Deficits of the “Good” Eye in Amblyopia: Processing Geometric Properties

Abstract

Purpose: Although fellow eyes of amblyopia are typically considered normal, recent studies have revealed impairments in certain aspects of vision. However, it remains unclear at which level of object processing these impairments occur. This study aims to investigate the functional level of visual perception impairment in the fellow eye of children and adults with amblyopia using the geometric functional hierarchy discrimination task based on Klein Mathematics methodology.

Methods: Seventy-six patients with amblyopia (40 children and 36 adults) and 77 age-matched healthy controls (40 children and 37 adults) were recruited for this study. The participants completed four sets of geometric hierarchies (in ascending order of stability: Euclidean, affine, projective, and topology) and one set of color discrimination tasks. They were instructed to rapidly and accurately select a distinct shape from the four quadrants.

Results: The participants’ performance was evaluated using the inverse efficiency (IE) score (IE = response time (RT)/accuracy). The results of IEs show that the fellow eye of children with amblyopia exhibits normal topological processing, yet displays higher IEs in other geometric properties and color processing, suggesting impairments in these specific discrimination abilities. However, adults with amblyopia did not show deficits on any discrimination types compared with adult controls.

Conclusions: The lack of compromised topological processing suggests that amblyopia may not have inflicted any damage to the subcortical visual pathways. Furthermore, these deficits observed in the fellow eye tend to diminish significantly during adulthood, implying that amblyopia may potentially hinder the maturation process of the fellow eye.

Amblyopia is a neurodevelopmental disorder typically characterized by uncorrected visual acuity loss in one eye and cortical deficits.^1,2 It is believed to be associated with abnormal early childhood visual experiences, such as strabismus and anisometropia.¹ The impairments caused by amblyopia are not limited to the visual functions of the amblyopic eye alone, encompassing grating acuity, contrast sensitivity, and form perception,^3,4 but also extend to binocular visual functions like stereopsis.⁵ Occlusion therapy, which involves covering the nonamblyopic fellow eye, has traditionally been the primary treatment for amblyopia. This approach is based on the assumption that amblyopia arises from an imbalance in visual input between both eyes, with the fellow eye suppressing the amblyopic eye.⁶ Consequently, it is expected that the visual function of the fellow eye should be equal to or superior to that of healthy controls rather than being impaired by amblyopia. 

Indeed, historically, the fellow eye has been regarded as a healthy control for the amblyopic eye in numerous studies.^7–9 Nevertheless, emerging evidence has gradually shed light on abnormalities in visual function within the fellow eye, such as reduced visual acuity and diminished grating sensitivity compared with typical eyes.^10,11 Furthermore, beyond spatial vision deficits, impairments have also been observed in higher-level cognitive processes, like degraded attentional modulation in the normal-acuity fellow eye.¹² Although deficits in the fellow eye have been observed, the underlying causes, specific aspects of impairment, and potential persistence into adulthood remain unclear. 

As amblyopia is known to result in abnormal development of binocular cells,¹³ it is plausible that the deficits observed in the fellow eye may arise from developmental modifications occurring within the binocular regions, encompassing various levels of visual processing involving the binocular cortex. Previous neuroimaging studies have demonstrated that amblyopia-related abnormalities are not only manifested as morphological alterations in the occipital and higher temporal lobes but also as disruptions in functional connectivity within these regions.^14,15 Cortical deficits have been observed in both child and adult individuals with amblyopia.¹⁶ Numerous neuroimaging studies have specifically distinguished between inputs from the amblyopic eye and those from the fellow eye.^12,17–19 For instance, Hou et al.¹² discovered a reduction in attentional modulation on the input of the amblyopic eye in V1 and the extrastriate cortices. In contrast, attentional modulation on the fellow eye was only decreased in the extrastriate cortices but not in V1. This finding suggests that higher-level visual processing of the fellow eye may be impacted by amblyopia while lower-level visual processing may remain unaffected. Interestingly, a recent study investigating the impact of amblyopia on subcortical pathways revealed a decrease in activation of the amblyopic eye within the superior colliculus (SC), whereas activation of the fellow eye within SC instead increased.²⁰ These findings suggest that the subcortical processing of the nonamblyopic eye may remain intact. In summary, in contrast to extensive research on the visual processing deficits of amblyopic eyes, there is a lack of studies on the impairment in the nonamblyopic eye and its underlying neural mechanisms. 

