Evidence that convergence rather than accommodation controls intermittent distance exotropia

Abstract

Purpose

This study considered whether vergence drives accommodation or accommodation drives vergence during the control of distance exotropia for near fixation. High accommodative convergence to accommodation (AC/A) ratios are often used to explain this control, but the role of convergence to drive accommodation (the CA/C relationship) is rarely considered. Atypical CA/C characteristics could equally, or better, explain common clinical findings.

Methods

19 distance exotropes, aged 4-11 years, were compared while controlling their deviation with 27 non-exotropic controls aged 5-9 years. Simultaneous vergence and accommodation responses were measured to a range of targets incorporating different combinations of blur, disparity and looming cues at four fixation distances between 2m and 33cm. Stimulus and response AC/A and CA/C ratios were calculated.

Results

Accommodation responses for near targets (p=0.017) response gains (p=0.026) were greater in the exotropes than the controls. Despite higher clinical stimulus AC/A ratios, the distance exotropes showed lower laboratory response AC/A ratios (p=0.02), but significantly higher CA/C ratios (p=0.02). All the exotropes, whether the angle changed most with lenses (“controlled by accommodation”) or on occlusion (“controlled by fusion”), used binocular disparity not blur as their main cue to target distance.

Conclusions

Increased vergence demand to control intermittent distance exotropia for near also drives significantly more accommodation. Minus lens therapy is more likely to act by correcting over-accommodation driven by controlling convergence, rather than by inducing blur-driven vergence. The use of convergence as a major drive to accommodation explains many clinical characteristics of distance exotropia, including apparently high near stimulus AC/A ratios.

INTRODUCTION

It has long been accepted that the change in blur of an approaching or receding image drives accommodation, while convergence and divergence are mainly stimulated by changes in retinal image position. Crossed disparity outside Panum’s Area is a cue for convergence, and uncrossed disparity is a cue for divergence. Gross binocular disparity is therefore just as important a cue for motor fusion as the fine disparities within Panum’s Area are for stereopsis.

Cross-links between convergence and accommodation allow change in blur to drive vergence or change in disparity to drive accommodation. Strabismologists are familiar with the AC/A (accommodative convergence to accommodation) ratio (Muller 1826) which can be tested clinically and is known to influence strabismus. The convergence accommodation to convergence (CA/C) cross-linkage that enables vergence (or more precisely, disparity) to drive accommodation is much less familiar in clinical settings, mainly because it is so difficult to measure. Recent studies of accommodation and vergence responses in typical infants, children and adults, however, have shown that binocular disparity often provides a stronger cue for both vergence and accommodation than blur (or the proximal cues that also play a part) in naturalistic conditions (Bharadwaj & Candy 2008; Horwood & Riddell 2008; Bharadwaj & Candy 2009; Horwood & Riddell 2010). This suggests, at least in non-clinical populations, that disparity and CA/C linkages can be more important drives to near/distance change than blur or the AC/A linkage.

If “vergence drives accommodation” more than “accommodation drives vergence”, then intermittent exodeviations, where excessive convergence requirement exists, might show more accommodation than in orthophoria. Conventional theories and classifications of distance exotropia suggest that where control is better for near, accommodative convergence is a major factor aiding control (Kushner 1988; Clarke 2007; Hatt et al. 2010), as blur cues on near fixation induce accommodation, which then change the angle of strabismus via a high AC/A ratio. The alternative hypotheses – that the convergence used to control the deviation for near might cause over-accommodation, or a low CA/C ratio may allow extra convergence without accommodation – are more rarely considered (Rutstein & Daum 1987; Nonaka et al. 2004), and when they are, usually only in relation to myopia progression (Kushner 1999; Shimojyo et al. 2009; Ekdawi et al. 2010).

Current classifications of different sub-categories of distance exotropia (e.g. Kushner 1988) imply that there may also be differences in the weightings of the three main near cues of blur, disparity and proximity/looming between clinical types. For example, blur cues might be predicted to carry more weight where manipulating accommodation with lenses has a large influence on the angle of deviation (“high AC/A ratio” types); while disparity cues might predominate where preventing fusion by occlusion affects the angle most (“simulated by fusion” types); and proximal cues could predominate in cases where occlusion or lenses have less effect but the angle still reduces for near (“true” types).

