A review of normative data for parameters of functional non-strabismic binocular vision

Introduction According to O’Connor,1 normative data comprise observations that characterise what is usual or expected in a defined or reference population. This definition emphasises ‘reference population’ indicating that normative data vary among populations. In relation to binocular vision (BV), normative data here refer to population-expected visual function parameters for vergence and accommodation. These parameters of accommodation and vergence are important measures to consider in assessing and classifying non-strabismic BV status and anomalies.2,3 Recent studies4,5,6,7,8,9 have acknowledged that visual function parameters differ among different populations and indicate the need for population-specific normative data. Population, in this sense, is defined in terms of race, ethnicity, gender and age as these are the variables thought to influence accommodation and vergence.4,10,11 These differences in parameters can be attributed to the anatomic differences in the eye,12,13 which can lead to differences in refractive status14,15 and in parameters of accommodation and vergence.2,3 Accurate BV examination, diagnosis and management require reference to the Background: There was a need to document population-expected normative data for parameters of non-strabismic binocular vision (NSBV) as the analysis and diagnosis of binocular vision disorders required comparison of patient’s clinical signs with expected data in their specific population.


Introduction
normative data in the specific patient's population. 6,7.8,9 Even though the aetiology of BV anomalies is either functional or non-functional in origin, 2 this article reviews existing literature on normative data for vision parameters of functional, non-strabismic accommodative and vergence systems.

Methods
A review of literature was conducted using search engines, namely, Google Scholar, Microsoft Academic, Web of Science database and Ovid MEDLINE database. Keywords such as 'normative or expected non-strabismic BV functions', 'normative or expected vergence functions', 'normative or expected accommodative functions', 'normal stereopsis' and 'normative or expected with specific visual function parameter' (e.g. normative or expected near point of convergence [NPC]) revealed numerous papers. For original studies, all articles in their references were also included in the search. This article presents studies written in English only and is aimed at establishing evidencebased normative data for BV parameters. Emphasis was placed on the following: general studies in terms of race, specific studies of children, adults, and clinic and nonclinic patients. Studies are presented according to geographical region and year of publication arranged chronologically. Emphasis is also placed on the specific test techniques used in studies. The use of the term 'distance' means the technique was performed at 6 m, and the use of the term 'near' means the technique was performed at 0.4 m. A summary of observed challenges with reviewed papers and recommendations for future studies are also presented. This article is limited to studies published between 1910 and September 2019.

Ethical considerations
Ethical clearance was obtained from the Biomedical Research Ethics Committee (BREC) at the University of KwaZulu-Natal (number: BE275/17).

Normative data studies in North and South America
Early studies on normative data for BV parameters (Table 1) commenced in the 1940s and were conducted mainly in the United States. Some early studies 16 had investigated problems in schoolchildren and found most of these to be near vision function anomalies. Other studies investigated the most probable or expected data to compare findings. Commonly, Donder's and Duane's tables and Hofstetter's equations served as standard expected measures for evaluating amplitude of accommodation (AA). 17 Haines 18 and Morgan 19 determined normal values for visual function parameters of accommodation and vergence in pre-presbyopic patients. Shepard 20 determined expected vergence function data in 56 adults and children. Morgan 19 indicated that his expected values applied to populations and not to individuals and emphasised that they do not necessarily indicate that a patient has an anomaly of BV if only one parameter falls outside the normal range. 21 Wesson 22 focused on studying fusional vergences with the use of prism bars in 79 clinic participants aged 4-70 years.
The Optometric Extension Programme (OEP) expected values were not derived from population statistics but resulted from thousands of clinic participants of varying age groups. 23 These values went through a standardisation process from the clinical experiences of practitioners; 23 the specific process of standardisation, however, was not defined

BV Test
Haines 18 Shepard 20 Morgan 19 34 reported normative data for heterophorias and distance fusional vergence amplitudes at far among healthy optometry studens with no asthenopic sympotns (Table 1). However, the authors did not indicate whether values were applicable to all age groups or to specific ages only.
The challenge with studies conducted in the United States is that the racial profile of a specific population studied, whether white, black or Latino Americans, was not specified.
Most of the early studies conducted in the United States did not specify the age range of participants but only described the study population as presbyopic, pre-presbyopic, schoolchildren, adults and clinic patients (Table 1).
More recent studies (

