Evaluating Relative Accommodations in General Binocular Dysfunctions

ORIGINAL ARTICLE

ÁNGEL GARCÍA, DOO, PILAR CACHO, DOO, and FRANCISCO LARA, DOO Departamento Interuniversitario de Óptica, Universidad de Alicante, Spain (AG, PC), Departamento de Oftalmología, AP y ORL, Universidad de Murcia, Spain (FL)

ABSTRACT: Purpose. To examine the relationship between relative accommodation and general binocular disorders and to establish their importance in the diagnosis of these anomalies. Methods. We analyzed data of negative relative accommodation (NRA) and positive relative accommodation (PRA) in 69 patients with nonstrabismic binocular anomalies. Results. Statistical analysis showed that low values of NRA and PRA were not associated with any particular disorder. High values of PRA (>3.50 D) were related to the disorders associated with accommodative excess, whereas high values of NRA (>2.50 D) were not related to accommodative excess. Statistical differences suggested that a high value of PRA could distinguish between anomalies. Sensitivity analysis revealed that high PRA was the most sensitive sign in patients with convergence insufficiency combined with accommodative excess (0.89) and one of the most sensitive signs for subjects with accommodative excess (0.72) and for those with convergence excess combined with accommodative excess (0.70). Conclusions. Anomalous results of NRA were not clearly associated with any dysfunction. High values of PRA were related to disorders associated with accommodative excess, so the sign of a high value of PRA should be considered as one of the diagnostic signs of these anomalies. (Optom Vis Sci 2002;79:779–787)

Key Words: negative relative accommodation, positive relative accommodation, general binocular dysfunctions

linical evaluation of accommodative and vergence system far and near distance are known, relative accommodations do not is an essential part of the study of visual function. The offer new information. Due to the interactions between accommo- Cdiagnosis of general binocular disorders is performed by dation and vergence, the values of fusional vergences and relative means of analysis of accommodative and binocular tests. Some of accommodations are so related that one would think that it is not these tests can be cataloged specifically as accommodative or bin- necessary to study them together in a visual analysis. In fact, some ocular, basically being assessed in open-loop conditions for the authors2–6 do not use relative accommodations for diagnosing vergence system. This is the case for the cover test, monocular general binocular disorders, more because of a question of duplic- accommodative amplitude, or monocular accommodative facility. ity than for not being a valid test. However, other authors use However, the remaining tests offer results that are notably influ- relative accommodations as a reference in the diagnosis of accom- enced by the interactions between accommodation and vergence. modative and vergence dysfunctions7–11 or as tests associated with As an example, we have the monocular estimate method of dy- the visual function.12 namic retinoscopy (MEM method), fusional vergences, or relative In most of the previous cases, positive relative accommodation accommodation. (PRA) and negative relative accommodation (NRA) are used as Special attention is given to fusional vergences and relative ac- complementary diagnostic tests of some disorders. Hokoda7 used a commodations. They evaluate the amount of vergence and accom- low PRA (Յ1.25 D) as one of two supplementary signs that needed modation that varies while the stimulus that generates the response to be present in accommodative insufficiency. Scheiman et al.8 also in the other system remains constant. Any alteration in the accom- used PRA for diagnosing accommodative dysfunction and consid- modative or vergence system could influence the other system and ered that a low value of NRA (Ͻ1.50 D) was related to conver- result in abnormal values of these tests. gence insufficiency. Traditionally, fusional vergence results have been considered Porcar and Martínez-Palomera9 considered a low NRA (Յ1.50 more important than the findings of relative accommodation. D) and PRA (Յ1.25 D) associated with accommodative infacility, Thus, Saladin1 suggests that if the accommodative amplitude, the and they also used this low value of PRA for diagnosing accommo- values of accommodative facility, and those of fusional vergences at dative insufficiency. Finally, García et al.10 and Lara et al.11 used