This study aims to investigate the visual processing of the nonamblyopic eye in order to gain insights into the specific functional level at which amblyopia impacts its functioning. We used a paradigm that can measure the visual processing of different geometric functional hierarchy. When a form undergoes transformations, some properties change while others remain the same. Properties with relatively high shape stability are more prone to remain invariant under transformations. Shape stability, as defined by Klein in the Erlangen Program, encompasses various levels of invariance of geometric properties under different transformations, thus providing a mathematical framework for shape stability. For instance, when a square is transformed into a diamond by altering its side length and angles, the Euclidean properties change. However, the parallel attributes of the opposite sides remain unaffected, thereby preserving the affine properties. This example shows that affine properties exhibit higher stability compared to Euclidean properties. If we stretch or bend the four sides of a square arbitrarily, or even transform it into an ellipse, its Euclidean, affine, and projective properties may change, however, as long as we do not tear it apart, the topological properties remain unchanged. Hence, topological geometry has the highest stability. According to Klein's Erlangen Program in mathematics, Euclidean geometry, affine geometry, projective geometry, and topological geometry represent a progression of shape stability levels from low to high. These geometric functional levels not only have mathematical basis, but also have been shown to be the hierarchical levels of information processed by the human visual system.^21–23 For instance, Zhuo et al.²¹ observed in their functional magnetic resonance imaging (fMRI) study that the activation level of the object recognition region in the anterior temporal lobe corresponded closely with Klein's geometric functional hierarchy, with topological differences eliciting the greatest activation, followed by projective, affine, and Euclidean differences. Another study, by Meng et al.,²³ revealed that age-related deterioration primarily affects Euclidean discrimination, followed by affine and projective discrimination, whereas topological discrimination remains largely unaffected. These findings suggest that topological properties represent the fundamental characteristics of objects, highlighting the unique role of topological perception in visual processing. Chen²⁴ has proposed a theory of topological perception, holding that topological properties describe the global characteristics of objects, while other geometric properties, such as Euclidean, affine, and projective properties, are local properties. The extraction of global topological properties is the basis of object representation. Chen²⁵ first discovered that compared with other local geometric property perception, human perception of topological properties is the most sensitive and rapid. A large amount of subsequent experimental evidence demonstrates that the visual systems of humans, mice, and even honey bees are all more sensitive to topological properties than other local attributes, reflecting the characteristic of “topological priority.”^24,26–30 Additionally, rapid extraction of topological properties has shown to be beneficial for the subsequent processing of other local properties.²⁸ Furthermore, a series of studies conducted on both humans and mice have demonstrated that the prioritization of topological properties is attributed to the rapid processing through a subcortical pathway, whereas other local properties are predominantly processed via the classical cortical visual pathway.^31–33 Therefore, the geometric functional hierarchy with global and local properties provides a unique approach for examining various levels of visual function. 

In addition, to investigate whether possible defects in the fellow eye persist into adulthood, we recruited both child and adult participants with amblyopia, as well as age-matched healthy vision controls. Participants engaged in a geometric shape discrimination task, wherein they was required to swiftly identify shapes that deviated from the other three quadrants. Alongside assessing Euclidean, affine, projective, and topological properties, there was an additional color discrimination task implemented as a control for task difficulty, because topological discrimination is faster than the discrimination of other geometric properties. Furthermore, given the reduced best corrected visual acuity (BCVA) in the amblyopic eye itself, which complicates meaningful comparison with the control group, we have chosen to exclusively compare the fellow eye with controls both possessing normal BCVA. By using these discrimination tasks, it is expected that a more comprehensive understanding can be gained regarding the visual processing of the fellow eye across various functional tiers. 