Clinical research in this area is difficult. Stimulus AC/A ratios are easily measured by presenting a blur cue with near targets or lenses, assuming an appropriate accommodative response has occurred, then using the measured vergence change to calculate the ratio. Response AC/A ratios (where the vergence response is related to the actual accommodation that has occurred, not the stimulus given) are much more difficult to measure, and usually involve objective refraction of one eye while measuring the dissociated convergence of the other. The CA/C ratio is even more difficult to measure, and is almost impossible to assess clinically in children, because accommodation must be assessed objectively in at least one eye at the same time as presenting and measuring vergence responses to a binocular fusional stimulus available to both eyes, and so is rarely attempted.

Our laboratory studies the relative weighting of disparity, blur and looming/proximity in binocular vergence and accommodation, as well as the response AC/A and CA/C relationships. This paper describes a group of children studied while controlling their distance exotropia in comparison to a group of orthophoric controls. From our previous normative data (Horwood & Riddell 2008), where we typically find disparity to be the primary near cue, we hypothesised that more accommodation would be driven by the effort to control the deviation for near and that the pattern of relative weighting of near cues might be characteristic of the different sub-categories of distance exotropia.

METHODS

The study adhered to the tenets of the Declaration of Helsinki and was scrutinised by NHS and University Ethics Committees who gave permission to proceed. Parents of all children gave fully informed consent, and children over six years of age gave informed assent appropriate to their level of understanding.

Equipment

Details of construction, calibration and validation are published elsewhere (Horwood & Riddell 2008; Horwood & Riddell 2009) but, briefly, the participants watched the target being presented via a two-mirror optical system, while a PlusoptiXSO4 PowerRefII photorefractor collected simultaneous eye position and refraction measurements via a hot mirror that reflected infra-red for collection of this data, but allowed a clear view through to the target moving in the same optical plane(Fig. 1). Targets moved between five different fixation distances (0.33m, 2m, 0.25m¹, 1m, 0.5m) in a pseudo-random order.

Figure 1.

The remote haploscopic videorefractor. A. Motorised beam. B. Target monitor. C. Upper concave mirror. D. Lower concave mirror. E. Infra-red “hot” mirror. F. Image of participant’s eye where occlusion takes place. G. PlusoptiX SO4 PowerRef II. H. Headrest J. Raisable black cloth screen. Clown and DoG targets illustrated lower right.

We could manipulate blur(b), disparity(d) and proximal(looming)(p) cues separately. Blur cues could be presented by using a detailed clown target or minimised by using a difference of Gaussian (DoG) image to open the accommodation loop as much as possible while retaining fusible features in the binocular conditions. Disparity cues were available when both eyes viewed the target, and could be eliminated by occluding half of the upper mirror (C in Fig. 1), so that the target was only visible to one eye. Proximal and looming cues were available when the target remained the same size on the screen and could be watched as it moved backwards and forwards, or these dynamic and size cues could be minimized by scaling the target so that it subtended the same retinal angle at each distance and hiding the screen from view with a black curtain while it moved between positions. Eight different targets were thus presented representing all combinations of the three cues; bdp (looming, unscaled, binocular clown presenting all three cues in the most naturalistic combination), bd(proximal cues minimised - scaled, binocular, clown), bp (disparity excluded - monocular, looming clown), dp (blur cues excluded – binocular, looming DoG), b (blur only – monocular, scaled clown), d (disparity only – binocular, scaled DoG), p (proximity only – looming, monocular DoG) and o (minimal cue – monocular, scaled, DoG). Thus three cues (naturalistic), two cues (showing the effect of eliminating a cue but leaving the other two intact, such as might occur naturally in refractive error or monocular vision), one cue (as common in controlled laboratory studies) or minimal cues were able to be compared.

