Strabismus, 2014; 22(3): 120–124 ! Informa Healthcare USA, Inc. ISSN: 0927-3972 print / 1744-5132 online DOI: 10.3109/09273972.2014.937445
Convergence Accommodation to Convergence CA/C Ratio: Convergence Versus Divergence Joshua M. Simmons,
B. Med. Sci
and Alison Y. Firth,
Msc DBO (T)
Academic Unit of Ophthalmology and Orthoptics, Faculty of Medicine, Dentistry and Health, University of Sheffield, Beech Hill Road, Sheffield, S10 2RX, UK
ABSTRACT Aim: To determine whether the convergence accommodation to convergence (CA/C) ratio during divergence with base-in (BI) prisms is of a similar or different magnitude to that measured during convergence with baseout (BO) prisms. Methods: Eighteen participants with normal binocular single vision were recruited. The participants viewed a pseudo-Gaussian target, which consisted of a light emitting diode (LED) behind a diffusing screen at 40 cm. After 5 minutes of dark adaptation, the refractive status of the eye was measured without any prism using a Shin-Nippon SRW-5000 autorefractor. The participant held the selected prism (5D or 10D BO or BI, counterbalanced) in front of their right eye and obtained a single, fused image of the target while refractive measures were taken with each. A 30-second rest period was given between measurements. The mean age of the participants was 20.6 ± 3.22 years. Results: The mean CA/C ratios for the 5D BO, 10D BO, 5D BI, and 10D BI were 0.108 (±0.074) D/D, 0.110 (±0.056) D/D, 0.100 (±0.090) D/D, and 0.089 (±0.055) D/D, respectively. A 2-factor repeated measures ANOVA found that the CA/C ratio did not significantly change with differing levels of prism-induced convergence and divergence (p = 0.649). Conclusions: Change in accommodation induced by manipulating vergence is similar whether convergence or divergence are induced. The CA/C ratio did not show any change with differing levels of prism-induced convergence and divergence. Keywords: Binocular single vision, convergence accommodation/convergence ratio, divergence, open loop accommodation
INTRODUCTION
measure the CA/C ratio, the vergence system must be under closed loop conditions, and accommodation open loop. Several authors have used a pseudo-Gaussian blob target consisting of an LED placed behind a diffusing screen at 40 cm from the participant’s eyes to open the accommodative loop. Base-out (BO) prisms are then used to induce convergence and objective changes in refraction measured to assess accommodation induced. Hasebe et al.1 found the mean CA/C ratio to be 0.08D ± 0.04 D/D and Hirani and Firth2 found an overall mean CA/C of 0.13 ± 0.04 D/D when using prisms of 5, 10, 15, and 20D BO. Nonaka et al.3
Convergence accommodation is accommodation that results when the eyes converge. In closed-loop conditions this accommodative response may be inhibited to maintain clear vision, or at least inhibited to the extent that the person is able to do so. However, in open-loop conditions the response may be measured. The convergence accommodation to convergence (CA/C) ratio is the ratio between how much convergence accommodation occurs (in dioptres [D]) when convergence is exerted (in prism dioptres, D). Thus to
Received 4 April 2014; Revised 12 June 2014; Accepted 18 June 2014; Published online 16 July 2014 Correspondence: Joshua M Simmons, Academic Unit of Ophthalmology and Orthoptics, Faculty of Medicine, Dentistry & Health, University of Sheffield, Beech Hill Road, Sheffield, S10 2RX, UK. E-mail: [email protected]
120
Convergence accommodation to convergence (CA/C) Ratio: Convergence versus Divergence 121 found similar values of 0.081 ± 0.042 D/D in a series of 78 patients with intermittent exotropia and decompensating heterophoria who had binocular single vision for near. This was not significantly different to their control group, which had a mean CA/C ratio of 0.091 ± 0.036 D/D. With a ratio of 0.1/1, in open loop conditions, a person with an interpupillary distance of 6 cm fixing at 1/3 m, ie, converging 18D, would produce 1.8D of convergence accommodation. To our knowledge, no previous research has looked at the effect of prism-induced divergence on the convergence accommodation/convergence ratio. There is no evidence to suggest that the effect of divergence on convergence accommodation would be different to that of convergence, except to be in the opposite direction, but this assumption cannot be made without investigation. This study therefore investigates the CA/C ratio with induced divergence, and compares this to the level with induced convergence.