Methods

Participants

We enrolled a total of 153 participants who were categorized into 4 groups: child amblyopia, child control, adult amblyopia, and adult control. The demographic characteristics including participant numbers, age ranges, and visual acuity levels for each group are presented in Table 1. Informed written consent was obtained from all participants or their guardians in accordance with the ethical guidelines outlined by the World Medical Association’s Code of Ethics and Declaration of Helsinki. Additionally, this research protocol received approval from the Ethics Committee of Shenzhen Eye Hospital. The inclusion criteria for patients with unilateral amblyopia were as follows: (1) with a diagnosis of unilateral amblyopia (visual acuity difference between the 2 eyes >0.2 LogMAR) associated with anisometropia or ametropia³⁴; (2) children aged between 6 and 14 years, and adults over the age of 18 years; and (3) BCVA of the fellow eye better than 0.1 logMAR. Age-matched healthy controls met the following criteria: (1) children aged between 6 and 14 years, and adults over the age of 18 years; (2) ametropia but BCVA better than 0.1 logMAR for both eyes; and (3) no history of amblyopia or strabismus. The exclusion criteria for patients and controls included: (1) other ocular pathologies, such as strabismus, refractive interstitial opacity, fundus lesions, and nystagmus; (2) a history of ocular trauma or surgery; and (3) other neuropsychiatric disorders. 

Table 1.

 

Number, Age, and Best Corrected Visual Acuity (BCVA) of Participants in Each Group

 

Stimuli and Procedure

The stimuli and procedure are similar to those adopted in Meng et al.²³ As shown in Figure 1A, there were 5 types of target stimuli. The first four represented different levels of geometry, stratified in ascending order of stability: Euclidean geometry, affine geometry, projective geometry, and topology geometry with the highest stability. The final color stimulus (red: red, green, and blue [RGB] value [255 0 0]; and blue: RGB value [0 0 255]) was used as the control condition for task difficulty. According to previous studies,²³ we used a color discrimination task of comparable difficulty to the topological discrimination task as a control. Each target stimulus consisted of items located in four quadrants, with one quadrant being different from the other three. Specifically, the odd quadrant contained arrows with a different orientation, representing the difference in the Euclidean property. The odd quadrant can be oriented in either an upward or downward direction, and it can be positioned within any of the four quadrants. Consequently, the Euclidean discrimination task involved a total of eight stimuli (4 quadrants × 2 orientations). Similarly, parallelism, collinearity, and the number of holes are taken as proxies for affine, projective, and topological properties, respectively. We tried to control for the interference caused by changes in the lower sensory level in the topological difference discrimination. Specifically, in the topological discrimination task, the subgraph of each quadrant was a square or four corners which were derived by dividing the original square. Consequently, this subgraph comprising these four corners exhibited identical characteristics in terms of length, thickness, and contrast of line segments when compared to the initial square. Hence, these confounding factors were controlled to ensure the differences between figures in the four quadrants during the topological discrimination task mainly reflect disparities in topology. 

Figure 1.

 

Stimulus examples and experimental procedure. (A) Examples of five types of target stimuli, each representing Euclidean, affine, projective, topology, and color, respectively. (B) Stimulus sequence in a trial. A stimulus array was presented until response. The five types of target stimuli were presented in separated blocks with the order balanced between subjects.

In a dimly lit room, all participants were instructed to maintain central fixation of one eye on a computer monitor at a viewing distance of 57 cm. The amblyopic group covered their amblyopic eye and observed the stimuli with their “good” eye, referred to as the fellow eye. In the control group, one eye (either the left or right) was randomly assigned as the test eye, ensuring equal distribution among subjects. Each trial (Fig. 1B) consisted of a 400-ms fixation point followed by the presentation of a target stimulus within an 8° × 8° region in the center of a white screen. Participants were asked to keep their eyes on the central fixation point throughout the trial. They completed an odd quadrant task, where they had to identify which quadrant differed from the other three. To ensure precise measurement of reaction time, we opted for a custom-designed microswitch box featuring four buttons strategically positioned in alignment with the four quadrants. Participants placed their index fingers and thumbs on the four buttons respectively. Participants were instructed to respond as accurately and quickly as possible by pressing a button. Response time (RT) and accuracy were recorded, followed by the presentation of feedback in the center of the screen. A brief interval of 1 to 2 seconds preceded the beginning of each subsequent trial. The five distinct types of target stimuli were presented in separate blocks, with a balanced order across subjects. Within each block, participants completed 8 practice trials initially, followed by 32 formal trials for each discrimination type. Adequate rest periods between blocks were ensured to mitigate eye fatigue. Each participant successfully completed a total of 200 trials within an approximate duration of 20 minutes. 

