Optimizing the algorithm for assessing the efficacy of treatment for amblyopia in astigmats through the investigation of the features of meridional acuity characteristics as vector quantities

Background: Refractive asymmetry associated with astigmatism may cause a special form of amblyopia, meridional amblyopia (MA). MA manifests itself as alterations in selective mechanisms of visual stimulus processing during recognition of contours of a certain orientation. Current routine examination of amblyopes does not include meridional acuity assessment and thus does not allow determining whether MA is present or not, as well as performing a more detailed evaluation of the efficacy of treatment for amblyopia in astigmats. Purpose: To optimize the algorithm for assessing the efficacy of stand-alone and complex methods of treatment for amblyopia in astigmats through the determination of the features of changes in visual acuities in orthogonal retinal meridians as vector quantities. Material and Methods: Twenty-four hyperopic astigmats with amblyopia (48 eyes) aged 5 to 12 years were involved in the study. Patients were treated by accommodative facility training only and, in 3 months, by complex therapy (accommodative facility training plus the use of device-based methods). Treatment course duration was 10 days. The results were assessed by changes in best-corrected visual acuity (Sivtsev Chart) and meridional separable visual acuity (MSVA) determined with the software which generates Landolt ring optotypes. Results: The study sample was found to be heterogeneous regarding the features of asymmetries in MSVA. Separable visual acuity in the horizontal meridian was equal in magnitude to that in the vertical meridian in 16.65% of patients. Asymmetries in separable visual acuity that may be considered MA were found in dominant and non-dominant (fellow) eyes in 83.35% of astigmats with amblyopia. Two different clusters were determined in the group with asymmetries in MSVA. Separable visual acuity in the horizontal meridian was higher than that in the vertical meridian in 35.45% of eyes in cluster 1, and lower than that in the vertical meridian in 47.85% of eyes in cluster 2. After treatment, mean separable visual acuity value in the vertical meridian was practically similar to that in the horizontal meridian in both groups for the dominant and fellow eyes, which allowed concluding that both methods were equally effective in treating the disease. However, the number of eyes with the same MSVA in orthogonal meridians increased by 10.41% after MA treatment with accommodative facility training only versus 18.75% after complex treatment. Conclusion: Assessing the features of changes in visual acuities in orthogonal retinal meridians as vector quantities enables obtaining principally new information on the performance of sensory functions in patients with amblyopia and assessing more reliably the efficacy of stand-alone and complex pleoptic methods as methods of treatment for MA.


Introduction
Refractive asymmetry associated with astigmatism may cause a special form of amblyopia, meridional amblyopia (MA) [1][2][3][4][5][6].MA manifests itself as selective alterations in visual acuity (VA) during recognition of contours of a certain orientation, which results in an alteration in the mechanisms of mechanisms of integrated processing of visual stimulus, cognitive perception and visual performance [3,7].It is noteworthy that current visual acuity charts do not allow to determine meridional VA and, consequently, to determine the presence or absence of MA.In addition, studies have demonstrated low sensitivity and accuracy for these charts in the evaluation of VA in amblyopes [8].For this reason, it is still unknown whether certain individual or comprehensive pleoptic methods are effective for the treatment of MA.It is believed that including the method of determination of meridional acuity in the standard examination of patients with amblyopia will allow for a more accurate evaluation of the efficacy of treatment for amblyopia in astigmatic patients.