We used a macro to calculate dioptres of accommodation (D) and metre angles of vergence (MA) from the raw refraction and eye position data, making individual corrections for measured angle lambda and inter-pupillary distances (IPD). By using MA we were able to compare simultaneous vergence and accommodation responses in relation to target demand more accurately between participants with different IPDs and also plot both on the same scales e.g. a 0.5m target demands 2D of accommodation and 2MA of vergence. A response gain of 1.0 indicates a full response to target demand and a lower gain shows under-response to target change. In our paradigm, the accommodation responses and gain in the disparity-only (d) condition reflect how much binocular disparity can drive accommodation (CA/C) and the vergence responses and gain in the blur-only (b) condition reflect blur driven vergence (AC/A). Laboratory response AC/A ratios were also calculated from change in vergence divided by change in accommodation between 2m and 33cm in this b condition. For example, a blur-driven vergence gain of 0.5 and an AC/A ratio of 0.5MA:1D would equate to a typical clinical value of 3Δ:1D, meaning that 50% of the total convergence necessary for perfect alignment on a near target is driven by blur. Response CA/C ratios were likewise calculated from the change in accommodation divided by the change in vergence in the d condition.

Participants

An opportunistic sample of 19 children with distance exotropia between 4-11 years old was recruited from the Orthoptic Clinic at the Royal Berkshire Hospital. All presented clinically with an intermittent exotropia that was manifest or intermittent at 6m and but well-controlled to binocular single vision at 33cm. All but two had a smaller angle for near than distance on initial alternate prism cover testing prior to prolonged occlusion. Median angles were 14Δ exo (range 4-50Δ) at 33cm and 25Δ exo (range 6-45Δ) at 6m. All had normal stereopsis (≤120”TNO), convergence to <7cm from nose and visual acuity of 0.1 logMAR (6/7.5) in each eye. None wore spectacles (mean cycloplegic MSE was +0.02D (range −0.75/+1.00D), except for one +2.5D hypermetrope being kept uncorrected in a successful attempt to aid control. None suppressed on 4Δ base in and base out prism testing when controlled and none complained of diplopia when manifest. They were not selected on the basis of any specific sub-classification of distance exotropia e.g. true /simulated, controlled by accommodation /fusion, but represented a wide range within published classifications(Kushner 1988, Plenty 1988, Santiago & Rosenbaum 2005).

A control group comprised 27 children between 5-9 years of age. All were orthophoric (near exophoria <4Δ), emmetropic, and had stereopsis ≤ 120” arc.

Testing procedure

Two laboratory testing sessions were performed before and after a clinical testing session and laboratory data were averaged. Alternate prism cover tests were performed at 33cm and 6m, before and after 45 minutes monocular occlusion and (after occlusion and while maintaining full dissociation) with +3.00D lenses at 33cm and −3.00D lenses at 6m so that near and distance clinical stimulus gradient AC/A ratios could be calculated (Kushner 1988). We took extreme care when testing with the lenses, only swapping occlusion to the other eye when subjective image clarity through the lens was confirmed, so that our stimulus AC/A ratios were as accurate as possible.

Laboratory data could be analyzed for both controlled and strabismic periods of testing because we were easily able to detect from the plotted responses when a deviation had decompensated during testing; as the eye position trace of one eye diverged on decompensation, the total vergence reduced dramatically (Fig. 2). The data for strabismic periods has been presented in a separate paper (Horwood & Riddell 2011).

Figure 2.

Example of decompensation events in a single participant during a testing session. “Controlled” episode - dashed circle; “strabismic” episode - dotted circle. When one eye diverges the total vergence (the sum of two monocular adductions not shown on the chart) reduces dramatically at times, resulting in large negative vergence values. Use of meter angles (MA) enables vergence, accommodation (in dioptres (D)) and target demand to be plotted on same scale. In this case decompensation occurred during fixation at 33cm(3D& MA demand), 2m(0.5D & MA demand),25cm(4D demand) and (briefly) 50cm (2D & MA demand), but not at 1m(1D & MA demand). Accommodation was generally poor, with considerable lag, and changed by little more than 1D as vergence reduced by approximately 4MA. This child was +1.0D hyperopic R&L (reflected by “negative accommodation” at times).