Results

Inverse Efficiency

The performance of the discrimination task was recorded in terms of accuracy and RT. To address the challenge of combining speed and accuracy, and taking into account the effect of the trade-off between the two, we calculate an inverse efficiency score (IES) by dividing the RTs by the accuracy. For instance, if a participant’s RT is 500 ms with an accuracy of 95%, the IES would be calculated as 500/0.95 = 526 ms. The IES was introduced to effectively combine speed and error measures, and it has been widely utilized in various experimental psychology studies.^23,35,36 The detailed results regarding accuracy and RTs are presented in the Supplementary Materials. 

The IES was subjected to a 3-way ANOVA, with group and age as between-subject factors and discrimination type as a within-subject factor. The results presented in Table 2 indicate that all 3 factors had significant main effects (P values < 0.01). Additionally, the 2-way interactions and the 3-way interaction were found to be significant (P values < 0.05), except for the interaction between amblyopia and age (P = 0.115). Figure 2A illustrates that, for children, both discrimination type and amblyopia had significant main effects, along with their interaction (discrimination type: F(4, 312) = 280.889, P < 0.001, partial η² = 0.783; amblyopia: F(1, 78) = 10.626, P = 0.002, partial η² = 0.120; the interaction: F(4, 312) = 5.020, P = 0.001, partial η² = 0.060). Further post hoc analyses with Bonferroni correction revealed that the deficits in IES for Euclidean, affine, projective, and color discrimination were significant among individuals with amblyopia (Euclidean: P < 0.001, Cohen's d = 0.749; affine: P = 0.003, Cohen's d = 0.552; projective: P = 0.004, Cohen's d = 0.582; color: P = 0.022, Cohen's d = 0.511), whereas no significant deficit was observed for topological discrimination (P = 0.500, Cohen's d = 0.153). For adults, a significant main effect of discrimination type was found (F(4, 284) = 589.328, P < 0.001, partial η² = 0.892), indicating that IES decreased as geometric stability increased. However, neither the main effect of amblyopia nor its interaction reached significance (P values > 0.1). Further post hoc analyses with Bonferroni correction confirmed the significance of differences between any two types of discrimination (P values < 0.05). 

Table 2.

 

Results of the Three-Way ANOVA Conducted on the IES

 

Figure 2.

 

Results of the accuracy (A), RTs (B) and IES (C) for both the child and adult groups in five types of discrimination tasks. *P < 0.05, **P < 0.01, ***P < 0.001.

Discussion

In the present study, we investigated potential impairments in the fellow eyes of individuals with amblyopia, both children and adults by using a geometric functional hierarchy paradigm. This was done by assessing participants’ discrimination performance in four geometric tasks (Euclidean, affine, projective, and topology), as well as a color task as a control. The participants' performance was measured using the IE indicator (IE = RT/accuracy). The results revealed that children with amblyopia exhibited poorer performance compared with control children in discriminating three local geometries (Euclidean, affine, and projection) as well as color discrimination. These findings suggest significant deficits in fellow eyes affected by amblyopia. However, no significant deficits were observed in discriminating topological properties. In contrast, adults with amblyopia demonstrated slightly worse but nonsignificant performance compared with control adults across all discrimination conditions. 

Our findings indicate that the fellow eyes of children with amblyopia exhibits impairments in both local geometry and color discrimination. Due to variations in both color and luminance among the red and blue stimuli used in our color discrimination task, the observed decrease in color discrimination of the fellow eye may be attributed to deficits in either color or luminance perception. The hypothesized initial occurrence of visual dysfunction in amblyopia lies within the V1 area, with potential amplification of deficits downstream of V1.^37,38 The processing of object properties, such as shape and color, is conveyed from the retina through the lateral geniculate nucleus (LGN) to V1, subsequently undergoing progressive refinement along the classical cortical visual pathway towards the temporal lobe. The deficits in discriminating the three local geometric properties suggest an impairment in the cortical visual pathway associated with the fellow eye. The primate visual system is generally thought to be organized into magnocellular (M) pathways, which exhibit rapid information processing related to motion and achromatic stimuli, and parvocellular (P) pathways, which demonstrate slower processing of details such as shape and color. The processing of local geometric properties was observed to predominantly take place in the cortical P pathway.³³ The impairment observed in the current study on the discrimination of local geometric properties of the fellow eye suggests that there is a defect in the processing of cortical P pathways corresponding to the fellow eye. Davis et al.³⁵ found that the fellow eye exhibits decreased color sensitivity compared with normal controls, while demonstrating superior luminance sensitivity. Using visual evoked potential (VEP) as a physiological indicator, Davis et al.^39,40 observed a delay in color processing in the amblyopic eye compared to the fellow eye and the healthy control eye. However, they also noted that both the amblyopic eye and the fellow eye exhibited faster motor onset processing than the healthy control eye. Their findings suggest that amblyopia may accelerate M pathway processing while slowing down P pathway processing. Consequently, they proposed an M-P view suggesting that amblyopia has distinct effects on the M and P pathways, with a predominant impairment of the P pathway relative to the M pathway. This M-P view aligns with anatomic findings in nonhuman primates that cells in the M laminae of the LGN exhibit less susceptibility to visual deprivation compared to those in the P laminae.^41,42 This view does not deny the presence of certain abnormalities in the cortical M pathway, as evidenced by studies^43,44 demonstrating impaired motion-related processing in both the amblyopic eye and the fellow eye. 