Normative data studies in Europe
The oldest study reviewed 40 among Europeans was published in 1990. Dowley 40 sampled 925 participants aged 18-42 years and recorded a distance heterophoria of orthophoria using modified Maddox techniques. The participants had stable refractive errors, were asymptomatic and had stereopsis of 60 sec arc using the TNO stereo test. All other studies reviewed were conducted in the 21st century and few have investigated both vergence and accommodation parameters.
Jimenez et al. 5 conducted a study in a non-clinical paediatric population in Spain to evaluate the evolution of accommodative functions and development of ocular movements. In this study, 5 they provided mean expected values for each age group for the parameters of accommodation, namely, accommodative amplitude, accommodative facility and accommodative response. The mean values with standard deviations of accommodative parameters measured for participants (aged 6-12 years) are provided in Table 4. Another report by Jimenez et al. 10 in elementary schools in the city of Granada, Spain, investigated binocular function in a paediatric population. Participants in that study 10 had no ocular diseases, suppression or systemic diseases. According to the authors, 10 differences in age groups, although statistically significant, were not clinically relevant.
Sterner et al. 41 investigated AA in schoolchildren in Sweden. Normal participants for the study comprised children with no astigmatism, amblyopia, strabismus or anisometropia. According to the study, 41 the AA measures (Table 4) were not as good as expected when compared with Hofstetter's minimum values. McClelland 42 reported normative data for accommodative lag using dynamic retinoscopy (Nott retinoscopy) in healthy school-age children in Northern Ireland. In that study, 42 only schoolchildren with visual acuity of 6/6 or better and children with no uncorrected refractive errors were selected as normal participants. McClelland 42 recorded age-expected normative data across age groups for each of three stimuli test distances with accommodative demands of 4 D, 6 D and 10 D as indicated in Table 4. There was no statistically significant difference in mean accommodative responses across the age groups for the three stimuli test distances. 42 Álvarez et al. 43 studied whether reference values for distance heterophoria and fusional vergence ranges for classic studies were applied to all age groups. Álvarez et al. 43 determined ranges for these parameters in age categories in a visually normal large non-clinic general Spanish population. However, Alvarez et al.'s data only for the age group of 21-30 years and 31-40 years are provided here (Table 4) and there seem to be some differences among these age groups. 43 Glerow et al. 44 in their study of Swedish schoolchildren with normal stereopsis have reported expected measures for the AA, accommodative facility and vergence facility (Table 4). Glerow et al. 44 found values for binocular AA to be similar to Hofstetter's average, whilst monocular AA values were significantly lower. Lanca and Rowe, 45 in a cross-sectional study, reported certain BV measures in asymptomatic Portuguese children (Table 4). These children had bestcorrected visual acuity of 0.0 Log MAR in either eye, compensated heterophoria of 10 prism dioptres, full ocular rotations, presence of fusional vergence and stereopsis of 60 sec arc or better.
There is an observed larger difference in expected stereo acuity measures between the children in Spain 5 and that in Portugal. 45 Stereo acuity of 60 sec arc or better could serve as a current guide for children in Europe. With limited information on NPC in Europe, the current standards for push-up NPC break for European children aged less than 14 years are within an estimated average of 6.4 cm as obtained from two European studies. 10,45 The expected distance and near-lateral heterophoria (NLH) for European children may range from 5 ∆ esophoria to 1 ∆ exophoria, and orthophoria to 4 ∆ exophoria, respectively. 10,43,45 These three studies, however, used different techniques, making value applicability difficult. The expected average push-up monocular AA for European children aged 6-13 years is estimated to be at 10 D -16 D. 5,41,44 The accommodative response (lag) for European children aged 4-15 years may be estimated at 0.00 D -0.80 D 5,42 The monocular accommodative facility (MAF) and binocular accommodative facility (BAF) measures for European children are estimated at not more than 11 cpm 5,44 and 9 cpm, respectively. The authors did not find any study in Europe that has investigated normative data for positive relative accommodation (PRA) and negative relative accommodation (NRA). Jimenez et al. 5,10 did not evaluate for NRA and PRA, indicating that these parameters evaluate interactions between accommodative and vergence systems.