Somewhat contrary to expectations, the deviation was often “straight” (i.e. not the obvious marked divergence seen in all the exotropes when clinically manifest) even for targets which did not include disparity so the term did not necessarily imply binocularity, and any manifest deviation was minimal. “Straight” was defined as less than 0.5MA (approximately 3Δ) more divergent than orthophoria (the maximum divergence seen in the controls) and “strabismic” was defined as at least 2.5MA more divergent than orthophoria (approximately 14Δexo). Any periods of exotropic alignment between 0.5 and 2.5MA (which were rare), were not analysed because it was not possible to differentiate between true exotropia and mere failure of convergence to a near target. We included data where at least 12 steady data points (0.5 sec of continuous data) were recorded at each target position. Where response gains (the calculated slope of the accommodation and vergence responses plotted against the different target distances) are compared, data from at least two of the four possible fixation distances per cue condition were necessary. e.g. a child who was “straight” for the 1m and 0.5m targets, divergent for the 2m target and showed both alignment and divergence at 0.3m could be included in this “controlled” analyses by using the 0.3m response (when controlled), 0.5m and 1m targets.

Analysis was carried out using 3-way mixed ANOVA, post hoc testing with Bonferroni correction for multiple comparisons, and non-parametric tests where appropriate. For sake of brevity we have only reported significant interactions that are relevant to the paper.

RESULTS

Clinical Data

We tried to group the children on the basis of existing detailed classifications of distance exotropia. (Kushner 1988, Plenty 1988, Santiago & Rosenbaum 2005). Although such classification was possible, the data were spread across a continuum of increases after occlusion or lenses, and near/distance differences (Fig. 3). One child refused occlusion, but for the remaining 18 exotropes after occlusion and +3.00 lenses, four children showed >10Δ exodeviation for near than distance (“convergence weakness”), four showed >10Δ greater exodeviation for distance than near (“true distance exotropia”) and the remaining 11 had similar near and distance angles (“basic type”). This was despite similar habitual behaviour of control for near and exotropia for distance.

Figure 3.

Alternate prism cover test deviation in prism dioptres at 33cm and 6m before and after occlusion and with +3.0D lenses at 33cm and −3.00 lenses at 6m (after 45 mins. occlusion) for each participant. Each vertical set of points represents one participant. Negative figures denote exodeviation.

We felt that forcing each participant into one single classification failed to reflect the complexity of the clinical characteristics. For example, one participant showed an initial exodeviation of 4Δ at 33cm, and 30Δ at 6m; after occlusion the near deviation increased by 21Δ (to 25Δ) and the distance deviation by 15Δ (to 45Δ), suggesting fusion was aiding control. The near deviation increased a further 5Δ with +3.00D lenses after occlusion (near stimulus AC/A ratio of 1.66Δ:1D), and reduced 25Δ (to 20Δ) with −3.00D lenses at 6m (distance AC/A ratio of 8.33Δ:1D), suggesting accommodation also influenced the deviation, although it stayed 15Δ larger in the distance, so also retaining some “true distance exotropia” characteristics.

We decided to analyse the data by grouping the children according to whether there was a clinically large (≥10Δ) or small (<10Δ) change in exodeviation for near or distance, with additional lenses, after occlusion, or between near and distance. 10Δ was a somewhat arbitrary threshold but it allowed a more “theory based” analysis exploring the concept that individuals might use idiosyncratic weightings of blur, disparity and proximity, and may use more than one cue. For example a deviation which altered with lenses but not occlusion might be predominantly blur-responsive, but one which increased with lenses and occlusion might use more equal weightings of blur and disparity. Although the literature might suggest that changes in these deviations on occlusion would be greatest for near, this was often not the case. Using the 10Δ threshold, only a few deviations increased only for near (22%), a further few increased only for distance (22%), most increased ≥10Δ for both distances (39%) and a few for neither (17%). Only 22% had an angle that increased ≥10Δ more for near than distance on occlusion (e.g. 30Δ increase in exodeviation for near and 10Δ in the distance) and 11% changed more for distance than near. After occlusion, 61% increased a further ≥10Δ with +3.00 lenses for near. There was considerable overlap between the groups, suggesting that the children were using a range of idiosyncratic strategies to achieve control of their deviation.