MATERIALS AND METHODS This cross-sectional study used a repeated measures design. The ethics committee of the Academic Unit of Ophthalmology and Orthoptics at the University of Sheffield approved the study, which followed the tenets of the Declaration of Helsinki. Eighteen participants were recruited via advertisement from the student population of the University of Sheffield. Each was given the participant information sheet, which detailed the study methods and the rights of a participant. After being given the opportunity to ask questions, written consent was obtained from each participant. The inclusion criteria were: No manifest ocular deviation. This was to ensure that the participant had normal binocular single vision. Emmetropic or refractive error corrected with contact lenses. This was done to avoid any prismatic effect that could be induced by the spectacles or difficulties due to reflections in refractive measurements. Vision of 0.2 logMAR or better in each eye. A good level of motor fusion consisting of the ability to be able to overcome a 5 and 10D prism both BO and base in (BI) at 40 cm. No pathological defects. To create the pseudo-Gaussian target of approximately 2 cm in size, a red light emitting diode (LED) powered by a battery was placed behind a diffusing screen 40 cm in front of the participant’s eyes.2 As there is a slow decrease in luminance of the light from the center, this creates weak contours that create cues for retinal disparity but not blur. This in turn opens the accommodative loop and allows convergence !
2014 Informa Healthcare USA, Inc.
accommodation to be measured. The refractive state of the eye was measured using a Shin-Nippon SRW-5000 autorefractor. Convergence and divergence were induced by using loose prisms, BO and BI, respectively. Prisms used were 5D and 10D both BO and BI. The participant’s age and refractive status were recorded, as was whether the participant wore contact lenses or not. If the participant did wear contact lenses, they were worn throughout the testing. A cover test was performed at 40 cm using an accommodative target of 6/6 (Snellen); visual acuity was tested using the LogMAR Bailey-Lovie test at 3.8 m; the prism reflex test was performed using a 10 D BI prism to an accommodative target. This test is done to determine the presence of motor fusion. Any heterophoria detected was recorded. The participant was seated at the autorefractor and the LED light position was altered slightly until the participant was looking directly at it with their left eye in order to avoid off axis measurements. They were asked to binocularly fixate on the LED light and obtain a single image. They were then asked to practice placing the prism in front of their right eye with the lights turned on, to ensure that they could do this accurately. The room lights were then turned off, along with the red LED light, and the participants were given 5 minutes of dark adaptation. It has been found that dark adaptation of cone cells takes between 5 and 8 minutes, whereas rod cells take between 35 and 40 minutes.4 The first measurement of refraction was taken without any prism to measure the baseline refractive status of the eye. Counterbalancing was used in order to determine the sequence in which the different conditions (prisms) were used. Convergence and divergence was induced by using BO and BI prisms, respectively. Strengths of 5 and 10D prisms were placed before the right eye and readings were taken from the left. The participants were asked to hold up the prism (ensuring this was not tilted), fuse the images, and maintain fusion. Three readings were taken quickly to avoid significant adaptation effects and were taken when the participant reported that the target was single. The time taken for fusion was not measured, but occurred within a 10-second time frame. The participant was given a 30-second rest between readings and in total the experiment lasted about 30 minutes.
Data Handling and Statistical Analysis The median value from the 3 readings (as selected by the autorefractor) was used to calculate the best spherical equivalent (BSE) (sphere + ½ cylinder). To calculate the accommodative response, the BSE was
122 J. M. Simmons and A. Y. Firth
The data were interval and were analyzed using a one-factor and two-factor Analysis of Variance (ANOVA). The mean, standard deviation, and standard error were also calculated for each data set. Results were considered significant if p = 0.05 or less.
strength of the prism (F = 0.088; p = 0.770). There was no significant interaction between prism strength and base direction (F = 0.216; p = 0.649). When looking at the entire set of CA/C ratio data, it was calculated that the overall mean CA/C ratio for the group was 0.102 ± 0.069 D/D. The range of the CA/C ratios were found to be from 0 to 0.275 D/D. When taking the individual data for each participant it is apparent that some of the subjects have a larger degree of nonlinearity than others (Figure 2.) Ten of the 15 subjects showed a variation between 2 of the 4 measures of greater than 2 standard deviations from the group mean (ie, 0.138).