Normative binocular vision data studies in Asia
The first study in Asia by Kim 46 in 1979 determined normal values for AA among South Koreans and divided participants into 13 groups based on age. This study used the minus-lensto-blur technique using Duane's single fine thread as the target. Values for age groups less than 30 years are indicated in Table 6. All other studies reviewed were published in the 21st century and four out of six studies reported measures for both parameters of accommodation and vergence; however, these four studies did not report on all parameters of accommodation and vergence.
Chen et al. 47 in their study on near visual functions in children sampled 268 participants aged 2-15 years using the Modified Maddox technique that found distance phoria of 1.29 ∆ exophoria. Chen and Abidin 4 conducted a study comprising normal primary schoolchildren in Malaysia with a visual acuity of 6/6 and better with no history of previous eye problems. Parameters measured included accommodative facility, accommodation accuracy, relative accommodation,      Tables 5 and 6. Chen and Abidin 4 found significant differences among different age groups for measures of positive and negative fusional reserve at distance and negative fusional reserve at near. The specific average values of these measures are, however, not reported.
Razavi et al. 48 investigated normative data for fusional vergence parameters in Iranian adults who were the target group for keratorefractive surgery (Table 5). For Razavi et al. 48 , the selection criteria for normal participants were adults with no significant eye disorders, including high refractive errors with best-corrected visual acuity better than 20/25, stereopsis of more than 60 sec arc and no heterotropia. There was no significant correlation between the age of participants for fusional amplitudes. 48 Abraham et al. 6 have investigated for normative data for NPC, accommodation and phoria in an Indian population. They used techniques that have good repeatability and reliability such as a penlight with red and green anaglyph for NPC, minus lens technique for AA and the modified Thorington method for horizontal and vertical phoria at distance and near. Patients with asthenopic symptoms were excluded using a selfadministered symptom questionnaire (a shortened version of the Convergence Insufficiency and Reading Study group questionnaire). The participants were categorised into three groups: group 1: aged 10-18 years, group 2: aged 19-27 years and group 3: aged 28-35 years. Data were recorded on the basis of these three groups (Tables 5 and 6).
Hussaindeen et al. 49 designed the 'Binocular Vision Anomalies and Normative Data' (BAND) study conducted in rural and urban schoolchildren in Tamil Nadu, India. All children underwent an initial screening protocol that involved a series of testing (e.g. visual acuity, external exams, internal exams, refraction and stereopsis assessment). After screening, children with no abnormalities had a comprehensive BV and accommodative assessment. Asymptomatic children who passed the comprehensive BV assessment protocol with no difficulty in any of the procedures were included in the normative data study. Using the above protocol, Hussaindeen et al. 7 conducted a population-based cross-sectional study in a sample of Indian children and established normative data for some parameters of BV and accommodation. The mean values and standard deviations of the measured parameters (Tables 5 and 6) are compared with the measures of other studies in Asia.
Hashemi et al. 50 determined normal values of accommodative amplitudes among adolescent high school students in Iran ( Table 6) and found that the AA is lower in Iranian teenagers than that calculated with Hofstetter's formula. Yekta et al. 9 conducted a cross-sectional study in normal young adult Iranian university students to determine binocular and accommodative characteristics and their association with age and gender. Participants with visual acuity of less than 20/25 in each eye, strabismus, pseudo myopia, latent hyperopia, ocular or systemic diseases, using topical or systemic medications and with stereopsis less than 400 sec arc were excluded. The binocular and accommodative characteristics and their mean values in the studied sample are shown in Tables 5 and 6. Yekta et al. 9 also presented mean values and standard deviations for each of the parameters measured according to age group. The measures of positive fusional vergence break and recovery at near were higher in women, but exophoria was significantly higher in men. Some parameters, namely, NPC, distance exophoria, distance base-in-recovery and distance base-in-break, increased with age, whilst other parameters, namely, near base-out-break, AA, BAF, MAF and PRA, significantly decreased with age. The study result indicated that age and gender affect certain parameters of vergence and accommodation.
A summary of expected BV parameters from the existing studies in Asia is included below. The norms of stereo acuity for the Asian population with an age range of 18-40 years are estimated to be 45 sec arc -19.5 sec arc. 7,48 The push-up NPC break norms for Asian population with an age range of 7-35 years are estimated at 3 cm -8.87 cm, 7,9 and the push-up recovery norms for Asian children aged 7-18 years are estimated to be 4 cm -8 cm. 7 The standards for distance lateral heterophoria (DLH) for Asians aged 6-35 years are estimated to be 1 ∆ esophoria to -3 ∆ exophoria. 4,6,7,9 The standards for NLH for Asians children are estimated at 2 ∆ esophoria to 6 ∆ exophoria, 4,6 and for adults, it ranges from 3 ∆ esophoria to 10 ∆ exophoria. 6,9 The norms for vergence facility for Asian children are not less than 8 cpm. 4,7 The expected accommodative response for Asian children aged 6-18 years is estimated at 0.25 D -0.67 D. 4,7 This is applicable to children in Malaysia and India. The expected values of MAF for the Asian population aged less than 35 years are estimated at 7 cpm -17 cpm 7,9 using 2 D flippers. The expected AC/A ratio for Asian children is estimated at 5/1, 7,9 the expected estimated range of PRA is 2.16-5.22 4,9 and that for NRA is 1.75-4.04. 4,9 Normative data studies in Africa The first study in 1988 by Kaimbo et al. 51 Table 7.