32% had a clinical near stimulus AC/A ratio of ≥5Δ:1D and 58% had a distance stimulus AC/A ratio of ≥5Δ:1D, but only 31% showed AC/A ratios >5Δ:1D both near and distance. There was an extremely poor correlation between the two ratios (Pearson’s r²=0.09, p=0.24)

The exotropes’ distance mean stimulus AC/A was 6.7Δ:1D (1.20 MA/D) and near stimulus AC/A was 3.5Δ:1D (0.62MA/D) compared to 1.35Δ:1D (0.24MA/D) and 1.84Δ:1D (0.32MA/D) in the controls (t(17.7)=5.9,p<0.0001) and t(29.8)=2.22,p=0.034 respectively).

Laboratory Data

This paper only describes the data recorded when the strabismus was controlled and because some children were constantly exotropic for the more impoverished targets, particularly when occluded, numbers were reduced for these targets e.g. ≥18 children provided data for all the binocular targets, while only 13 provided “straight” data for the minimal cue target (which was the minimal n of any group).

For any target distance the ideal response would be an equal amount of accommodation in D and vergence in MA equivalent to the demand of the target distance. Responses from the control group are illustrated in the upper chart of Figure 4 and are very similar to typical adult responses published previously (Horwood and Riddell 2008, Horwood and Riddell 2010). Both vergence and accommodation response gains are generally better for the most naturalistic targets (all-cue and two-cue conditions) and particularly for all binocular targets (where disparity cues are available). To the naturalistic bdp target, accurate vergence was typically accompanied by accommodative lag (under-response) of approximately 0.5D.

Figure 4.

Response gains of controls (upper chart) vs. “straight” exotropes (lower chart). Response gains of 1.0 represent the ideal response to the stimulus across target distance e.g. a gain of 0.5 suggests only 50% of the full response to target distance has been made. Cue conditions: blur=blur available, disp= disparity available, prox=proximal cues available, plus the minimal cue condition. There were significantly steeper accommodation gains across all cue except for the “prox only” and “minimal cue” conditions. The overall profiles of weighting of different cues are similar between the two groups.

Vergence responses showed few differences between the exotropes and controls, with no overall significant difference (F(2,37)=2.05,p=0.16), although in the bdp, bd and d conditions the controls had slightly sleeper vergence response gains than the exotropes (t(44)=2.29,p=0.03; t(43)=2.39,p=0.02; t(42)=2.25,p=0.03 respectively) as they converged slightly more accurately for near.

In the controls it was typical to find better vergence than accommodation for all target distances and in all cue conditions. In comparison, the exotropic children were more likely to accommodate better for near than they converged (χ²=9.82, p=0.002), which is rare in typical groups. The exotropes’ accommodation to the 3D target was on average 0.65D more than their vergence response in MA, whereas the controls accommodated on average 0.33D less than vergence in MA across the different cues (t(36)=2.52,p=0.017).

This over-accommodation is unlikely to be clinically noticeable in most cases, however. In the most naturalistic and clinically relevant bdp condition, although 26% of exotropic participants accommodated (in D) more than they converged (in MA) at 33cm, and 21% accommodated more than the ideal 3.00D, this over-accommodation to the target (accommodative lead) was less than 0.30D in 95% of cases, and only one child would have had subjectively detectable blur due to over-accommodation of greater than 0.50D. As cues were removed in the more impoverished cue conditions both vergence and accommodation responses reduced, but with accommodation remaining slightly better than vergence in the exotropes.

Despite “straight” episodes being found at all distances, and no significant difference in the exotropes’ dissociated angle between near and distance overall (t(17)=0.72, p=0.48), more accommodation in comparison to vergence to the same target (relative lead) was most marked at 33cm, suggesting that responding to near cues, rather than mechanical convergence effort to control similar near and distance angles, contributes to the additional accommodation for near. The larger angles had more of this relative lead of accommodation than the smaller angles at 33cm, but not at 2m. The size of accommodative lead correlated positively with maximum angle of deviation (r=0.459, p=0.048) at 33cm).