RESULTS
DISCUSSION
Data were collected from 18 participants. However, results from 3 participants showed a reduction of accommodation on convergence or an increase in accommodation on divergence. Therefore these participants were excluded from the analysis. The mean age of the remaining 15 subjects was 20.6 ± 3.22 years (range, 18–31). Of these subjects, 3 were male and 12 were female. Of the participants, 5 wore contact lenses. At the test distance of 40 cm, 10 of the participants showed a minimal exophoria with rapid recovery and 5 had a minimal esophoria with rapid recovery. The mean logMAR vision that was found in the group was 0.065 ± 0.063 in the right eye and 0.092 ± 0.057 in the left eye. The mean BSE measurements for the differing strength prisms are given in Table 1. This shows an increase in accommodation for the BO prisms and a decrease in accommodation for the BI prisms. The absolute change in the accommodation elicited from the use of either 5D BI and BO or 10D BI and BO were not significantly different (t = 0.217, p = 0.831; t = 0.977, p = 0.345; respectively). The mean CA/C ratios for the 10D BO, 5D BO, 5D BI, and 10D BI were 0.110 (±0.056) D/D, 0.108 (±0.074) D/D, 0.100 (±0.090) D/D, and 0.089 (±0.055) D/D, respectively (Figure 1). A two-factor repeated measures ANOVA was used to determine if there was any effect of prism strength or orientation on the CA/C ratio. It was found that there was no statistical significance between the prism being either BO and BI (F = 0.307; p = 0.588) or the
We have explored the effect of divergence on convergence accommodation and have found absolute levels of accommodative change to be similar irrespective of the direction of the vergence. Further, no significant difference in the CA/C ratio with differing levels of convergence and divergence was found. When looking at the overall mean CA/C ratio, this was found to be 0.102 ± 0.069 D/D. This is similar to the CA/C ratio mean found by Hirani and Firth,2 who reported an overall mean CA/C ratio of 0.13 ± 0.05 D/D when looking at prism-induced convergence and the CA/C ratio. It is also close to results found by Suryakumar and Bobier,5 who found a mean CA/C ratio of 0.10 D/D in 8 adults with a mean age of 23 years. Previous literature has found that the CA/C ratio can range from as low as 0.019 D/D6 to as high as 0.15 D/D.7 It was found that the mean ratios of the accommodative response for the BO and BI prisms increase and decrease in a fairly linear fashion, which results in a similar CA/C ratio. Hirani and Firth2 and Wick and Currie6 have found a slight nonlinearity in the CA/C ratio, but this was only demonstrated in a few subjects. In the research by Hirani and Firth, 4 of 24 subjects showed a slightly greater amount of non-
CA=C ratio ¼ accommodative response ðDÞ =prism power ðDÞ
TABLE 1. Mean BSE for each prism.
Mean BSE (D) SD SE
10 D BO
5 D BO
0D
5 D BI
10 D BI
2.88 1.05 0.27
2.32 0.63 0.16
1.78 0.84 0.22
1.38 0.66 0.17
0.88 0.64 0.16
0.140 0.120 Mean CA/C Rao (D/ΔD)
subtracted from the reference measurement, which was the reading from the autorefractor with no prism. The CA/C ratio was calculated using the following equation:
0.100 0.080 0.060 0.040 0.020 0.000 10ΔBO
5ΔBO
5ΔBI
10ΔBI
Prism Strength (ΔD)
FIGURE 1. Mean CA/C ratios for differing strength prisms. Strabismus
Convergence accommodation to convergence (CA/C) Ratio: Convergence versus Divergence 123 Prism Strength (Δ) 5ΔBO 5ΔBI
10ΔBO
10ΔBI
Prism Strength (Δ) 5ΔBO 5ΔBI
10ΔBI
0.0000
0.0500
Subject 1 Subject 2
0.1000
Subject 3
0.1500
Subject 4 Subject 5
0.2000 0.2500
Mean CA/C Rao (D/ΔD)
Mean CA/C Rao (D/ΔD)
0.0000
10ΔBO
0.3000
0.0500
Subject 6 Subject 7
0.1000
Subject 8
0.1500
Subject 9 Subject 10
0.2000 0.2500 0.3000
10ΔBO
Prism Strength (Δ) 5ΔBO 5ΔBI
10ΔBI
Mean CA/C Rao (D/ΔD)
0.0000 0.0500 0.1000 0.1500 0.2000
Subject 11 Subject 12 Subject 13 Subject 14 Subject 15
0.2500 0.3000
FIGURE 2. Individual data found for the mean CA/C ratio.
linearity in their CA/C ratios.2 However, in the current research a greater number of subjects show this difference, which seems to be masked by the mean values of the CA/C ratio. Methods of testing do vary. Wick and Currie6 opened the accommodative loop by using 1.3-mm pinholes in front of each eye and pupils were dilated. The accommodative response was measured using the SRI Dual Purkinje image Eyetracker and infrared optometer. Hirani and Firth used similar methods to ours.2 Hirani and Firth proposed that nonlinearity may be connected to the varying effort used by the individual in order to maintain fusion.2 It could also be due to difficulty in maintaining precise fusion when viewing the difference of Gaussian (DoG) target for a prolonged period of time. Although the measurements were taken quickly, this could still have been too long for the subject to maintain good fusion, which could have resulted in variability in the CA/C ratio. If inaccurate vergence was responsible for the nonlinearity, perhaps further research could look into this using eye tracking technology. A possible reason for the variation may have been if the participant did not know the image was fused. Because a pseudo-Gaussian target consists of a light behind a diffusing screen, this looks like a blurry red ‘‘blob’’ to the participant. It is possible that because !
