Aniseikonia occurs when a subject’s visual system has difficulty combining two perceived images of different size and/or shape in a single perceived image. The condition is considered clinically significant when there is a size difference of ≥1% between the right and left images. When aniseikonia produces symptoms of asthenopia or suppression, its treatment will have to be considered.1–5
Aniseikonia was initially described and explored in the 1940s and 1950s. Today, there is renewed interest in this visual anomaly as a result of the considerable increase in the number of patients who experience aniseikonia.6 The large number of patients with symptoms attributable to aniseikonia make this condition a significant public health issue.4 Aniseikonia is mostly observed in patients with an anisometropia >1.00 D corrected with lenses, representing between 5% and 10% of the population.7 Individuals at risk of experiencing aniseikonia are those with anatomic differences between the eyes, patients undergoing refractive surgery (laser in situ keratomileusis, photorefractive keratectomy, and so on), and pseudophakes. Refractive or cataract surgery frequently gives rise to residual refractive differences between the eyes.8–10 Kramer established that around 40% of pseudophakes have symptoms associated with aniseikonia.11
The asthenopic symptoms referable to aniseikonia are not specific to this anomaly. There is therefore a need for an efficient, precise clinical instrument that will easily identify and measure aniseikonia and help prescribe the appropriate treatment. Traditional estimation methods show low repeatability in clinical terms and are inappropriate for deciding on the treatment of aniseikonia.12–14
There are basically two methods of measuring aniseikonia: 1) stereoscopic techniques and 2) direct comparison methods. Stereoscopic eikonometers cannot be used in patients who lack central binocular vision, whereas the direct comparison eikonometers do provide a measure of aniseikonia in many of these patients. The best reference test for methods of evaluating aniseikonia is the Space Eikonometer (American Optical Co., New York, NY). However, although it is generally accepted that this system is the most precise, the instrument has not been produced for several decades. Among the direct comparison tests for measuring aniseikonia currently available, the New Aniseikonia Test (NAT; Handaya Co., Tokyo, Japan) is one of the best known. However, reports in the literature concerning the clinical use of the NAT are mixed and several authors have warned of its tendency to underestimate aniseikonia.15,16 In contrast, the repeatability of the NAT has not been the focus of previous studies. There is thus a need to examine the validity of this test on a large sample population and to explore its repeatability for measuring aniseikonia in subjects, including risk groups.
To establish the diagnostic value of the NAT, we set the following specific objectives: 1) to estimate the validity of its measurements by comparing the measured aniseikonia with the aniseikonia simulated through calibrated size lenses; 2) to assess its repeatability by comparing initial and final measurements in three groups of subjects comprised of controls, anisometropes, and pseudophakes; and 3) to establish whether anisometropia corrected with lenses is the main cause of aniseikonia. To verify the expected direct relationship between anisometropia and aniseikonia, we also determined the correlation between subjective refraction and aniseikonia.
Subjects were recruited from the students and teachers of the School of Optics of the Complutense University of Madrid and from the San Francisco de Asis Hospital in Madrid. Informed consent to participate was obtained after the nature of the study had been fully explained. The study protocol fulfilled the tenets of the Declaration of Helsinki. The final study population was comprised of 100 subjects who satisfied the inclusion criteria. Individuals were excluded if they were incapable of fusing the images formed on the retina or experienced any eye disease. We also checked that all the subjects were able to simultaneously view the red and green parts of the aniseikonia test chart. The specific inclusion criteria for each subject group were:
- Control group: subjects with <1 D of anisometropia, a best-corrected visual acuity (VA) for each eye greater than or equal to 20/20 and stereopsis greater than or equal to 30” of arc.
- Anisometropia group: anisometropes showing 1 D or more of anisometropia and a best-corrected VA for each eye greater than or equal to 20/25.
- Pseudophakia group: patients operated on for cataracts implanted with an intraocular lens as a group at risk of having aniseikonia.10,11 These patients with bilateral pseudophakia were selected to complete the repeatability study and showed a best-corrected VA for each eye greater than or equal to 20/25 at distance and near.
A questionnaire was completed to record the age, sex, and ocular history of each subject. The optometric characteristics of the subjects were then established in refraction and binocular vision tests.