Optometry and Vision Science, Vol. 79, No. 12, December 2002 780 Positive and Negative Relative Accommodation—García et al. anomalous values of relative accommodations for diagnosing ac- normal ocular and systemic health, and all of them had at least commodative and binocular anomalies: a low value of PRA (Յ1.25 20/20 visual acuity with their best correction. None of the subjects D) for accommodative insufficiency and convergence excess and a wore contact lenses, and subjects with strabismus were also re- low value of NRA (Յ1.50 D) for accommodative excess and con- jected. All subjects gave informed consent after an explanation the vergence insufficiency. nature of the tests to be performed, and subjects authorized the All reports mentioned use abnormally low values of relative authors to apply the results obtained in this research. accommodations as diagnostic signs of certain dysfunctions, a sit- All patients underwent a complete visual examination including uation that is justified by the proper etiology of these anomalies. In the following procedures: this sense, a low value of PRA indicates that the patient does not • A case history, reflecting the full range of symptoms presented accept the introduction of negative lenses, which could be due to by the patient. two situations. The first would be that the subject is not able to • Ocular health examination with direct ophthalmoscopy and increase his/her accommodation by the same value as the addi- biomicroscopy. tional negative lenses, a situation that may be related to an accom- • Assessment of refractive error. Static retinoscopy procedure was modative dysfunction as accommodative insufficiency. The sec- done while the subject was instructed to watch the 20/400 letter ond situation implies that the patient presents an inadequate E on the distant chart at 6 m. The subjective examination was negative fusional vergence to counter the accommodative vergence performed by means of a monocular fogging method with cross- generated by the increase in accommodation due to the inserted cylinder, followed by binocular balancing to a standard end- negative lenses, a situation that would occur in convergence excess. point of maximum plus for best visual acuity. This result was A low value NRA indicates that the subject does not accept the called the subjective refractive examination. binocular interposition of positive lenses. In the same manner, this • Accommodative and binocular vision testing. With the results result can be related to an accommodative or vergence problem. If of the subjective refractive examination in place (maximum plus the patient does not accept plus lenses because he is not able to relax for best visual acuity), we conducted an evaluation of accom- the accommodation, it probably indicates accommodative excess. modative and binocular vision including different tests16:as- On the other hand, when the subject has an inadequate positive sessment of direction and magnitude of horizontal and vertical fusional vergence he will not be able to counteract the diminution phoria with cover test and prism bar at 6 m and 40 cm, AC/A of accommodative vergence due to the relaxation of the accommo- ratio measured with both calculated and gradient methods, dation generated by plus lenses. This would be an example of a MEM dynamic retinoscopy assessed at 40 cm by means of a trial patient with convergence insufficiency. frame and trial lenses, positive and negative relative accommo- Although high values of PRA and NRA have been obtained in dation, monocular and binocular accommodative facility with some reports,13 in no study cited above are high values of relative Ϯ2.00 D flip lenses using a card with acuity suppression, mon- accommodations considered as a sign for diagnosing general binocular accommodative amplitude by the push-up method, pos- ocular disorders. The only clear relationships seem to be between itive and negative fusional vergence (smooth and step vergence high PRA and convergence insufficiency and between a high value with Von Graefe and prism bar method, respectively), near- of NRA and under– uncorrected hyperopia,14 more because of a point of convergence, and stereopsis measurement with Wirt question of a description of the pathophysiology of these alter- circles (Titmus stereotest). ations than of a diagnostic sign of them. Concerning the high values of NRA and the under– uncorrected hyperopia, their rela- Tests were performed by one examiner who was limited to the tion is obvious due to the etiology of this ametropia. procedures. Another author analyzed the data from the patients. In regard to high values of PRA and convergence insufficiency, Thus, examiner bias for particular test results was avoided. Results it is known that a robust adaptation of accommodation exists in of each test were compared with the norms established by patients with this binocular anomaly.15 This, together with their Scheiman and Wick16 and then grouped according to their devia- developed negative fusional vergence, causes the patients to easily tion from the normal values. Accommodative and binocular accept the binocular interposition of minus lenses, resulting in a anomalies were identified following the criteria of these authors,16 possible high value of PRA.14 taking into account the number of signs used by Lara et al.,11 Despite the previous considerations, other relationships be- which are the most restrictive criteria of those proposed by previous tween the values of relative accommodation and general binocular authors. Thus, we used a high number of signs in the diagnosis of disorders have not been described. Therefore, the aim of this study these anomalies to use data of those patients who clearly presented was to examine the results of relative accommodations in patients some type of dysfunction. Table 1 shows the criteria used in this with nonstrabismic binocular dysfunctions to determine the pos- study for diagnosing accommodative and binocular disorders. sible relations between their values with each disorder and to in- From all patients studied, we only recorded for this study the data vestigate how they could be used in diagnosis. of those anomalies that were present in more than five subjects to avoid an excessively small sample. With the criteria established, we classified 69 patients (40 females and 29 males) with an age range METHODS of 13 to 35 years and a mean (ϮSD) age of 20.8 Ϯ 4.7. The From symptomatic patients presenting consecutively to an op- anomalies were classified as follows: 13 subjects with accommoda- tometric clinic, we examined 328 subjects between the ages of 13 tive insufficiency, 18 patients with accommodative excess, 13 sub- and 35 years. The upper limit of 35 years was to avoid patients with jects with convergence excess, 6 patients with convergence insuffi- accommodative problems that were related to age. All subjects had ciency, 10 subjects with convergence excess combined with

Optometry and Vision Science, Vol. 79, No. 12, December 2002 Positive and Negative Relative Accommodation—García et al. 781 TABLE 1. Diagnosis criteria for accommodative and binocular disorders