2014 Informa Healthcare USA, Inc.
the fixation target is blurry, it may appear to be single to the participant, but may in fact be double, which is overlapped. We found 3 participants to have a paradoxical change in accommodation to the vergence stimulus and considered this to be due to not overcoming the prism. It is possible that this was not the reason and further study would be necessary to explore this. Eadie et al.8 found that some adaptation occurs in the CA/C ratio and suggested there is some degree of plasticity in the cross links between accommodation and convergence. Convergence accommodation has also been found to decrease as vergence adaptation occurs.8–10 Nonaka,3 when measuring the accommodative change of the eye to prisms, took readings in quick succession to minimize the effect of vergence adaptation. Although in the current research measurements were also taken quickly to try and negate the effect of any degree of adaptation, it is possible that this is responsible for the degree of variation found in the results of individual data and the CA/C ratio. Previous research by Rosenfield et al.11 has shown that there is a decrease in the CA/C ratio with age. However, our oldest participant was aged 31 years, and did not appear different from the younger subjects, so we cannot comment on this. Heron
124 J. M. Simmons and A. Y. Firth et al.12 suggest the CA/C ratio decreases after the age of 48 years. In the study by Brautaset and Jennings,13 the subjects viewed a DoG target for 5 minutes before measurements began to allow accommodation to stabilize. We allowed 5 minutes in the dark before measurements were taken to take away any prior accommodative adaptation effects. Schor et al.14 found that when measured in darkness, the accommodative adaptation had the shortest effects when compared with other open loop accommodation states. It is possible that participants may have been holding the prisms in slightly different positions. Although they were observed doing this for the first time in the light, as the room was completely darkened it became impossible to assess. This may have caused slight errors in the level of vergence induced if the prism was not held correctly for its calibrated position. However, this effect would only be minimal as only small strength prisms (5 and 10D) were used. We cannot extrapolate our findings to a clinical population. However, attention has recently been given to the role of convergence accommodation in strabismus.15,16 Notably, when considering the mechanism for control of intermittent exotropia, there is evidence that disparity drives a large proportion of accommodation,16 and so we wanted to investigate the effect of divergence on negation of accommodation, that is, whether the disparity drive of divergence had the opposite effect. This we have found in our normal population, but further work will be needed to discover the role of convergence accommodation in esotropia. It is possible that repeatability is an issue when looking at the CA/C ratio. To our knowledge, no study has looked at the repeatability of the CA/C ratio and if it does vary throughout measurements or indeed if it is variable throughout the day. The CA/C ratio did not change significantly with differing levels of prism- induced convergence and divergence when using 5 and 10D both BO and BI. The data found suggest that there may be a larger degree of nonlinearity within individuals than reported in previous literature, but this may be due to repeatability of the CA/C ratio or a slight fluctuation in accommodation.
DECLARATION OF INTEREST The authors report no conflicts of interest.
REFERENCES 1. Hasebe S, Nonaka F, Ohtsuki H. Accuracy of accommodation in heterophoric patients: Testing an interaction model in a large clinical sample. Ophthalmic Physiol Opt 2005;25: 582–591. 2. Hirani K, Firth AY. Convergence accommodation to convergence (CA/C) ratio: Stability with different levels of convergence demand. Br Ir Orthopt J 2009;6:60–64. 3. Nonaka F, Hasabe S, Ohtsuki H. Convergence accommodation to convergence (CA/C) ratio in patients with intermittent exotropia and decompensated exophoria. Jpn J Ophthalmol 2004;48:300–305. 4. Reuter T. Fifty years of dark adaptation 1961–2011. Vision Res 2011;21–22:2243–2262. 5. Suryakumar R, Bobier WR. Gain and movement time of convergence-accommodation in preschool children. Optom Vis Sci 2004;81:835–843. 6. Wick B, Currie D. Convergence accommodation: Laboratory and clinical evaluation. Optom Vis Sci 1991;63: 226–231. 7. Suryakumar R. Study of the dynamic interactions between vergence and accommodation [unpublished thesis presented to the University of Waterloo]. 2005. Accessed January 20, 2014. http://www.collectionscanada.gc.ca/ obj/s4/f2/dsk3/OWTU/TC-OWTU-654.pdf. 8. Eadie A, Gray L, Carlin P, Mon-Williams M. Modelling adaptation effects in vergence and accommodation after exposure to a simulated virtual reality stimulus. Ophthalmic Physiol Opt 2000;20: 242–251. 9. Firth AY. Convergence accommodation does regress with vergence adaptation. Transactions of the 32nd European Strabismus Association Meeting. Munich, September 2008:191–192. 10. Thiagarajan P, Lakshminarayanan V, Bobier WR. Effect of vergence adaptation and positive fusional vergence training on oculomotor parameters. Optom Vis Sci 2010;87: 487–493. 