The corneal radius and objective refraction were determined using a Shin Nippon SRW 5000 autorefractometer (Shin Nippon, Tokyo, Japan). Subjective refraction was established by the conventional method using Snellen optotypes projected at 6 m and a manual phoropter. In the pseudophakes, near refraction was also determined. The control subjects and the anisometropes underwent several binocular vision tests; they were checked for their accommodative facility, horizontal phoria using the von Graefe technique, horizontal fusional vergence range, and stereopsis (Randot and TNO).
Tests of Aniseikonia
The NAT developed by Awaya is a printed direct comparison test of aniseikonia. Dissociation is achieved using anaglyphic filters. In this test, the starting point is two semicircles of the same size (one red and one green) and the subject has to say if he or she perceives them as equal in size or if one semicircle is larger than the other. If the semicircles appear the same, the measured aniseikonia is 0%. In contrast, if the image sizes appear different, the subject is presented with semicircles of different sizes until they are perceived as having the same dimensions. Aniseikonia was measured in vertical and horizontal directions. The distance between the eyes and the test was 40 cm. Before recording the first aniseikonia measurements, the subjects were given time to familiarize themselves with the test protocol. We also took a trial measurement to verify if the subjects had understood the task.
Because of anaglyphic dissociation, heterophorias may generate instability of the images17 and make it difficult to compare the size of the semicircles. To compensate for uncorrected heterophorias, prisms were inserted in front of the left eye in all the subjects who required them.
Measurement of Aniseikonia
The measurement of aniseikonia is a subjective test in which the examiner limits himself or herself to recording the results observed by the patient. During the measures of aniseikonia, both the subject and the examiner were masked to the test conditions.
During the measurements, control and anisometropic subjects used their best correction for far sight and pseudophakes their best near correction. Examiner 1 placed the subject’s best optical correction and the size lenses in a trial frame. Examiner 2 (repeatability study)/examiner 3 (validity study), who were blind to the subject’s correction, were responsible for measuring aniseikonia. According to Bland and Altman,18 the best way of assessing the repeatability of an instrument is to take several measurements in a series of subjects. We determined aniseikonia at two different time points separated by an interval of at least 24 hours between them. In postsurgery patients, owing to mobility problems, tests 1 and 2 were performed in the same session. These data were obtained by the same optometrist (examiner 2) and the first set of measurements was not inspected until the second tests had been completed.
To avoid the learning effect, during the second set of tests, aniseikonia measurements were interspersed with other measurements to distract the subject. In these distracting tests, image size increases or decreases were induced through the use of afocal trial lens magnifiers. After the repeatability study was complete, control subjects were given another appointment to examine the validity of the NAT in a double-blind study. Aniseikonia was induced with afocal trial lens magnifiers (−3%, −1.5%, 0%, 1.5%, and 3%) and both horizontal and vertical aniseikonia was measured. Given that the magnitude of the size lenses can be guessed from their thickness, the margins of the lenses in the trial frame were covered.
The order in which the magnifier was used was randomized by: 1) alternating horizontal and vertical measurements; and 2) randomly mixing different levels of simulation such that each subject was requested to pick out a numbered ball to determine the two first elements (vertical and horizontal) of the sequence of measurements from a list with all the possibilities. Examiner 1 randomly selected the order of the rest of the measurements.
Trial Lens Magnifiers
The percentage of induced magnification was +3%, +1.5%, 0%, −1.5%, and −3%. To check the accuracy of the trial lens magnifiers, we measured all the variables that determine the shape factor and power factor of an ophthalmic lens. The power factor was zero, independently of the distant vertex, and the shape factor was equal to the magnification of the lens. These lenses were inserted in front of the right eye in the outermost groove of the trial frame. To avoid vertical misalignment (deviation) of the two semicircles, it should be ensured that the trial frame is adjusted correctly and that the subject is positioned directly in front of the test when the measurements of aniseikonia are taken through the simulation lenses.
Vectorial Notation of Spherical– Cylindrical Refraction
During the data analysis, we used vectorial notation of spherical–cylindrical refraction following the criteria of Harris.19 This notation allows a direct comparison to be made of the subject’s refraction in different meridians; in particular, it allowed us to calculate anisometropia separately for the horizontal and vertical meridian. Depending on the degree of anisometropia, the subjects were classified as controls or anisometropes.