Study rationale
Various techniques are used for treating amblyopia.Current pleoptic methods are based on stimulation of the central and peripheral retina using structured patterns.Physiotherapeutic adjuncts (transcutaneous electric or magnetic stimulation of the retina and optic nerve, vasolidator drug magnetophoresis or electrophoresis, optical-reflection accommodation stimulation method, etc.) are used to improve the efficacy of treatment for amblyopia [9,10].To the best of our knowledge, no study has been performed to assess the effect of well-known pleoptic methods on meridional acuity.This is due to the fact that current routine examination of amblyopes does not include meridional acuity assessment and thus does not allow determining whether MA is present or not [8].
At present, the efficacy of pleoptic methods is assessed with the help of complex optotypes using the criterion of minimum cognoscible, an integrative index of the state of various detector systems in cortical mechanisms of visual perception.This methodological approach does not allow us to determine meridional indices of visual acuity, establish a diagnosis of MA, and assess the efficacy of treatment for meridional amblyopia with pleoptics.Selective vernier acuity or meridional separable visual acuity (MSVA) is most commonly used to determine meridional acuity.
There are individual reports aiming to assess the efficacy of optical correction and/or occlusion for the treatment of MA [11][12][13][14][15][16].There have been several reports on the development of device-based treatments for MA which allow activating meridional retinocortical pathways by adequate structured stimuli [17][18][19][20][21].It has been reported on the effect of modified computer games on meridional acuity in patients with astigmatism associated with amblyopia.A game was performed by the patient, while the foveal and macular region of his or her amblyopic eye was stimulated by the sinusoidal drifting grating pattern in the background of the computer screen.In another game performed by the patient, the grating pattern remained still with respect to the playing pattern [17][18][19].These amblyopia treatment methods do not provide for selective stimulation of retinal meridians with a low acuity.Method efficacy was assessed based on changes in meridional Landolt acuity (the criterion of minimum separable).There was an improvement in corrected MSVA after treatment with the game using the sinusoidal drifting grating pattern.No statistically significant improvement in corrected MSVA was observed after exercises with the stationary grating [19].
It is noteworthy that some researchers question the necessity of using complex and expensive amblyopia treatment methods and hypothesize that using simple methods may result in treatment outcomes comparable to those achieved with complex and expensive amblyopia treatment methods [22,23].Many researchers, however, advocate using complex amblyopia treatment methods.They explain that each stand-alone simple method exerts an effect on a certain aspect of the pathological process, whereas using a combination of simple methods allows for many-sided effects on the visual system with improved treatment effects.The success rate of complex amblyopia treatment methods has been reported to range from 41.3% to 86.9% [24].A wide variation in the rate among studies may be caused by different combinations of methods and different treatment success criteria used.Since no study has assessed in detail the impact of current pleoptic methods on selective indices of visual acuity, it may be expected that both stand-alone simple methods and complex methods may result in an effective improvement in meridional acuity.To check whether this hypothesis holds true, we selected the optical-reflection accommodation stimulation method as a stand-alone amblyopia treatment method.This method is based on the stimulation of the accommodation reflex by image defocusing through alternating contraction and relaxation of the ciliary muscle with the help of an optical lens with a variable power.Ciliary massage may improve hemodynamics in the ciliary body, and in the eye in general, and causes an improvement in near and far vision, normalization of accommodation, suppression of anisoaccommodation, and restoration of visual performance [25].Accommodative therapy has been reported to result in an improvement in visual acuity in 40-76.9% of patients with both amblyopia and hypermetropic refraction [22,26,27].
In the current study, the efficacy of amblyopia treatment was assessed based on changes in integrative and meridional indices of visual acuity after accommodative training only versus accommodative training plus complex treatment with pleoptic methods.Meridional indices of visual acuity were determined based on the criterion of minimum separable (MSVA) which allows assessing the capacity of the visual system for the analysis of complex patterns [3,8].In addition, we have proposed to use a new algorithm analyzing meridional asymmetries in visual acuity to improve the reliability of the assessment of treatment outcomes.In this algorithm, meridional asymmetries in visual acuity are considered as vector quantities which take into account the interrelationship of the magnitude and direction of meridional asymmetries in visual acuity with the magnitude and direction of refractive asymmetries [28,29].This is due to the fact that, among amblyopes with similar type of astigmatism, one may distinguish groups differing in the direction of asymmetry in meridional acuity in relation to refractive characteristics.In one of these groups, selective visual acuity in the vertical meridian may be equal to that in the horizontal meridian; in the second group, selective visual acuity in the horizontal meridian may be larger than that in the vertical meridian, and in the third group, vice versa [29].If this factor is not taken into account, meridional asymmetries in visual acuity in the study sample will be neglected in the statistical analysis, and average values will give false evidence of the absence of meridional amblyopia.Therefore, a change in the magnitude and type of meridional asymmetries in visual acuity in patients with astigmatism may be an indicator of the efficacy of treatment for meridional amblyopia.
The purpose of the study was to optimize the algorithm for assessing the efficacy of stand-alone and complex methods of treatment for amblyopia in astigmats through the determination of the features of changes in visual acuities in orthogonal retinal meridians as vector quantities.