11. Rosenfield M, Ciuffreda K, Hung G, Gilmartin B. Tonic accommodation: A review II. Accommodative adaptation and clinical aspects. Ophthalmic Physiol Opt 2004;14: 265–277. 12. Heron G, Charman W, Schor C. Age changes in the interactions between the accommodation and vergence systems. Optom Vis Sci 2001;78:754–762. 13. Brautaset R, Jennings A. Effects of orthoptic treatment on the CA/C and AC/A ratios in convergence insufficiency. Invest Ophthalmol Vis Sci 2006;47: 2876–2880. 14. Schor C, Kotulak J, Tsuetaki T. Adaptation of tonic accommodation reduces accommodative lag and is masked in darkness. Invest Ophthalmol Vis Sci 1986;27: 820–827. 15. Horwood AM, Riddell, PM. Decreased accommodation during decompensation of distance exotropia. Br J Ophthalmol 2012;96:508–513. 16. Horwood AM, Riddell, PM. The clinical near gradient stimulus AC/A ratio correlates better with the response CA/C ratio than with the response AC/A ratio. Strabismus 2013;21:140–144.
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Convergence Accommodation to Convergence CA/C Ratio: Convergence Versus Divergence Joshua M. Simmons,
B. Med. Sci
and Alison Y. Firth,
Msc DBO (T)
Academic Unit of Ophthalmology and Orthoptics, Faculty of Medicine, Dentistry and Health, University of Sheffield, Beech Hill Road, Sheffield, S10 2RX, UK
ABSTRACT Aim: To determine whether the convergence accommodation to convergence (CA/C) ratio during divergence with base-in (BI) prisms is of a similar or different magnitude to that measured during convergence with baseout (BO) prisms. Methods: Eighteen participants with normal binocular single vision were recruited. The participants viewed a pseudo-Gaussian target, which consisted of a light emitting diode (LED) behind a diffusing screen at 40 cm. After 5 minutes of dark adaptation, the refractive status of the eye was measured without any prism using a Shin-Nippon SRW-5000 autorefractor. The participant held the selected prism (5D or 10D BO or BI, counterbalanced) in front of their right eye and obtained a single, fused image of the target while refractive measures were taken with each. A 30-second rest period was given between measurements. The mean age of the participants was 20.6 ± 3.22 years. Results: The mean CA/C ratios for the 5D BO, 10D BO, 5D BI, and 10D BI were 0.108 (±0.074) D/D, 0.110 (±0.056) D/D, 0.100 (±0.090) D/D, and 0.089 (±0.055) D/D, respectively. A 2-factor repeated measures ANOVA found that the CA/C ratio did not significantly change with differing levels of prism-induced convergence and divergence (p = 0.649). Conclusions: Change in accommodation induced by manipulating vergence is similar whether convergence or divergence are induced. The CA/C ratio did not show any change with differing levels of prism-induced convergence and divergence. Keywords: Binocular single vision, convergence accommodation/convergence ratio, divergence, open loop accommodation
INTRODUCTION
measure the CA/C ratio, the vergence system must be under closed loop conditions, and accommodation open loop. Several authors have used a pseudo-Gaussian blob target consisting of an LED placed behind a diffusing screen at 40 cm from the participant’s eyes to open the accommodative loop. Base-out (BO) prisms are then used to induce convergence and objective changes in refraction measured to assess accommodation induced. Hasebe et al.1 found the mean CA/C ratio to be 0.08D ± 0.04 D/D and Hirani and Firth2 found an overall mean CA/C of 0.13 ± 0.04 D/D when using prisms of 5, 10, 15, and 20D BO. Nonaka et al.3
Convergence accommodation is accommodation that results when the eyes converge. In closed-loop conditions this accommodative response may be inhibited to maintain clear vision, or at least inhibited to the extent that the person is able to do so. However, in open-loop conditions the response may be measured. The convergence accommodation to convergence (CA/C) ratio is the ratio between how much convergence accommodation occurs (in dioptres [D]) when convergence is exerted (in prism dioptres, D). Thus to
Received 4 April 2014; Revised 12 June 2014; Accepted 18 June 2014; Published online 16 July 2014 Correspondence: Joshua M Simmons, Academic Unit of Ophthalmology and Orthoptics, Faculty of Medicine, Dentistry & Health, University of Sheffield, Beech Hill Road, Sheffield, S10 2RX, UK. E-mail: [email protected]
120
Convergence accommodation to convergence (CA/C) Ratio: Convergence versus Divergence 121 found similar values of 0.081 ± 0.042 D/D in a series of 78 patients with intermittent exotropia and decompensating heterophoria who had binocular single vision for near. This was not significantly different to their control group, which had a mean CA/C ratio of 0.091 ± 0.036 D/D. With a ratio of 0.1/1, in open loop conditions, a person with an interpupillary distance of 6 cm fixing at 1/3 m, ie, converging 18D, would produce 1.8D of convergence accommodation. To our knowledge, no previous research has looked at the effect of prism-induced divergence on the convergence accommodation/convergence ratio. There is no evidence to suggest that the effect of divergence on convergence accommodation would be different to that of convergence, except to be in the opposite direction, but this assumption cannot be made without investigation. This study therefore investigates the CA/C ratio with induced divergence, and compares this to the level with induced convergence.