Once the data had been collected for the whole sample, they were processed statistically using the Analyze-It program for Excel. To evaluate the test’s validity, the aniseikonia data were subjected to linear regression analysis and the slope compared with –1.0.
Test repeatability analysis was also carried out using the Bland and Altman method.18,20 This test is useful when between-session differences (initial and final) are approximately normal and the mean difference is close to zero. To check these assumptions, a preliminary Anderson-Darling test for normality and a matched-paired t test were conducted. If both of these tests were nonsignificant, then we continued with the Bland-Altman method.21 Mean differences (biases), standard deviation (SD) of the differences, coefficients of repeatability (COR, 1.96 × SD), and 95% limits of agreement (bias ± COR) were computed. When any of the preliminary tests were significant, we considered the distribution of absolute differences. In place of the COR, we computed the 95th percentile of the absolute differences. Like the COR in the case of normality and a zero mean, this 95th percentile of the differences is a threshold for the differences in successive measures that would have to be exceeded to conclude that a true shift in value had occurred as opposed to an observed difference that can be explained by the natural variation in the measure. In clinical terms, the advantage of this method is that the repeatability of the test is expressed in the same units of measurement as the test itself and thus allows the clinician to establish his or her own criteria as to whether or not a change is significant.
The initial sample (n = 100) was divided into three groups:
- Control group (n = 45). The subjects allocated to the control group had <1 D of anisometropia. The age range was 19 to 44 years (mean, 23 years). The range of ametropia was –5.25 to +6.50 D for the sphere and up to –3.50 D of astigmatism. Ten participants were tested with a prism in front of the left eye, power range: 7Δ BO to 10Δ BI (mean, 0.1Δ BO; SD, 5.8Δ).
- Group of anisometropes (n = 29). These subjects presented 1 D or more of anisometropia (range, 1.00–4.00 D). The age range was 19 to 25 years (mean, 22 years). The range of ametropia was –9.00 to +4.25 D for the sphere and up to –4.50 D of astigmatism. Twelve participants were tested with a prism in front of the left eye, power range: 15Δ BO to 8Δ BI (mean, 3Δ BO; SD, 6.6Δ).
- Group of pseudophakes (n = 26). This group was comprised of subjects with bilateral pseudophakia. Ages ranged from 55 to 86 years with 73 being the average age. Near refraction was –1.50 to +4.75 D for the sphere and up to –2.50 D of astigmatism. Twelve participants were tested with a prism in front of the left eye, power range: 6Δ BO to 1Δ BI (mean, 4Δ BO; SD, 1.4Δ).
This part of the experiment was designed to determine whether the aniseikonia test is able to adequately estimate the degree of simulated aniseikonia in normal subjects.
When aniseikonia was induced using afocal lenses of known magnification, the aniseikonia measured by the NAT was less than expected. Figure 1 shows the values of aniseikonia measured related to the induced magnification in the control group. The dotted line of slope –1.0 indicates the expected values for a normal subject (without aniseikonia). The continuous line represents the least squares adjustment of the data with the equation shown in the lower left corner of each graph. The offset bars correspond to a standard deviation. It can be seen that the slope differs significantly from –1.0, which is interpreted as underestimated aniseikonia. The slope was –0.17 less in the vertical direction (p < 0.0001) and – 0.35 less in the horizontal (p < 0.0001); i.e., the underestimation is greater in the horizontal direction. The Y-axis intercept only differs significantly from zero in the horizontal direction (intercept at –0.20 [p = 0.02]). The Y-intercept represents inherent aniseikonia in the subjects (0% induced magnification) and because they belonged to the control group, they would not be expected to display significant inherent aniseikonia (>1%) given their anisometropia was ≤1.00 D.
Table 1 shows the COR or the 95th percentiles and biases for the NAT measurements. These data were categorized according to the subject group (control, anisometropes, pseudophakes) and the direction of measurement (vertical, horizontal). Although we discuss these results below in more detail, in the table, it can be seen that there are no substantial differences in the reliability coefficients of the different states.
To interpret the signs correctly, it is important to remember that the simulation lenses must always be inserted in front of the right eye. The +3% and +1.5% lenses increase the size of the image and the –3% and –1.5% lenses reduce the size of the image. According to the sign convention adopted in our study, we defined the conditions:
Negative aniseikonia: image perceived by the right eye greater than that viewed by the left eye. Simulated with +3% and +1.5% lenses.