ACCOMMODATIVE INSUFFICIENCY (AI) Symptoms. Blurred near vision, discomfort and strain associated with near tasks, fatigue associated with near point tasks, difficulty with attention and concentration when reading. Signs. Need to present signs 1 and 2, and two of complementary signs (3–5). 1. Reduced amplitude of accomodation. Push-up accommodative amplitude at least 2 D below Hofstetter’s calculation for minimum amplitude: 15–0.25 ϫ age. 2. Fails monocular accommodative facility with Ϫ2.00 D, Յ 6 cpm. 3. Fails binocular accommodative facility with Ϫ2.00 D, Յ 3 cpm. 4. High MEM finding, Ͼϩ0.75 D. 5. Low PRA, Յ 1.25D. ACCOMMODATIVE EXCESS (AE) Symptoms. Blurred distance vision worse after reading or other close work and often worse toward the end of the day, headaches and eyestrain after short periods of reading, difficulty focusing from far to near, sensitivity to light. Signs. Need to present signs 1–3 and two of complementary signs (4–6). 1. Variable visual acuity findings. 2. Variable static retinoscopy and subjective refraction. 3. Difficulty clearing ϩ2.00 D with monocular accommodative facility, Յ 6 cpm. 4. Difficulty clearing ϩ2.00 D with binocular accommodative facility, Յ 3 cpm. 5. Low MEM finding, Յ ϩ0.25 D. 6. Reduced Negative Relative Accommodation (NRA), Յ1.50 D. CONVERGENCE EXCESS (CE) Symptoms. Associated with reading or other near tasks and generally worse at end of day. The most common includes asthenopia and headaches, intermittent blur. Signs. Need to present signs 1–2, and two of complementary signs (3–6). 1. Significant esophoria at near, Ͼ 2 ⌬. 2. Reduced negative fusional vergence at near, Յ 8/16/7 for blur, diplopia and recovery (at least one of three). 3. High calculated AC/A ratio, Ͼ7/1. 4. Fails binocular accommodative facility with Ϫ2.00 D, Յ3 cpm. 5. High MEM, Ͼϩ0.75 D. 6. Low PRA, Յ 1.25 D. CONVERGENCE INSUFFICIENCY (CI) Symptoms. Associated with reading or other near tasks, asthenopia, headaches, intermittent blur. Signs. Need to present signs: 1–3, and two of complementary signs (4–7). 1. Moderate to high exophoria at near, Ͼ6 ⌬. 2. Reduced positive fusional vergence at near, Յ 11/ 14/ 3 for blur, diplopia and recovery (at least one of three). 3. Receded near point of convergence, Ͼ10 cm for loss of fusion or Ͼ 17.5 cm for recovery. 4. Low calculated AC/A ratio, Ͻ3/1. 5. Fails binocular accommodative facility testing with ϩ2.00 D, Յ 3 cpm. 6. Low MEM, Ͻϩ0.25 D. 7. Low NRA, Յ 1.50 D.

accommodative excess, and 9 patients with convergence insuffi- While the patient fixated the horizontal line of 20/20 letters at 40 ciency combined with accommodative excess. cm, the examiner added spherical lenses binocularly. Negative rel- The diagnosis of combined accommodative and binocular dis- ative accommodation was measured first, adding plus lenses bin- orders was done by joining the signs according to Table 1. In the ocularly in 0.25 D steps at the rate of one step every 2 s1 until the case of combined convergence excess with accommodative excess, subject reported the first sustained blur. The net amount of plus some signs are opposite for both disorders; we classified these pa- added was recorded as plus to blur or negative relative accommo- tients when they had the signs that needed to be present for both dation. Then, the amount of plus was reduced or minus was in- anomalies and at least one of the complementary signs of conver- creased binocularly in 0.25 D steps per 2 s over the refraction gence excess. In regard to combined convergence insufficiency placed in the phoropter until the first sustained blur was again with accommodative excess, most of the complementary signs in reported. PRA was recorded as the amount of minus lenses added both cases are the same; we classified them when the patients with over the subjective refractive examination. convergence insufficiency also had the signs needed to be present To diagnose dysfunctions and analyze the results, we considered in the accommodative excess. the normal values proposed by Scheiman and Wick.16 With these Positive and negative relative accommodation were assessed us- norms, PRA has a mean (Ϯ SD) value of 2.37 Ϯ 1.00 so that a low ing a visual acuity card situated at 40 cm and with the maximum result is considered as being Յ1.25 D, a high value as Ն3.50 D, plus for best visual acuity correction placed in the phoropter. and normal as between these values. In regard to the NRA, the