MATERIALS AND METHODS This cross-sectional study used a repeated measures design. The ethics committee of the Academic Unit of Ophthalmology and Orthoptics at the University of Sheffield approved the study, which followed the tenets of the Declaration of Helsinki. Eighteen participants were recruited via advertisement from the student population of the University of Sheffield. Each was given the participant information sheet, which detailed the study methods and the rights of a participant. After being given the opportunity to ask questions, written consent was obtained from each participant. The inclusion criteria were: No manifest ocular deviation. This was to ensure that the participant had normal binocular single vision. Emmetropic or refractive error corrected with contact lenses. This was done to avoid any prismatic effect that could be induced by the spectacles or difficulties due to reflections in refractive measurements. Vision of 0.2 logMAR or better in each eye. A good level of motor fusion consisting of the ability to be able to overcome a 5 and 10D prism both BO and base in (BI) at 40 cm. No pathological defects. To create the pseudo-Gaussian target of approximately 2 cm in size, a red light emitting diode (LED) powered by a battery was placed behind a diffusing screen 40 cm in front of the participant’s eyes.2 As there is a slow decrease in luminance of the light from the center, this creates weak contours that create cues for retinal disparity but not blur. This in turn opens the accommodative loop and allows convergence !
2014 Informa Healthcare USA, Inc.
accommodation to be measured. The refractive state of the eye was measured using a Shin-Nippon SRW-5000 autorefractor. Convergence and divergence were induced by using loose prisms, BO and BI, respectively. Prisms used were 5D and 10D both BO and BI. The participant’s age and refractive status were recorded, as was whether the participant wore contact lenses or not. If the participant did wear contact lenses, they were worn throughout the testing. A cover test was performed at 40 cm using an accommodative target of 6/6 (Snellen); visual acuity was tested using the LogMAR Bailey-Lovie test at 3.8 m; the prism reflex test was performed using a 10 D BI prism to an accommodative target. This test is done to determine the presence of motor fusion. Any heterophoria detected was recorded. The participant was seated at the autorefractor and the LED light position was altered slightly until the participant was looking directly at it with their left eye in order to avoid off axis measurements. They were asked to binocularly fixate on the LED light and obtain a single image. They were then asked to practice placing the prism in front of their right eye with the lights turned on, to ensure that they could do this accurately. The room lights were then turned off, along with the red LED light, and the participants were given 5 minutes of dark adaptation. It has been found that dark adaptation of cone cells takes between 5 and 8 minutes, whereas rod cells take between 35 and 40 minutes.4 The first measurement of refraction was taken without any prism to measure the baseline refractive status of the eye. Counterbalancing was used in order to determine the sequence in which the different conditions (prisms) were used. Convergence and divergence was induced by using BO and BI prisms, respectively. Strengths of 5 and 10D prisms were placed before the right eye and readings were taken from the left. The participants were asked to hold up the prism (ensuring this was not tilted), fuse the images, and maintain fusion. Three readings were taken quickly to avoid significant adaptation effects and were taken when the participant reported that the target was single. The time taken for fusion was not measured, but occurred within a 10-second time frame. The participant was given a 30-second rest between readings and in total the experiment lasted about 30 minutes.