Material and Methods
Twenty-four amblyopic children (48 eyes) with simple with-the-rule hyperopic astigmatism or compound withthe-rule hyperopic astigmatism were involved in the study.The children's age ranged from 5 to 12 years.Spherical and cylindrical refractive errors ranged from +0.5D to +4.5D.Best-corrected visual acuity (Sivtsev Chart) was assessed.Mild amblyopia was found in 43 eyes (89.6% of patients), and moderate amblyopia, in 5 eyes (10.4% of patients).
Special computer software was used to determine corrected MSVA.Patients were shown Landolt ring objects.Landolt ring gaps were shown consequently in the orthogonal retinal meridians which coincided with the direction of refractive asymmetry in the major meridians of the astigmatic eye.The angular size of the optotype was accurately reduced to determine the smallest optotype at which the gap in the optotype could be still recognized reliably by the examinee.Stimuli were presented monocularly at a distance of 5 m.The stimuli were presented monocularly on a 15-inch screen at a resolution of 1,600×1,200 pixels.A displacement per pixel was 0.12 arc min.A Landolt ring gap was oriented vertically to assess MSVA in the horizontal meridian, and horizontally to assess MSVA in the vertical meridian.
Optical-reflection training of accommodative facility was performed monocularly under conditions of the best lens correction.The patient was asked to look at the lowest line on the distant vision optotype he could read, and a +0.5-diopter sphere was placed just in front of the best lens correction for the study eye in order to blur this line.The +0.5-D sphere was replaced by a -0.5-D sphere after the optotypes became clearly visible.Each of the abovementioned lenses was presented 10 times.Thereafter, the cycle was repeated using a ±0.75-D sphere and, subsequently, a ±1.0-D sphere.If the patient succeeded in fulfilling the task, lens power was gradually increased in increments of 0.25D or 0.5D until it could be compensated by accommodation.
A course of complex treatment included pleoptic methods with the use of special devices (like amblyotrainer ATR-1, ASO-3 and laser stimulator) and special software ("Crosses" and "Relax").In addition, it included accommodative facility training as per the above methodology [30].Treatment course duration was 10 days.
The study adhered to national bioethics regulations and the tenets of the Declaration of Helsinki of 1975 as revised in 2000.Informed consent of children as well as written informed consent of their parents was obtained.
Statistical analyses were conducted using Statistica for Windows 5.5 (StatSoft, Tulsa, OK, USA) software.The normal distribution of quantitative data was tested using the Kolmogorov-Smirnov test.Mean values and standard error of mean were calculated.Student's t test was used to compare mean values.Coefficient of variation was calculated to determine whether the sample was homogeneous or not.Pearson's chi-square test and a 2x2 contingency table were used to compare nominal values.Percentages were compared using a descriptive statistics calculator.The level of significance p ≤ 0.05 was assumed.