Positive aniseikonia: image perceived by the right eye smaller than that viewed by the left eye. Simulated with −3% and –1.5% lenses.
There was no uniform tendency toward an increase or decrease in the measured aniseikonia in the final evaluation compared with the initial one. All the 95% difference intervals were relatively high, so that we can say that the reliability was low. The 95% difference intervals in repeated measurements ranged from ±1.49% (control group, vertical) to ±2.75% (pseudophakes, horizontal). No significant differences were found between groups.
Correlation Between Subjective Refraction and Aniseikonia
We tested the hypothesis that a greater degree of anisometropia is related to a greater degree of aniseikonia. For the whole subject group (n = 74), this correlation study revealed that without simulation (0%) of aniseikonia, there was moderate positive correlation between these two factors for the vertical (r = 0.63, p < 0.0001) and horizontal (r = 0.29, p = 0.01) directions. When only the anisometropic subjects were considered, results were similar (see Fig. 2) for the vertical direction (r = 0.68, p = 0.0005), but there was a discrepancy for the horizontal direction (r = 0.05, p = 0.83).
Comparing Vertical and Horizontal Aniseikonia Measurements in the Control Group
This behavior led us to think that the precision of the test could be different for the two directions. To explore this idea, aniseikonia measurements obtained in the vertical and horizontal directions in the control group were compared. We used only control group data because in these subjects, we would expect no differences between horizontal and vertical aniseikonia measurements given the fact that they lacked clinically significant anisometropia (Table 2). The bias corresponds to the mean difference (horizontal – vertical). The t test for paired samples revealed statistically significant differences between the vertical and the horizontal directions in many of the percentages of induced aniseikonia.
It may be observed in Table 2 that in the majority of cases, the vertical aniseikonia was significantly greater than the horizontal. This finding was coherent with the fact that the underestimation found in the measurement of aniseikonia was greater in the horizontal direction than in the vertical, as already mentioned when discussing the validity of the test. This behavior may be linked to the greater precision in the measurements of aniseikonia in the vertical direction noted by other authors.16,22
Our study is limited in its assessment of validity because there is no good gold standard available with which to compare this feature of the NAT. In the past few years, the method most widely used to assess the validity of aniseikonia tests has been to simulate different levels of known aniseikonia with size lenses and compare the measured percentage of aniseikonia with the simulated percentage.
Our validity results indicate that if the test behaves in the same way with patients as with our study subjects, individuals with a real substantial difference between the size of the images perceived by the two eyes (2–5%)1 could give rise to a test result of clinically insignificant aniseikonia with the NAT (<2%) because of its reported tendency to underestimate this condition, especially in the horizontal direction.
In a similar study but with fewer subjects (n = 15) performed by McCormack et al.,16 no differences were observed between the horizontal and vertical direction. In both directions, the slope was –0.31, significantly less than expected (p = 0.0001) and the Y-intercept, –0.97, differed significantly from zero (p = 0.0001). Our difference in slope for the horizontal direction was comparable to that obtained by McCormack, −0.35 (p < 0.0001), whereas for the vertical direction, the difference was smaller at −0.17 (p < 0.0001). In addition, the intercept with the Y-axis of −0.20 recorded here only differed significantly from zero in the horizontal direction (p = 0.02) and was four times less that found by McCormack. Stewart and Whitte15 also found that the mean aniseikonia in 16 subjects was normally less than that simulated with different size lenses. On average, this measured aniseikonia was one-third lower than the simulated aniseikonia.
Awaya et al.23 attributed the underestimation of the NAT in normal subjects to the vertex distance of the size lenses, which is difficult to justify if we take into account that these are afocal lenses and the induced increase does not depend on the vertex distance.
The work by Bradley et al.24 on the chromatic magnification of ocular images indicates that the anaglyphs used in the measurements can only account for a small proportion of the underestimation of aniseikonia (<0.25%). In McCormack’s study,16 it was speculated that the main factor causing underestimation is a sensorial fusion response, which leads to rescaling of the image. This argument, with which we concur, was already suggested by Awaya et al.23 in the early 1980s.
A possible explanation for the lower validity of tests of aniseikonia in the horizontal direction compared with the vertical is the higher incidence of heterophorias and fixation disparity on the horizontal plane, which may provoke image instability17 and make it difficult to compare the sizes of the semicircles.