Optometry and Vision Science, Vol. 79, No. 12, December 2002 782 Positive and Negative Relative Accommodation—Garcíaetal. mean value is established as 2.00 Ϯ 0.50 D, so that a low value is low value of NRA distinguishes between the group with AE and Յ1.50 D, a high value is Ն2.50 D, and normal values are situated the others because there are no differences between this dysfunc- between both extremes. tion and the group with CI. There are no significant differences between the two groups of RESULTS disorders that were associated with a high NRA, AI and CE. More- over, there were no significant differences between the disorders Of the 69 patients in the sample, 31 had accommodative dys- with normal values16 of NRA: CI, CE ϩ AE, and CI ϩ AE. functions (13 with accommodative insufficiency and 18 with ac- According to the disorders with high NRA (AI and CE), there commodative excess), 19 had binocular anomalies (13 with con- were differences between these anomalies and the disorders of AE vergence excess and six with convergence insufficiency), and 19 and CI. Despite these statistical differences, it cannot be assured had combined accommodative and binocular disorders (10 with that a high value of NRA is clearly related to some type of dysfunc- convergence excess combined with accommodative excess and tion. As an example, a high NRA could be associated with a disor- nine with convergence insufficiency combined with accommoda- der such as AI or CE. However, because there are no differences tive excess). In total, there were six different groups of anomalies with the anomaly of CE ϩ AE, or between AI and CI ϩ AE, it is from which PRA and NRA values were selected for analysis. There not possible to assure that this high value of NRA is only related to were no significant statistical differences between these groups of accommodative insufficiency or convergence excess. patients according to age (p Ͼ 0.05), therefore the age of patients did not affect the results. Positive Relative Accommodation Negative Relative Accommodation Table 4 shows some descriptive statistics for the PRA data of Table 2 shows the descriptive statistics of NRA for each group of each group of anomalies. Fig. 2 shows the mean value and 1 SD of dysfunctions, and Fig. 1 represents the mean value of NRA with 1 PRA for each dysfunction, together with two lines that indicate the SD error bars for each dysfunction; the two lines in Fig. 1 indicate limits of the standard deviation for the normal population.16 As the limits of standard deviation for the normal population. It can can be observed, mean values of PRA for convergence excess and be established that accommodative excess (AE) is related to rela- convergence insufficiency can be classified as normal. PRA in ac- tively low values of NRA. Convergence insufficiency (CI) and commodative insufficiency is related to a low value, whereas the convergence insufficiency combined with accommodative excess other three groups of dysfunctions are associated with high values (CI ϩ AE) are associated with normal values. Accommodative of PRA. insufficiency (AI) and convergence excess (CE) are associated with To determine whether there were differences between values of high values of NRA, and the dysfunction of convergence excess PRA, we performed an analysis of variance, having verified that the combined with accommodative excess (CE ϩ AE) is related to a six groups had a normal distribution (Shapiro-Wilk test, p Ͼ 0.05 normal-high value of NRA. for all cases) and proved the equality of variances between them Having investigated the normality of the six samples (Shapiro- (Levene test, p Ͼ 0.05). Analysis of variance showed that there Wilk test, p Ͼ 0.05 for all groups) and the equality of variance were significant statistical differences between the six groups of between them (Levene test, p Ͼ 0.05), we performed an analysis of dysfunctions according to the mean value of PRA (F ϭ 14.99, p Ͻ variance, which showed that significant statistical differences ex- 0.01). Table 5 shows post hoc analysis using the Scheffè test, as- isted between the mean NRA values (F ϭ 20.289, p Ͻ 0.01). Post sessed for determining significant differences between groups. hoc analysis using the Scheffe´ test determined the differences be- Analyzing the differences between groups, it is possible to estab- tween the groups (Table 3). lish certain considerations. First, significant differences exist be- As can be observed, there are statistical differences between the tween PRA mean values of AI and those groups where AE appears. AE group and the rest of the dysfunctions, except for the CI group. Because accommodative insufficiency is related to low PRA,7–9 it Because the AE group is related to a low value of NRA,10, 11 it can can be established that a low value of PRA will not be related to the be assured that a high value of NRA is not associated with the dysfunctions where accommodative excess is present. accommodative excess. In this sense, it cannot be affirmed that a On the other hand, there are no significant differences between

TABLE 2. Summary of results for negative relative accommodation in each diagnostic group

No. of Dysfunction Mean SD Minimum Maximum Subjects

AIa 13 2.75 0.38 2.00 3.25 AE 18 1.64 0.47 1.00 2.50 CE 13 2.87 0.26 2.50 3.25 CI 6 1.75 0.22 1.50 2.00 CE ϩ AE 10 2.45 0.40 2.00 3.00 CI ϩ AE 9 2.22 0.51 1.50 3.00 a AI, accommodative insufficiency; AE, accommodative excess; CE, convergence excess; CI, convergence insufficiency.

Optometry and Vision Science, Vol. 79, No. 12, December 2002 Positive and Negative Relative Accommodation—García et al. 783

FIGURE 1. Mean value of negative relative accommodation (NRA) Ϯ1 SD for each group of dysfunction. AI, accommodative insufficiency; AE, accommodative excess; CE, convergence excess; CI, convergence insufficiency.