Results
Table 1 shows the distribution of eyes of astigmats with amblyopia among various categories of integrative VA in the amblyopic eyes and fellow eyes before and after accommodative facility training.After treatment, visual acuity improved by 0.01 to 0.15, and the number of eyes with a VA of 0.75 to 0.9 increased.
Table 2 shows MSVA values for patients with withthe-rule hyperopic astigmatism and amblyopia before accommodative facility training.MSVA asymmetries may be an indicator of the presence of MA.
Mean separable visual acuity value in the vertical meridian was practically similar to that in the horizontal meridian in both groups for the dominant and fellow eyes (Table 3).However, MSVA variances with respect to mean values suppose that MSVA asymmetries may be present both in dominant and non-dominant (fellow) eyes.Table 3 shows the distribution of astigmats with amblyopia among categories where separable VA in the vertical meridian is equal to, greater or smaller than that in the horizontal meridian before treatment.Table 3 demonstrates that the study sample was heterogeneous regarding the features of asymmetries in separable visual acuity.No MA was found in 16.65% of study patients.Asymmetries in separable visual acuity that may be considered MA were found in 83.35% of eyes with both astigmatism and amblyopia.
Our analysis of asymmetry directions revealed that the group with asymmetries in visual acuity between meridians may be split into two different clusters.Separable visual acuity in the horizontal meridian was higher than that in the vertical meridian in 35.45% of eyes in cluster 1, and lower than that in the vertical meridian in 47.85% of eyes in cluster 2.
Table 4 shows data on the effect of accommodative facility training on separable visual acuity in meridians in astigmats with amblyopia.Accommodative facility training demonstrated a positive impact on separable visual acuity in meridians in dominant and non-dominant (fellow) eyes in astigmats with amblyopia, with the improvement being more apparent in the former eyes.
Table 5 shows data on changes in the type of asymmetry in separable visual acuity in meridians.After treatment the percentage of eyes without separable visual acuity asymmetry between the orthogonal meridians significantly increased from 16.65% to 27.08%.
We used a similar approach to data array analysis to assess the efficacy of complex treatment.
Table 6 shows the distribution of eyes of astigmats with amblyopia among various categories of integrative VA in the amblyopic eyes and fellow eyes before and after complex treatment.After complex treatment, there was an increase in the number of eyes with a VA of 0.75 to 0.9.
Table 7 shows values of separable visual acuity in meridians for patients with with-the-rule hyperopic astigmatism and amblyopia before complex treatment.Mean separable visual acuity value in the vertical meridian was practically similar to that in the horizontal meridian in both groups for the dominant and fellow eyes (Table 7), allowing to make a preliminary conclusion on the absence of MA.However, variances in separable visual acuity in meridians with respect to mean values suppose that asymmetries in separable visual acuity in meridians could be present both in dominant and non-dominant (fellow) eyes.Table 8 shows the distribution of astigmats with amblyopia among categories where separable visual acuity in the vertical meridian in dominant and non-dominant (fellow) eyes is equal to, greater or smaller than that in the horizontal meridian before treatment.Table 8 demonstrates that the study sample was heterogeneous regarding asymmetries in separable visual acuity.No MA was found in 25% of study patients.Asymmetries in separable visual acuity that may be considered MA we found in 75% of eyes with both astigmatism and amblyopia.Our analysis of asymmetry directions in these subgroups revealed that the group with asymmetry in visual acuity between the meridians may be split into two different clusters.Separable visual acuity in the horizontal meridian was higher than that in the vertical meridian in 50% of eyes in cluster 1, and lower than that in the vertical meridian in 25% of eyes in cluster 2. Of note that separable visual acuity asymmetry between orthogonal meridians was noted not only in non-dominant eyes, but also in dominant eyes.
Table 9 shows data on the effect of complex treatment on separable visual acuity in meridians in patients with with-the-rule hyperopic astigmatism and amblyopia.Complex treatment demonstrated a positive impact on separable visual acuity in meridians in dominant and nondominant (fellow) eyes in astigmats with amblyopia.
While assessing the efficacy of treatment for amblyopia in astigmats, we need to pay attention to changes in the magnitude and direction of separable visual acuity asymmetry between meridians.Table 10 shows data on changes in the type of asymmetry in separable visual acuity in meridians.After treatment the percentage of eyes without asymmetry in separable visual acuity between orthogonal meridians significantly increased from 25% to 43.75% (χ2 = 3.74, р = 0.05).
The use of complex treatment had a positive impact on meridional characteristics of visual acuity, with a decrease in asymmetry in separable visual acuity between orthogonal meridians in dominant and non-dominant (fellow) eyes in all subgroups of patients.In addition, after complex treatment, a more apparent increase in MSVA was noted in non-dominant (fellow) eyes, whereas after accommodative facility training, a more apparent increase in MSVA was noted in dominant eyes.