We tried to establish whether the repeatability of the test varied between the control group, anisometropia group and pseudophakes group, because subjects in these last two groups have a high risk of aniseikonia. However, our results indicated no significant differences in the repeatability of the test between groups of subjects.
The biases observed were not statistically different from zero and irrelevant in clinical terms. Nevertheless, the COR corresponds to clinically significant differences in the degree of aniseikonia measured. This could be explained by the fact that the majority of subjects with aniseikonia-related symptoms show size differences of between 2% and 5%.1,25,26 From Table 1 it may be observed that the mean repeatability coefficients were ±1.75% (vertical) and ±2.09% (horizontal) so that only aniseikonia measurements with NAT >2% can be considered reliable indicators of a visual problem.
Recently, another test to measure aniseikonia has appeared on the market, the Aniseikonia Inspector Version 1 (Optical Diagnostic, Culemborg, The Netherlands). According to the available data, this test seems to only slightly underestimate aniseikonia and as soon as its repeatability is improved, it might become a good alternative to the NAT.22,27
Few studies on aniseikonia have evaluated subjects with bilateral pseudophakia. Kramer et al.11 measured aniseikonia at distance with the Essilor Projection Space Eikonometer (Essilor, Paris, France) in subjects with uni- and bilateral pseudophakia. The range of aniseikonia in his group of patients operated on both eyes (n = 33) was 0% to 7% with a mean of 3.2% and a standard deviation of 2.6%. In our case, mean measured aniseikonia ranged from 0% to 3% of the absolute value with a mean of 0.68% and a standard deviation of 0.64%. As can be observed, our aniseikonia values are notably different from those of Kramer. This discrepancy could be attributed to the different measurement systems used: 1) Kramer et al. used a system based on space eikonometry, and the NAT is a direct comparison method; 2) their system presents different images to each eye through polarized filters, and we used more dissociative anaglyph filters; and (3) they measured aniseikonia for distance vision (6 m), and we measured it for near vision (40 cm).
A further finding of interest in our pseudophakia population was the low correlation between the level of postoperative residual anisometropia and aniseikonia. This behavior was also observed by Kramer.11
Most subjects undergoing cataract surgery are elderly and, as a result, have a lower adaptation capacity to visual changes. In addition, the percentage of subjects with significant residual anisometropia after a cataract operation is high (58% of our group of pseudophakes presented a residual anisometropia greater than or equal to 1.00 D) and so are a clear risk group for symptoms associated with aniseikonia. The inconclusive results of our study for this group of subjects suggest the need for future work in this area.
Our findings indicate aniseikonia is underestimated when simulated (±1.5% and ±3%) and that this underestimation is greater in horizontal than in vertical measurements. That is to say, the validity of the NAT in the vertical direction is greater than in the horizontal. Similarly, it was found there were more subjects in the control group in whom aniseikonia measured in the vertical direction was greater than in the horizontal. Thus, the clinician should be aware that it is likely that aniseikonia will be underestimated both because of the NAT and the capacity of the patient to tolerate eye image differences.
As far as we are aware, this is the first evaluation of the repeatability of the NAT such that our results cannot be compared with those of other researchers. There is therefore a need for future studies to confirm the conclusions drawn here. Although biases between repeated clinical measurements were not statistically significant, the 95% limits of agreement were high. Thus, it can be concluded that the repeatability of the test is low and only changes greater than ±2% fall outside the margin of error of the measurements at 95%. The test did not perform better in anisometropes or pseudophakes compared with the control subjects.
Although repeatability is not the only criterion to consider, in general, good repeatability is necessary for a test to discriminate well. Hence, a test with low repeatability such as the one assessed here should be used with caution to measure aniseikonia. For the time being, although direct comparison tests are not entirely reliable, they can be used to help the clinician confirm the presence of aniseikonia and to justify treatment in symptomatic patients in whom moderate aniseikonia (2–5%) is suspected.
This study was supported by grant PR3/04 to 12,368 from the Universidad Complutense de Madrid.
We thank Jesus Pizarroso for his help with testing pseudophakic subjects and Essilor-España for kindly donating the size lenses used to induce aniseikonia.
Escuela Universitaria de Óptica
(Universidad Complutense de Madrid)
C/Arcos de Jalón s/n, 28037 Madrid, Spain
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