Response gain profiles to different cues

We predicted not only that accommodation and vergence between the groups would differ overall, but their relative responses to the different cue elements might also be characteristic, with a different response profile, especially to blur, which might be influenced by the typically high clinical AC/A ratios. Figure 4 shows that, apart from the steeper accommodation gains in the exotropes, the general profile of response gains (and so the relative weighting placed on each cue) across targets were similar between the controls and the exotropic group (F(4.1,147.4)=0.50,p=0.74). Both groups showed good response gains in all cue conditions that contained disparity cues, with flatter response gains due to under-accommodation and vergence for near targets when disparity was excluded. This suggests that when controlled, exotropic children as a group weight the three near cues similarly to typical children and adults, with disparity predominating.

To analyse this statistically we used response gain and cue type as within group factors, and case/control as a between group factor in a 3-way mixed ANOVA with post-hoc tests. There were no overall differences between vergence and accommodation responses (F(1,36)=0.08,p=0.77) or the cases and controls (F(1,36)=0.0004,p=0.99), only the expected differences between the cue conditions (F(4.1,147.4)=27.25,p=<0.0001). A significant interaction between response type and case/control group (F(4,45)=4.81,p=0.003) confirmed that the exotropic groups produced steeper accommodation gains than the controls (F(1,48)=5.26,p=0.026)in all but the p and o conditions. The controlled exotropes had slightly shallower vergence gains to the bdp and bd targets (Tukey’s test p=0.027 and 0.021 respectively) and steeper accommodation gains to the d target (p=0.029).

AC/A & CA/C relationships

The above findings still do not determine whether the steeper accommodation slopes in the exotropes are due to blur-driven accommodation being used to recruit additional vergence (high AC/A) or whether disparity cues drive the controlling vergence, which then drives extra accommodation (CA/C), but we could explore this with our paradigm. If accommodation “controls the deviation”, then the blur-driven vergence gains and AC/A ratios during controlled episodes should be higher in exotropes. If conversely, the extra convergence needed to control the deviation (and then drive additional vergence for near) is driving additional accommodation, then the disparity-driven accommodation gain and the CA/C ratio should be higher.

There were no significant differences between the exotropes and the controls in terms of blur-driven (b target) responses (one measure of the AC/A linkage), with similar response gains for both accommodation (t (30.7) =0.52, p=0.61) and vergence (t (27.9) =0.49, p=0.62). This suggests that for both groups blur was diving similar amounts of vergence. Despite the much higher clinical stimulus AC/A ratios, the laboratory response AC/A ratios calculated from changes in accommodation and vergence between near and distance were slightly lower for the exotropes than the controls (0.87MA/D (5.04Δ/D) vs 0.93MA/D (5.59Δ/D) respectively (t (33) =2.4, p=0.02)) (Fig. 5).

Figure 5.

Mean response charts. Open symbols and dotted line: vergence. Filled symbols and solid line: accommodation. Upper charts: Mean vergence and accommodation responses to the blur-only (B) target (reflecting AC/A linkage). There were no differences in AC/A gain (although the exotropes were somewhat more divergent overall due to dissociative effect of occlusion). Lower charts: mean vergence and accommodation responses to the disparity-only (D) target (reflecting CA/C linkage). Exotropes show significantly steeper accommodative gain and less accommodative lag for near than the controls to the disparity-only target.

In contrast, the disparity-only (d) cue drove steeper disparity-driven accommodation (CA/C) gains than the controls (t (29.9) =2.14, p=0.04), and slightly shallower vergence gains (t (39.6) =1.6, p=0.12). Calculated CA/C ratios were significantly higher in the exotropes (mean 1.46±1.16 D/MA) than in the controls (mean (0.87±0.29 D/MA) (t (42) =2.42, p=0.02). So, although blur was driving no more vergence between near and distance in the controlling exotropes, disparity cues were driving more accommodation.

Profile differences between different exotropia groups

Our final analysis was in relation to whether a particular target manipulation (near/ distance measurement, prolonged occlusion at both near and distance, plus lenses at 33cm, minus lenses at 6m) changed the angle by more or less than 10Δ to see if response profiles differed accordingly. For example, a larger change on occlusion might suggest increased sensitivity to disparity than with a small change; a larger angle change to lenses might suggest greater weighting for blur; an increase with both occlusion and lenses might suggest equal weighting for both; while a persistence of large near/distance differences after occlusion and lenses might suggest greater use of proximal cues.