Discussion
We proposed to use a new visual acuity assessing algorithm for assessing the results of treatment for amblyopia in astigmats, with this algorithm allowing the evaluation of integrative and selective MSVA indices.This approach allowed us to reveal that the group of patients with the same type of astigmatism was heterogeneous regarding the magnitude and direction of separable visual acuity asymmetries in orthogonal retinal meridians with respect to the direction of refractive asymmetries [21,25].This is confirmed by the fact that asymmetries in separable visual acuity that may be considered MA were found in dominant and non-dominant eyes of 83.35% astigmats.In addition, our analysis of asymmetry directions in these groups revealed that each group may be split into two different clusters.SVA in the horizontal meridian was higher than that in the vertical meridian in 35.45% of eyes in cluster 1, and lower than that in the vertical meridian in 47.85% of eyes in cluster 2. This indicates that, for a detailed assessment of the efficacy of pleoptic methods, MA characteristics in orthogonal meridians should be considered as vector quantities.
The number of eyes with no difference in the magnitude of MSVA between orthogonal meridians increased by 10.41% after treatment for MA with accommodative facility training only versus 18.75% after complex treatment.Not only the meridional acuity improved, but also integrative VA improved after treatment.The number of eyes with a visual acuity of 0.7 to 0.9 increased by 8.33% after MA treatment with accommodative facility training versus 12.5% after complex treatment.
Therefore, we propose to use the following criteria for assessing the efficacy of treatment for MA: a decrease in the magnitude of VA asymmetry between retinal orthogonal meridians due to an increase in meridional acuity in one or two meridians; a change in the direction of VA asymmetry in retinal orthogonal meridians, and/or a removal of asymmetry in VA between retinal orthogonal meridians.

Conclusion
The optimization of the algorithm for assessing the efficacy of treatment for amlyopia in astigmats through the determination of the features of changes in visual acuities in orthogonal retinal meridians as vector quantities enables obtaining principally new information on the performance of sensory functions in patients with amblyopia, and to determine the most effective stand-alone and complex methods of treatment for meridional amblyopia.

Table 1 .
Distribution of dominant and non-dominant (fellow) eyes of patients with both hyperopic astigmatism and amblyopia among two best-corrected visual acuity categories before and after a course of accommodative facility training

Table 2 .
Meridional separable visual acuity values for eyes of patients with both hyperopic astigmatism and amblyopia before accommodative facility training

Table 3 .
Distribution of patients with both hyperopic astigmatism and amblyopia among the categories related to the features of the direction of separable visual acuity asymmetry between the vertical and horizontal meridians in dominant and nondominant (fellow) eyes before treatment by accommodative facility training

Table 4 .
Changes in separable visual acuity between orthogonal meridians in dominant and non-dominant (fellow) eyes of patients with both hyperopic astigmatism and amblyopia after treatment by accommodative facility training

Table 5 .
Distribution of eyes with both hyperopic astigmatism and amblyopia among categories related to types of asymmetry in separable visual acuity between orthogonal meridians before and after treatment by accommodative facility training

Table 6 .
Distribution of dominant and non-dominant (fellow) eyes of patients with both hyperopic astigmatism and amblyopia among two best-corrected visual acuity categories before and after a course of complex treatment

Table 7 .
Meridional separable visual acuity values for eyes of patients with both hyperopic astigmatism and amblyopia before complex treatment

Table 8 .
Distribution of patients with both hyperopic astigmatism and amblyopia among the categories related to the features of the direction of separable visual acuity asymmetry between the vertical and horizontal meridians in dominant and nondominant (fellow) eyes before complex treatment

Table 9 .
Changes in separable visual acuity in vertical and horizontal meridians in dominant and non-dominant (fellow) eyes of patients with both hyperopic astigmatism and amblyopia after complex treatment

Eye under investigation Direction of the meridian under investigation Separable visual acuity before and after treatment (arc second)
Note: р, significance of difference <0.05; n, number of eyes; ∆, difference between post-treatment and pre-treatment visual acuity values (arc second)

Table 10 .
Distribution of eyes with both hyperopic astigmatism and amblyopia among categories related to types of asymmetry in separable visual acuity between orthogonal meridians before and after complex treatment