Data Handling and Statistical Analysis The median value from the 3 readings (as selected by the autorefractor) was used to calculate the best spherical equivalent (BSE) (sphere + ½ cylinder). To calculate the accommodative response, the BSE was
122 J. M. Simmons and A. Y. Firth
The data were interval and were analyzed using a one-factor and two-factor Analysis of Variance (ANOVA). The mean, standard deviation, and standard error were also calculated for each data set. Results were considered significant if p = 0.05 or less.
strength of the prism (F = 0.088; p = 0.770). There was no significant interaction between prism strength and base direction (F = 0.216; p = 0.649). When looking at the entire set of CA/C ratio data, it was calculated that the overall mean CA/C ratio for the group was 0.102 ± 0.069 D/D. The range of the CA/C ratios were found to be from 0 to 0.275 D/D. When taking the individual data for each participant it is apparent that some of the subjects have a larger degree of nonlinearity than others (Figure 2.) Ten of the 15 subjects showed a variation between 2 of the 4 measures of greater than 2 standard deviations from the group mean (ie, 0.138).
RESULTS
DISCUSSION
Data were collected from 18 participants. However, results from 3 participants showed a reduction of accommodation on convergence or an increase in accommodation on divergence. Therefore these participants were excluded from the analysis. The mean age of the remaining 15 subjects was 20.6 ± 3.22 years (range, 18–31). Of these subjects, 3 were male and 12 were female. Of the participants, 5 wore contact lenses. At the test distance of 40 cm, 10 of the participants showed a minimal exophoria with rapid recovery and 5 had a minimal esophoria with rapid recovery. The mean logMAR vision that was found in the group was 0.065 ± 0.063 in the right eye and 0.092 ± 0.057 in the left eye. The mean BSE measurements for the differing strength prisms are given in Table 1. This shows an increase in accommodation for the BO prisms and a decrease in accommodation for the BI prisms. The absolute change in the accommodation elicited from the use of either 5D BI and BO or 10D BI and BO were not significantly different (t = 0.217, p = 0.831; t = 0.977, p = 0.345; respectively). The mean CA/C ratios for the 10D BO, 5D BO, 5D BI, and 10D BI were 0.110 (±0.056) D/D, 0.108 (±0.074) D/D, 0.100 (±0.090) D/D, and 0.089 (±0.055) D/D, respectively (Figure 1). A two-factor repeated measures ANOVA was used to determine if there was any effect of prism strength or orientation on the CA/C ratio. It was found that there was no statistical significance between the prism being either BO and BI (F = 0.307; p = 0.588) or the
We have explored the effect of divergence on convergence accommodation and have found absolute levels of accommodative change to be similar irrespective of the direction of the vergence. Further, no significant difference in the CA/C ratio with differing levels of convergence and divergence was found. When looking at the overall mean CA/C ratio, this was found to be 0.102 ± 0.069 D/D. This is similar to the CA/C ratio mean found by Hirani and Firth,2 who reported an overall mean CA/C ratio of 0.13 ± 0.05 D/D when looking at prism-induced convergence and the CA/C ratio. It is also close to results found by Suryakumar and Bobier,5 who found a mean CA/C ratio of 0.10 D/D in 8 adults with a mean age of 23 years. Previous literature has found that the CA/C ratio can range from as low as 0.019 D/D6 to as high as 0.15 D/D.7 It was found that the mean ratios of the accommodative response for the BO and BI prisms increase and decrease in a fairly linear fashion, which results in a similar CA/C ratio. Hirani and Firth2 and Wick and Currie6 have found a slight nonlinearity in the CA/C ratio, but this was only demonstrated in a few subjects. In the research by Hirani and Firth, 4 of 24 subjects showed a slightly greater amount of non-
CA=C ratio ¼ accommodative response ðDÞ =prism power ðDÞ
TABLE 1. Mean BSE for each prism.
Mean BSE (D) SD SE
10 D BO
5 D BO
0D
5 D BI
10 D BI
2.88 1.05 0.27
2.32 0.63 0.16
1.78 0.84 0.22
1.38 0.66 0.17
0.88 0.64 0.16
0.140 0.120 Mean CA/C Rao (D/ΔD)
subtracted from the reference measurement, which was the reading from the autorefractor with no prism. The CA/C ratio was calculated using the following equation:
0.100 0.080 0.060 0.040 0.020 0.000 10ΔBO
5ΔBO
5ΔBI
10ΔBI
Prism Strength (ΔD)
FIGURE 1. Mean CA/C ratios for differing strength prisms. Strabismus
Convergence accommodation to convergence (CA/C) Ratio: Convergence versus Divergence 123 Prism Strength (Δ) 5ΔBO 5ΔBI
10ΔBO
10ΔBI
Prism Strength (Δ) 5ΔBO 5ΔBI
10ΔBI
0.0000
0.0500
Subject 1 Subject 2
0.1000
Subject 3
0.1500
Subject 4 Subject 5
0.2000 0.2500
Mean CA/C Rao (D/ΔD)
Mean CA/C Rao (D/ΔD)
0.0000
10ΔBO
0.3000
0.0500
Subject 6 Subject 7
0.1000
Subject 8
0.1500
Subject 9 Subject 10
0.2000 0.2500 0.3000
10ΔBO
Prism Strength (Δ) 5ΔBO 5ΔBI
10ΔBI
Mean CA/C Rao (D/ΔD)
0.0000 0.0500 0.1000 0.1500 0.2000
Subject 11 Subject 12 Subject 13 Subject 14 Subject 15
0.2500 0.3000
FIGURE 2. Individual data found for the mean CA/C ratio.