AI and CE and CI with regard to mean value of PRA. As was observed in Fig. 2, these two disorders (CE and CI) can be associ- TABLE 3. Mean differences for negative relative accommodation by ated with a value of PRA between normal limits, thus normal dysfunctions using Scheffe’s method results or low values of PRA do not distinguish statistically between these three anomalies. 95% Confidence Interval Between the groups of disorders that were associated with a high Contrast of Mean of the Difference value of PRA, significant statistical differences do not exist. How- Means Differences ϩ Lower Limit Higher Limit ever, these differences appear when the groups of AE and CI AE are compared with disorders of CE and CI. There are no significant a b AI vs. AE 1.111 0.610 1.613 differences between these dysfunctions (CE and CI) and the group AI vs. CE Ϫ0.115 Ϫ0.656 0.425 with CE ϩ AE. These findings suggest that, in general, the high AI vs. CI 1.000b 0.320 1.680 AI vs. CE ϩ AE 0.300 Ϫ0.280 0.880 values of PRA can distinguish between dysfunctions, particularly AI vs. CI ϩ AE 0.528 Ϫ0.007 1.125 between those anomalies related to accommodative excess and the AE vs. CE Ϫ1.227b Ϫ1.728 Ϫ0.725 remainder. AE vs. CI Ϫ0.111 Ϫ0.761 0.539 As it has been shown up to this point, the clearest results connect AE vs. CE ϩ AE Ϫ0.811b Ϫ1.355 Ϫ0.268 the relative accommodation with the dysfunctions in which ac- ϩ Ϫ b Ϫ Ϫ AE vs. CI AE 0.583 1.146 0.002 commodative excess appears, so that a low value of PRA is not CE vs. CI 1.115b 0.435 1.796 associated with accommodative excess, whereas a high value is CE vs. CE ϩ AE 0.415 Ϫ0.164 0.995 CE vs. CI ϩ AE 0.643b 0.005 1.241 related to this disorder, and a high value of NRA is not associated CI vs. CE ϩ AE Ϫ0.700 Ϫ1.412 0.001 with this accommodative anomaly. To evaluate with greatest pre- CI vs. CI ϩ AE Ϫ0.472 Ϫ1.199 0.254 cision the importance of the relative accommodation in the disor- CE ϩ AE vs. CI ϩ AE 0.228 Ϫ0.405 0.861 ders associated with accommodative excess, we decided to study a AI, accommodative insufficiency; AE, accommodative ex- the specificity and sensitivity of all complementary signs that are cess; CE, convergence excess; CI, convergence insufficiency. used in the diagnosis of these anomalies together with the sign of b p Ͻ 0.05. PRA.

Optometry and Vision Science, Vol. 79, No. 12, December 2002 784 Positive and Negative Relative Accommodation—Garcíaetal. TABLE 4. Summary of results for positive relative accommodation in each diagnostic group

No. of Dysfunction Mean SD Minimum Maximum Subjects AIa 13 1.48 0.68 0.50 3.00 AE 18 4.43 1.71 2.00 8.75 CE 13 2.44 1.12 1.00 4.50 CI 6 2.42 0.74 1.75 3.75 CE ϩ AE 10 3.40 1.02 1.50 5.00 CI ϩ AE 9 5.25 1.30 3.25 7.25 a AI, accommodative insufficiency; AE, accommodative excess; CE, convergence excess; CI, convergence insufficiency.

Specificity and Sensitivity of Disorders Associated dative excess who fail the test analyzed and the total number of with Accommodative Excess patients studied who have accommodative excess. The criteria used for diagnosing the anomalies studied are Specificity can be understood as the percentage of subjects who shown in Table 1, where it is specified that in accommodative pass a particular test and are classified, in this case, without relation excess the complementary signs were MEM Ͻϩ0.25 D, NRA to the accommodative excess. It can be calculated by means of the Յ1.50 D, and difficulty clearing with ϩ2.00 D in binocular ac- ratio between the number of subjects without dysfunctions who commodative facility (BAF) Յ3 cpm. When convergence insuffi- pass the test analyzed and the number of patients without dysfunc- ciency is associated with accommodative excess, the complemen- tions studied. The sensitivity can be calculated as the percentage of tary signs are those listed before, together with a calculated ratio of subjects who fail the particular test and are classified with dysfunc- AC/A Ͻ3/1. In convergence excess combined with accommodations related to accommodative excess. It can be calculated by tive excess, certain flexibility in the use of the complementary signs means of the ratio between the number of subjects with accommo- is needed because some of them are contradictory in both dysfunc-

FIGURE 2. Mean value of positive relative accommodation (PRA) Ϯ1 SD for each group of dysfunction. AI, accommodative insufficiency; AE, accommodative excess; CE, convergence excess; CI, convergence insufficiency.

