation focused at a more distal plane can be improved by repeated practice using various procedures that uncouple the demand between accommodation and vergence. Importantly, this investigation found that this improved convergence ability as seen in increased amplitudes of clinically measured fusion limits does not come as a result of either a reduction in the CA/C ratio nor an increase in the AC/A ratio. Rather, it would appear that these improved fusion limits are achieved through an increase of the speed and magnitude of vergence adaptation.

Convergence insufficiency is perhaps the most common anomaly of vergence and accommodation.31 The condition is associated with large exophorias at near and reduced fusion limits or at least reduced in the context of compensating the large exophoria.31 It has been further shown that such subjects show a generalized reduction in vergence adaptation that is not just specific to near viewing.18,20 Further, such subjects have also shown an increase in vergence adaptation after training sessions18,22 such as that given here. It is reasonable to conclude that orthoptic training for such subjects provides an increase in prism adaptation onset and magnitude, which allows the clinical improvement in fusion limits. Importantly, the ability to overcome a large exophoria is now achieved by an improved convergence response, which does not yield significant amounts of over accommodation.

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During vergence adaptation, CA response decreases, which leads to a reduction in the CA/C ratio. Improvement in clinical measures of PFV limits after orthoptic training appears to be, at least to a significant part, explained by increases in the rate of onset and amplitude of vergence adaptation and subsequent reduction of CA response. However, the absolute value of the neural cross-link gain (CA) remains unaltered after the training, which in turn leads to little change in CA/C ratio. Similarly, AC cross-link gain remains unchanged with training, whereas the output of AC increases under vergence adapted state.

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NSERC Canada to WRB. This paper was presented as a poster at ARVO meeting, 27th April, 2008, Fort Lauderdale, Florida.

Preethi Thiagarajan

State College of Optometry

State University of New York

33 West 42nd Street

New York, New York 11426


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The appendix is available online at

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This article has been cited 2 time(s).

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accommodation; accommodative convergence (AC); convergence accommodation (CA); vergence adaptation; cross-link ratios; positive fusional vergence (PFV) training

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© 2010 American Academy of Optometry


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