linearity in their CA/C ratios.2 However, in the current research a greater number of subjects show this difference, which seems to be masked by the mean values of the CA/C ratio. Methods of testing do vary. Wick and Currie6 opened the accommodative loop by using 1.3-mm pinholes in front of each eye and pupils were dilated. The accommodative response was measured using the SRI Dual Purkinje image Eyetracker and infrared optometer. Hirani and Firth used similar methods to ours.2 Hirani and Firth proposed that nonlinearity may be connected to the varying effort used by the individual in order to maintain fusion.2 It could also be due to difficulty in maintaining precise fusion when viewing the difference of Gaussian (DoG) target for a prolonged period of time. Although the measurements were taken quickly, this could still have been too long for the subject to maintain good fusion, which could have resulted in variability in the CA/C ratio. If inaccurate vergence was responsible for the nonlinearity, perhaps further research could look into this using eye tracking technology. A possible reason for the variation may have been if the participant did not know the image was fused. Because a pseudo-Gaussian target consists of a light behind a diffusing screen, this looks like a blurry red ‘‘blob’’ to the participant. It is possible that because !
2014 Informa Healthcare USA, Inc.
the fixation target is blurry, it may appear to be single to the participant, but may in fact be double, which is overlapped. We found 3 participants to have a paradoxical change in accommodation to the vergence stimulus and considered this to be due to not overcoming the prism. It is possible that this was not the reason and further study would be necessary to explore this. Eadie et al.8 found that some adaptation occurs in the CA/C ratio and suggested there is some degree of plasticity in the cross links between accommodation and convergence. Convergence accommodation has also been found to decrease as vergence adaptation occurs.8–10 Nonaka,3 when measuring the accommodative change of the eye to prisms, took readings in quick succession to minimize the effect of vergence adaptation. Although in the current research measurements were also taken quickly to try and negate the effect of any degree of adaptation, it is possible that this is responsible for the degree of variation found in the results of individual data and the CA/C ratio. Previous research by Rosenfield et al.11 has shown that there is a decrease in the CA/C ratio with age. However, our oldest participant was aged 31 years, and did not appear different from the younger subjects, so we cannot comment on this. Heron
124 J. M. Simmons and A. Y. Firth et al.12 suggest the CA/C ratio decreases after the age of 48 years. In the study by Brautaset and Jennings,13 the subjects viewed a DoG target for 5 minutes before measurements began to allow accommodation to stabilize. We allowed 5 minutes in the dark before measurements were taken to take away any prior accommodative adaptation effects. Schor et al.14 found that when measured in darkness, the accommodative adaptation had the shortest effects when compared with other open loop accommodation states. It is possible that participants may have been holding the prisms in slightly different positions. Although they were observed doing this for the first time in the light, as the room was completely darkened it became impossible to assess. This may have caused slight errors in the level of vergence induced if the prism was not held correctly for its calibrated position. However, this effect would only be minimal as only small strength prisms (5 and 10D) were used. We cannot extrapolate our findings to a clinical population. However, attention has recently been given to the role of convergence accommodation in strabismus.15,16 Notably, when considering the mechanism for control of intermittent exotropia, there is evidence that disparity drives a large proportion of accommodation,16 and so we wanted to investigate the effect of divergence on negation of accommodation, that is, whether the disparity drive of divergence had the opposite effect. This we have found in our normal population, but further work will be needed to discover the role of convergence accommodation in esotropia. It is possible that repeatability is an issue when looking at the CA/C ratio. To our knowledge, no study has looked at the repeatability of the CA/C ratio and if it does vary throughout measurements or indeed if it is variable throughout the day. The CA/C ratio did not change significantly with differing levels of prism- induced convergence and divergence when using 5 and 10D both BO and BI. The data found suggest that there may be a larger degree of nonlinearity within individuals than reported in previous literature, but this may be due to repeatability of the CA/C ratio or a slight fluctuation in accommodation.
DECLARATION OF INTEREST The authors report no conflicts of interest.
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