Optometry and Vision Science, Vol. 79, No. 12, December 2002 Positive and Negative Relative Accommodation—García et al. 785 TABLE 5. To calculate the specificity of the diagnostic signs in accommo- Mean differences for positive relative accommodation by dative excess, a sample of patients without general binocular dys- dysfunctions using Scheffe’s method functions is needed. To perform this analysis, we randomly selected from our sample of patients the data of 20 normal subjects 95% Confidence who had this condition. The signs analyzed had the following Interval of the ϭ ϭ ϭ Mean specificity: BAF 0.9 (18/20); MEM 0.9 (18/20); NRA 1.0 Contrast of Means Difference Differences (20/20), and PRA ϭ 0.9 (18/20). In all cases, high values were Lower Higher reached, a finding that indicates that if the established cutoffs are Limit Limit used, there is a high probability that a patient who passes each test AI vs. AEa Ϫ2.950b Ϫ4.496 Ϫ1.404 could be classified as a subject without accommodative excess. This AI vs. CE Ϫ0.962 Ϫ2.628 0.704 result is logical, but has minimal clinical interest. AI vs. CI Ϫ0.936 Ϫ3.032 1.160 For the rest of the dysfunctions associated with accommodative AI vs. CE ϩ AE Ϫ1.919b Ϫ3.706 Ϫ0.133 excess, the specificity had similar values because the population was AI vs. CI ϩ AE Ϫ3.769b Ϫ5.611 Ϫ1.928 the same in all cases and the considerations about the results were b AE vs. CE 1.988 0.442 3.534 not different from those mentioned. b AE vs. CI 2.014 0.001 4.016 For the assessment of sensitivity, we took into account data from AE vs. CE ϩ AE 1.031 Ϫ0.645 2.706 ϩ ϩ Ϫ Ϫ 18 patients with AE, 9 subjects with CI AE, and the 10 patients AE vs. CI AE 0.819 2.553 0.915 ϩ CE vs. CI 0.003 Ϫ2.071 2.122 who presented CE AE. The sensitivity results for each comple- CE vs. CE ϩ AE Ϫ0.958 Ϫ2.744 0.829 mentary sign presented in these disorders are shown in Table 7. CE vs. CI ϩ AE Ϫ2.808b Ϫ4.650 Ϫ0.966 For accommodative excess, the most sensitive signs were BAF CI vs. CE ϩ AE Ϫ0.983 Ϫ3.177 1.210 Յ3 cpm with difficulty with plus lenses (0.72) and PRA Ն3.50 D CI vs. CI ϩ AE Ϫ2.833b Ϫ5.072 Ϫ0.595 (0.72). These results indicate that more than 70% of the patients CE ϩ AE vs. CI ϩ AE Ϫ1.850 Ϫ3.802 0.102 with accommodative excess will have high values of PRA or/and a AI, accommodative insufficiency; AE, accommodative ex- will fail the binocular accommodative facility test. The probability cess; CE, convergence excess; CI, convergence insufficiency. of encountering a high value of PRA in these patients was higher b p Ͻ 0.05. than a finding of a low MEM value or a result of NRA Ͻ1.50 D. In patients with CI ϩ AE, the most sensitive sign was high PRA tions. In CE, one finds a value of AC/A more than 7/1, BAF Յ3 (0.89), which was higher than failing BAF (0.78) or a low calcu- cpm failing with minus lenses, MEM Ͼϩ0.75 D, and PRA lated AC/A (0.78). Again, there was a high probability that a pa- Յ1.25 D. To these signs can be added a high value of PRA related tient with this accommodative combined binocular dysfunction to accommodative excess, as has been established in this paper. had a high value of PRA. Taking into account these criteria, to study the specificity Finally, in patients with CE ϩ AE, we studied the sensitivity of and sensitivity, it is necessary to know the cutoff for each sign to all complementary signs corresponding to CE and to AE. As can be establish when a patient passes or fails the test. Table 6 shows observed in Table 7, the most sensitive signs were the presence of a the cutoff values used, following the limits proposed by the high-calculated AC/A (0.90), followed by a high value of PRA standard deviation of the normal values suggested by Scheiman (0.70). Again, in these patients, there was a high probability of and Wick.16 encountering high values of PRA.

TABLE 6. Cutoff used to calculate specificity and sensitivity

Signs Fail the Test Pass the Test AEa BAF Յ3 cpm (fail with ϩ2.00 D) Ͼ3 cpm MEM Ͻϩ0.25 D Նϩ0.25 D NRA Յ1.50 D Ͼ1.50 D PRA Ն3.50 D Ͻ3.50 D CI ϩ AE All signs of AE together with: AC/A calculated Ͻ3/1 Ն3/1 CE ϩ AE All signs of AE together with: BAF Յ3 cpm (fail with Ϫ2.00 D) Ͼ3 cpm MEM Ͼϩ0.75 D Յϩ0.75 D PRA Յ1.25 D Ͼ1.25 D AC/A calculated Ͼ7/1 Յ7/1 AE, accommodative excess; BAF, binocular accommodative facility; MEM, monocular estimate method; NRA, negative relative accommodation; PRA, positive relative accommodation; CI, convergence insufficiency; CE, convergence excess.