Mixed ANOVA of response gains showed no significant differences between the profiles for any of these groups (main effect of group (F (4, 45) =0.217, p=0.93). All exotropic groups, however sub-divided, showed best responses to targets containing disparity cues and least to proximal cues, with no suggestion of even weak, non-significant trends that might have been significant in larger groups. For example, the strongest prediction we made was that patients whose angles were most influenced by introducing lenses (high clinical stimulus AC/A ratio) might have steeper blur-driven vergence response gains than those with greatest change in angle for near on occlusion but not with lenses, or the controls; but even this was not the case, with blur-driven vergence response gains of 0.53, 0.56 and 0.52 respectively (ANOVA (F (2, 39) =0.11, p=0.90). Both the exotropic groups, whether clinically appearing to control by using accommodation or by fusion, had steeper disparity-driven accommodation gains (CA/C) than the controls, but they were not significantly different from each other (t(21)=0.41,p=0.68). These results suggest no differences in the weighting that children with different patterns of exotropia placed on the different near cues, contrary to our expectations.

Numbers were smaller in the conventionally classified “true” and “convergence weakness”, “high AC/A” groups in relation to the more common “basic” types, so statistical analysis was limited, but there were no trends that suggested that response profiles differed between these groups either.

DISCUSSION

The first finding of this study was that all controlling distance exotropes accommodated more for near than the controls (with less accommodative lag and more lead in relation to the target demand), producing steeper accommodation response gains across targets. This, in itself, does not tell us whether convergence drives the accommodation, or vice versa, but our ability to assess responses to both blur and disparity cues in isolation enabled us to answer these questions. We found that blur driven vergence responses to near targets (response AC/A) were not significantly higher than the controls, despite high clinical stimulus ratios, as found by Cooper et al.(1982). The current convention of assessing the clinical AC/A ratio after a period of occlusion was developed to try to eliminate proximal vergence after-effects that were suggested as the cause, but in our study, even after occlusion we still found raised clinical stimulus AC/A ratios in the exotropes, but no difference in blur-cue only vergence gain and lower objective laboratory AC/A ratios.

This study serves as a further illustration of the limitations of any clinical AC/A ratio where accommodation is not objectively measured, as it cannot be assumed that children automatically accommodate accurately to a near target. Under-accommodation was typical to our detailed clown target. This was more pronounced in the controls than in the exotropes, and greatest in both groups when monocular (and it is monocular accommodation that is involved in clinical AC/A testing). Even when asked to keep a near target as clear as possible, accommodative lag of approximately of 0.5D is typical (Fincham & Walton 1957; Wick 1985) and may be even more in naïve or inattentive participants (Horwood & Riddell 2008), or in those with smaller pupils providing greater depth of focus. The assumed accommodative response that is used as the divisor to calculate the AC/A ratio is therefore likely to be an unknown overestimate, making any ratio only very approximate. Accuracy can be maximized by asking the patient to confirm that the image is clear at all times (e.g. at each swap of the occluder in a prism cover test), but any stimulus AC/A ratio still does not accurately reflect the true response ratio.

The size of the disparity-driven accommodation response (CA/C) was the significant difference between exotropes and controls in this study. In the exotropic group, the additional convergence necessary to control the deviation for near resulted in more accommodation than in the controls, with greater accommodation being induced for near fixation compared with distance and with the effect being greater in larger angles. Hasebe et al (2005) also found a greater lead of accommodation in larger angles.

We suggest that accommodative convergence is not “used to control the deviation”: instead the convergence effort needed to control the deviation causes more accommodation. This would intuitively be the more logical causal direction because the main problem for exotropes is the need to control the divergence, not abnormal accommodation demand. Laird et al.(2007) also suggested that disparity, rather than accommodative convergence, is a primary drive in controlling induced exodeviations.

The second prediction of the study was not supported. Despite predicting that those with greater angle change with additional lenses (“high AC/A”) would place greater weighting on blur cues, and that those with greater angle changes on prolonged occlusion would use disparity cues, no differences were found. All our exotropes showed a similar profile of cue use to that of the controls, with targets containing disparity cues producing better responses than any cue where disparity was excluded. While disparity was clearly the most important cue for controlling the exotropia in our clinical group, the fact that deviations could still be “controlled” in the occluded conditions suggests that other influences, such as looming or “awareness of nearness” cues, or proprioception, also aid control.