Comparing normative data across continents
Comparing the average values and range of normative data of studies conducted in similar age groups, the following findings and conclusions are made from the summary normative consensus from different continents. The average push-up NPC break is comparable between African (6.9 cm) and European children (6.4 cm); the average push-up NPC break is slightly lower for wider age range of American children and adults (5 cm) compared with a wider age range of Asian children and adults (6 cm). The range of push-up NPC recovery is, however, higher in African children (6 cm -13 cm) than in Asian children (4 cm -8 cm). The expected range for DLH in Americans is comparable with that of Asians (1 ∆ esophoria to 3 ∆ exophoria), slightly different from Africans (2 ∆ esophoria to 2 ∆ exophoria) but lower in range than Europeans (5 ∆ esophoria to 1 ∆ exophoria). The expected range values for NLH are different for different continents, being orthophoria to 6 ∆ exophoria for Americans, orthophoria to 4 ∆ exophoria for European children and comparable between Asian and African children (2 ∆ esophoria to 6 ∆ exophoria). It could be seen that the maximum NLH does not exceed 6 ∆ exophoria, being comparable for Americans, Asians and Africans. The expected range of stereo acuity for African children is wider (43.9 sec arc ± 25.2 sec arc) compared with Europeans (60 sec arc or better) than Asians (45 sec arc -19.5 sec arc).
The expected average MAF is higher for European children (11 cpm) as compared to African children (8.7 cpm), who have a lower average than American children (6.5 cpm). The expected average BAF measures in European and African children are comparable (9 cpm); however, it is wider in range for Africans (standard deviation [SD] ±3.5). The norms for vergence facility for Americans are higher (15 cpm ± 3 cpm) as compared to Asian children (˃ 8 cpm); however, the data from America were derived from a wider age range comprising children and adults. The range for accommodative response (0.25-0.75) is comparable among Americans, Asians, Europeans and Africans. It is, however, slightly higher for Europeans by approximately 1 D. The range of NRA is greater in Asian populations (1.75 ± 4), compared with Americans (2.00 ± 0.5) and Africans (2.17 ± 0.48). The expected range of PRA is wider for the Asian population (−2.16 to −5.22), and comparable between the American population (−2.37 ± 1.00) and African population (−2.44 ± 0.71). The expected gradient AC/A ratio is higher for Asian children (5:1) as compared to European children (1.9 ± 0.54:1). There is a lack of consensus on AA measures within and across continents. The Hofstetter's equations guide AA data for Americans; however, in other continents it may not be applicable.

Challenges regarding reviewed studies
The most commonly and widely used criteria for NSBV are that of Morgan 19 and Scheiman and Wick, 3 whose norms are considered as current standards. 6,7 The challenge with these standards is that they were derived from the American population and thus are basically applicable to Americans assumed to be in the age range of 6-40 years. 7,8 The various studies mentioned above were conducted in different populations with different age groups using different techniques; hence, this makes direct comparison of values difficult. Hussaindeen et al. 7 found certain parameters for It is still not clear as to whether gender influences the parameters of vergence and accommodation as very few studies 9,50,59 have investigated gender biases because these affect normative data for visual function parameters. Some studies 50,59 have reported that females have higher AA than age-matched males. According to other authors 60 , this gender difference is not caused by physiological differences in accommodation but rather because females have shorter arms than males. The shorter arms increase habitual accommodative demand for near work in females. As some BV parameters could be different at far and near, most studies investigated these parameters at far and near, whilst only one study 43 investigated and reported for heterophoria and fusional vergence parameters at distance only.