Optometry and Vision Science, Vol. 79, No. 12, December 2002 786 Positive and Negative Relative Accommodation—Garcíaetal. TABLE 7. excess, which is related to high values of NRA. Moreover, the Sensitivity of the complementary diagnostic tests for ac- sensitivity of a low value of NRA in these patients was only 22% commodative excess, convergence insufficiency ϩ accom- (Table 7), which is lower than other signs such as BAF or a low modative excess, and convergence excess ϩ accommoda- calculated AC/A. tive excess The high values of NRA can be associated with disorders such as accommodative insufficiency and convergence excess, although Signs Sensitivity statistically one must not rule out other anomalies when there is a AE (N ϭ 18)a high result of NRA. In view of these results, one could think that BAF Յ3 cpm (ϩ) 0.72 (13/18) the NRA results do not clearly distinguish between dysfunctions, MEM Ͻϩ0.25 D 0.67 (12/18) so their use should be complementary to other binocular tests NRA Յ1.50 D 0.61 (11/18) when diagnosing general binocular disorders, as is used currently. PRA Ն3.50 D 0.72 (13/18) In regard to PRA results, we encountered diminished values in ϩ ϭ CI AE (N 9) accommodative insufficiency, although this did not occur in con- BAF Յ3 cpm (ϩ) 0.78 (7/9) Ͻϩ vergence excess. Because there are no differences between accom- MEM 0.25 D 0.33 (3/9) modative insufficiency and convergence excess or convergence in- NRA Յ1.50 D 0.22 (2/9) sufficiency, we can suggest that a low value of PRA does not PRA Ն3.50 D 0.89 (8/9) AC/A calculated Ͻ3/1 0.78 (7/9) distinguish between these three dysfunctions. CE ϩ AE (N ϭ 10) The high results of PRA are related to anomalies in which ac- BAF Յ3 cpm (ϩ) 0.20 (2/10) commodative excess appears. In particular, values of PRA in ac- MEM Ͻϩ0.25 D 0.40 (4/10) commodative excess and in the combined dysfunction of conver- NRA Յ1.50 D 0 (0/10) gence insufficiency and accommodative excess showed statistical PRA Ն3.50 D 0.70 (7/10) differences from disorders not associated with accommodative ex- BAF Յ3 cpm (Ϫ) 0.30 (3/10) cess. In this case, we can assure that, in general, a high value of PRA Ͼϩ MEM 0.75 0.10 (1/10) can distinguish between the disorders related to accommodative PRA Յ1.25 D 0 (0/10) Ͼ excess and the others. AC/A calculated 7/1 0.90 (9/10) The values of PRA in combined convergence excess with accom- a AE, accommodative excess; BAF, binocular accommodative modative excess were also elevated, but not as much as in other facility; MEM, monocular estimate method; NRA, negative rela- dysfunctions in which accommodative excess appears. This is pos- tive accommodation; PRA, positive relative accommodation; CI, sibly because PRA in convergence excess has normal values that can convergence insufficiency; CE, convergence excess. be increased noticeably in those patients with an associated accommodative excess, although not enough to present significant differences with the disorders of normal PRA (CE and CI). DISCUSSION Some authors14–15 suggest that PRA values can be elevated in Values of relative accommodations have been used in several patients with convergence insufficiency. Our results reveal that in studies in a secondary way for diagnosing nonstrabismic binocular subjects with only CI, the values of PRA are within the normal dysfunctions. Traditionally, their importance has been less than limits. However, when the CI is associated with accommodative other binocular tests, and some authors have not included them excess, the PRA reaches high levels. In these patients, accommo- when assessing the diagnosis of general binocular anomalies.2–6 dative excess is secondary to convergence insufficiency, thus it can Depending on the authors,7–11 the anomalous values of relative be assured that the increase of PRA is directly related with the accommodations can be associated with particular dysfunctions. apparition of accommodative excess. Thus, a low value of NRA may be encountered in convergence The sensitivity of a high PRA in disorders associated with AE insufficiency and with accommodative excess, whereas a reduced (Table 7) corroborates the preceding considerations. In patients PRA is associated with accommodative insufficiency and with con- with CE ϩ AE, the sensitivity of a value of PRA Ն3.50 D is 0.70, vergence excess. only exceeded by the presence of a high-calculated AC/A (0.90). It The findings of this study partly confirm these opinions. In fact, is important to point out that in these subjects, the presence of a in accommodative excess, NRA values are diminished, but this low MEM finding, which is characteristic of AE, is more sensitive does not occur in convergence insufficiency because they are than the finding of a high MEM value, characteristic of CE. This within the limits established by the standard deviation for a normal fact corroborates the influence of accommodative excess in certain population.16 Despite this, there are no significant differences be- binocular parameters related with convergence excess. tween the values of NRA for these two groups. It can only be The sensitivity of high PRA in subjects with AE is 0.72, the same affirmed that a high value of NRA will not be related to the accom- result as the sign of failing BAF and only slightly higher than the modative excess. signs of low MEM and diminished NRA. In patients with conver- On the other hand, it could be thought that in those patients gence insufficiency combined with accommodative excess, the who show both convergence insufficiency and accommodative ex- most sensitive sign is a high value of PRA (0.89), followed by the cess, NRA values would be necessarily diminished. However, as is difficulty with BAF and the low calculated AC/A (0.78 in both shown in Table 2 and in Fig. 1, NRA in these patients can be cases) and very remote from the signs of low MEM and low NRA. considered normal and only differs statistically from accommoda- These results corroborate the importance of high PRA in disorders tive excess, which is related to low values of NRA, and convergence associated with accommodative excess, thus the finding of a PRA