We found that classifying our participants into conventional clinical groupings was difficult and of limited value: one case would show a larger increase for near with occlusion, another would increase more for distance, another equally for both distances; some angles would change as much with occlusion as with lenses, while others changed very little; plus lenses could produce great changes in angle, while minus lenses would produce very little in the same child. We found that responses to occlusion, lenses and near vs distance fixation fell along a continuum, as also found by Le et al. (2010).

The findings of higher response CA/C ratios reported here are different from the findings of Nonaka et al. (2004), which is the only other study to consider CA/C ratio in exotropia. They found lower CA/C ratios and higher response AC/A ratios, but the studies may not be comparable because they included all clinical types of intermittent exotropia, including near types, and also did not use prolonged occlusion before angle measurement, so they may not have measured maximum angles. In our control group, the CA/C ratio was higher than young adult values of 0.55 D/MA quoted by Fukushima et al,(2009) but this could reflect both the younger age of our participants, the “real life” nature of our disparity cue rather than prism-induced disparity and possibly our participants’ naivety to visual experiments in general.

Clinical relevance

If disparity is a more important drive to accommodation than blur in exotropia (as is also found in non-strabismic children (Bharadwaj & Candy 2008; Horwood & Riddell 2008; Bharadwaj & Candy 2009)), our results would point to an alternative explanation for some common clinical findings. Firstly, it might explain why minus lenses help some intermittent exotropias (Caltrider & Jampolsky 1983) and supports Firth (2008) who has recently re-appraised an idea originally proposed by Burian (1945) that the minus lenses do not induce accommodation which in turn induce convergence: instead they allow more controlling convergence to be recruited by correcting any secondary excessive accommodative (myopic) blur. This would ensure that a child does not have to choose between binocularity and clarity.

Our results may also provide an alternative explanation for the finding of reduced distance stereoacuity due to blur found by Walsh et al.(2000). Many distance exotropes control well and rarely break down even for distance, so some may be chronically over-accommodating while they do so. Subsequent tonic accommodation changes may contribute to the development of myopia in these patients (Ekdawi et al 2010).

The “elastic” nature of the association between accommodation and convergence (von Noorden & Campos(2002)) and confirmed by the variability of our laboratory findings suggest that habitually increased accommodation may only be a problem for some. Thus minus lenses would only help those whose controlling convergence also brings about excessive accommodation outside limits of noticeable blur, not those who can control without over-accommodation. The former group might also be predicted to be those most at risk of increasing myopia.

A strong role for disparity-driven vergence as the primary drive for accommodation may also explain why, post-operatively, a few distance exotropias become accommodative esotropias requiring plus lenses to relieve diplopia. Surgical removal of the need to converge suddenly removes a major drive to accommodation, since this was previously driven by convergence. Children with a stronger than average CA/C relationship may thus produce a “hypo-accommodative” convergence excess esotropia (Costenbader 1958) as they have to recruit the convergence they have habitually used in order to accommodate (supported by our results). We suggest this does not occur for most children because vergence and accommodation are not inflexibly linked and adaptation to a new vergence demand occurs quickly.

Our results may also help explain why near and distance stimulus AC/A ratios correlate so poorly (Havertape et al. 1999) especially in exotropia (Gage 1996). The near gradient method, using plus lenses “to relax accommodation”, could also be explained in terms of the dissociation used to measure the deviation. The dissociation of the prism cover test to measure the angle stops disparity-driven vergence, and because of the high CA/C ratio, also reduces large proportion of the accommodation. Although plus lenses are thought to “relax accommodation”, they might actually just correct the blur caused by loss of vergence accommodation, so the near “AC/A ratio” in fact may represent a CA/C response to the dissociation.

For a distance AC/A ratio, however, the more conventional explanation could still apply. Accommodation cannot relax beyond emmetropia on dissociation, and a blur stimulus is the only cue being manipulated (as the patient is dissociated and proximal cues are removed by distant fixation). Even if blur is usually a weak cue, making the AC/A ratio less important than the CA/C, the distance AC/A ratio is likely to reflect true blur-driven accommodation and vergence.