Measures for classifying vergence accommodative dysfunctions
The complicated nature of the accommodative and vergence system makes it inadequate to differentially diagnose such anomalies using only single parameters referred to as clinical signs. Correlated clinical signs or visual function parameters that form a syndrome for each anomaly best define the disorders of accommodation and vergence. 3,8,19 The most common clinical signs include NPC, heterophoria, fusional vergence amplitudes, accommodative amplitudes, accommodative facility, accommodative lag, relative accommodation and stereo acuity. 3 The visual parameters or clinical signs used to differentially diagnose anomalies of the vergence system include measures for fusional vergence amplitude at near and far, horizontal and vertical heterophorias at near and far, vergence facility and NPC. 10 Amplitude of accommodation, accommodative response (lag or lead) and monocular accommodative facility are used to characterise the accommodative system. 5 To evaluate interaction between the vergence system and the accommodative system, visual parameters, namely, NRA, PRA, BAF, stimulus AC/A ratio and stereo acuity, are used. 10 62 In controlling for suppression, the test is stopped if the suppression is detected, resulting in lower values for break.
One study reported that NPC is dependent on age, with younger ones having worse NPC than adults. 9 There is thus a need to document expected NPC results based on age. 8,63 During NPC testing, the patient's convergence ability is determined and all three aspects of convergence -namely, fusional, proximal and accommodative convergence -are used. The main targets for NPC are the accommodative target and light source but they have their limitations and advantages. 7 The accommodative target may not be ideal in cases of reduced AA. 7 However, it produces more accurate NPC measurements and gives less variability. 35,64 A light source target may cause accommodative vergence to fluctuate, possibly giving inconsistent readings because the target is a diffused low spatial frequency source. 35 However, measuring NPC with a red lens may reduce the effect of voluntary convergence. It is recommended that an accommodative target should be used first because it provides more accurate readings. 64 In cases where the results from an accommodative target are borderline, or there are signs and symptoms indicative of convergence insufficiency (CI), the NPC could be repeated using a penlight target with the patient wearing redgreen filters. 7,8 Studies have established that using a penlight target with red-green anaglyph is a more sensitive test for diagnosing convergence insufficiency. 57,64 Most studies measured AA using the push-up technique. 8 The minus-lens-to-blur technique, however, has been reported to underestimate AA, whilst the push-up technique tends to overestimate AA. 8 It is recommended that future studies must investigate for normative data using both pushup technique and minus-lens-to-blur technique. The accommodative facility measure is relevant to diagnose various accommodative anomalies. 3 According to Wajuihian 8 and others, it is recommended that suppression controls are used in measuring BAF even though some studies normally use the Worth Four-Dot test to screen for suppression as was performed in their study. According to Wajuihian, 8 expected data for accommodative response across studies seem to be the most consistent accommodative measure and this may be because the test is an objective one. The relative accommodation tests are influenced by changes in refraction and indirectly measure the vergence system. 3 Lastly, refractive errors, such as anisometropia, affect stereo acuity thresholds and thus must be corrected before checking stereo acuity. 8,65 This is because anisometropia presents with aniseikonia and retinal disparities, and there is more fovea suppression in defocused eyes. 65

Conclusion
Across the globe, most of the studies on this topic have been conducted in America, followed by Europe and Asia, with few studies conducted in Africa. Recent studies have investigated most visual function parameters for both accommodation and vergence. The reviewed normative data were determined for specific populations and age groups, and most of the studies have used different methodologies or testing. According to Hussaindeen et al.,7 'to optimise the sensitivity and specificity of diagnosis, ethnicity-specific cutoff values for BV parameters are mandatory'. Each of the expected values reviewed must be applied only to the population of the study. It was expected that studies that recorded different normative values 7,66,67 may attribute their differences to variations in population, race or ethnicity rather than to methodologies and techniques used. Different study designs and mostly smaller samples in reviewed studies make it difficult to attribute differences in normative data in different studies than to differences in the population used or differences in methodology and techniques.
Again with limited studies and data in and across continents, it is difficult to draw a global consensus on these parameters of NSBV. We recommend large population-based comprehensive normative data studies (targeting parameters of both accommodation and vergence) using most reliable and repeatable, objective and subjective techniques with good methodology in different populations of each continent to clarify these differences or otherwise. In selecting normal participants, we recommend Hussaindeen et al.'s 49 criteria with slight modifications, which include administering a reliable and validated asthenopic symptom questionnaire to select asymptomatic participants first before preliminary vision screening on asymptomatic participants. We also recommend including a suppression test such as the Worth Four-Dot test in preliminary vision screening to exclude participants with suppression and checking for suppression during fusional vergence and BAF measurements. Populations at risk, such as school-going children, should be the first point of consideration and authors must consider comparing these parameters among genders, as only one study 9 has determined that gender affects these parameters. A few studies have suggested contrary results for gender.