Optometry and Vision Science, Vol. 79, No. 12, December 2002 Positive and Negative Relative Accommodation—García et al. 787 value Ͼ3.50 D should be included as a diagnostic sign related to 6. Rouse MW, Hyman L, Hussein M, Solan H, the Convergence Insuf- accommodative excess. ficiency and Reading Study (CIRS) Group: frequency of convergence insufficiency in optometry clinic settings. Optom Vis Sci 1998;75: 88–96. CONCLUSIONS 7. Hokoda SC. General binocular dysfunctions in an urban optometry clinic. J Am Optom Assoc 1985;56:560–2. The use of NRA in the diagnosis of nonstrabismic binocular 8. Scheiman M, Gallaway M, Coulter R, Reinstein F, Ciner E, Herzberg dysfunctions must be complementary to other binocular tests be- C, Parisi M. Prevalence of vision and ocular disease conditions in a cause an anomalous value cannot be related particularly to any clinical pediatric population. J Am Optom Assoc 1996;67:193–202. dysfunction. This is corroborated by the absence of significant 9. Porcar E, Martinez-Palomera A. Prevalence of general binocular dys- differences between the high, normal, and low values of NRA. functions in a population of university students. Optom Vis Sci 1997; Concerning positive relative accommodation, it seems clear that 74:111–3. there is a relationship between the anomalies associated with ac- 10. Garcia A, Cacho P, Lara F, Megias R. The relation between accom- commodative excess and the presence of a high value of positive modative facility and general binocular dysfunction. Ophthalmic relative accommodation. The finding of a PRA Ͼ3.50 D in pa- Physiol Opt 2000;20:98–104. tients with convergence insufficiency combined with accommoda- 11. Lara F, Cacho P, Garcia A, Megias R. General binocular disorders: tive excess is of special interest because it is the most sensitive sign prevalence in a clinic population. Ophthalmic Physiol Opt 2001;21: 70–4. related to this combined dysfunction. Therefore, the results of this 12. Atchison DA, Schmid KL, Edwards KP, Muller SM, Robotham J. study suggest that a high value of PRA should be included as a The effect of under and over refractive correction on visual perfor- diagnostic sign in general binocular disorders associated with ac- mance and spectacle lens acceptance. Ophthalmic Physiol Opt 2001; commodative excess. 21:255–61. 13. Jackson TW, Goss DA. Variation and correlation of clinical tests of accommodative function in a sample of school-age children. J Am ACKNOWLEDGMENT Optom Assoc 1991;62:857–66. Received August 29, 2001; revision received April 8, 2002. 14. Newman JM. Analysis, interpretation and prescription for the ametropias and heterophorias. In: Benjamin WJ, Borish IM, eds. Borish’s Clinical Refraction. Philadelphia: WB Saunders, 1998: REFERENCES 776–822. 1. Saladin JJ. Phorometry and stereopsis. In: Benjamin WJ, Borish IM, 15. Schor C, Horner D. Adaptive disorders of accommodation and ver- eds. Borish’s Clinical Refraction. Philadelphia: WB Saunders, 1998: gence in binocular dysfunction. Ophthalmic Physiol Opt 1989;9: 724–73. 264–8. 2. Daum KM. Accommodative dysfunction. Doc Ophthalmol 1983; 16. Scheiman M, Wick B. Clinical Management of Binocular Vision: 55:177–98. Heterophoric, Accommodative and Eye Movement Disorders. 3. Matsuo T, Ohtsuki H. Follow-up results of a combination of accom- Philadelphia: Lippincott, 1994. modation and convergence insufficiency in school-age children and Ángel GarcíaMuñoz adolescents. Graefes Arch Clin Exp Ophthalmol 1992;230:166–70. 4. Russell GE, Wick B. A prospective study of treatment of accommo- Departamento Interuniversitario de Óptica dative insufficiency. Optom Vis Sci 1993;70:131–5. Apartado 99. Universidad de Alicante 5. Dwyer P, Wick B. The influence of refractive correction upon disor- 03080 Alicante ders of vergence and accommodation. Optom Vis Sci 1995;72: Spain 224–32. e-mail: [email protected]

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