On the other hand, we observed that amblyopia had no impact on topological discrimination of the fellow eye, although it impaired the ability to discriminate local geometric properties, such as Euclidean, affine, and projective. Previous studies^31–33 have demonstrated that global topological properties are prioritized over other local geometric properties due to their rapid processing by a subcortical M pathway, specifically the classical Superior Colliculus (SC)-Pulvinar-Amygdala subcortical pathway. This rapid subcortical pathway is thought to be responsible for the processing of critical events, such as fear-related stimuli and instinctual defensive behaviors.^45,46 Previous studies^47,48 have found that the subcortical fast pathway stemming from the SC has M response characteristics and that topological properties are processed through this subcortical M pathway.³³ Therefore, we suspect that amblyopia does not impact the topological processing of the fellow eye due to its lack of influence on the subcortical M pathway involved in topological processing. The effect of amblyopia on subcortical pathway processing has also been reported in a brain imaging study,²⁰ which revealed a diminished response to chromatic stimuli in the amblyopic eye and an enhanced response in the fellow eye within the SC. Moreover, it was observed that amblyopia did not affect the M processing in the subcortical pathway from the SC to pulvinar. Although both the cortical and subcortical M pathways exhibit the rapid response characteristics of M cells, their functions are relatively independent. Therefore, the impact of amblyopia on these pathways may differ. There have been limited research on the impact of amblyopia on subcortical processing, and current evidence from studies^20,43,44,49 suggests the subcortical pathway shows less susceptibility to amblyopia compared to the cortical pathway. We suspect that this might be related to self-preservation of subcortical pathways that process survival-related information. 

The present findings could potentially be impacted by various confounding variables, such as alterations in co-occurring factors related to topological changes, task difficulty, dominance of the eye, fixation stability, and eye-hand coordination. (1) Due to the difficulty in ensuring that all other confounding factors remain constant during topological changes, we have made efforts to control for potential low-level physical alterations associated with such changes, including stimulus luminance contrast, line segment thickness, and length. (2) Color tasks were used to exclude the impact of task difficulty. The smallest IEs observed in color discrimination indicate that this task is comparatively simpler than the topology task. However, even in the case of the color task, there are still deficits observed in the fellow eye. This finding suggests that our finding of topological properties is not a consequence of task difficulty. (3) The control group underwent testing with a randomly selected eye. Did the dominance of the eye have an impact? To address this question, we conducted Supplementary Experiment S1. Our findings (see Supplementary Fig. S1A) revealed that the dominant eye exhibited slightly superior performance compared to the non-dominant eye, although this difference was not statistically significant. Furthermore, there was no discernible variation in the influence of the dominant eye on different types of discrimination. In our experiment, if the control group had utilized their dominant eye for testing, it would have been expected to yield better performance and potentially amplify the observed defects in the fellow eye of amblyopia. (4) Previous research has shown that individuals with amblyopia may experience compromised fixation stability.⁵⁰ To further investigate the impact of maintaining strict central fixation on discrimination tasks, we conducted Supplementary Experiment S2. Interestingly, our findings revealed that performance under the condition without strict central fixation was numerically slightly better than under the strict central fixation condition, although this difference was not statistically significant (see Supplementary Fig. S1B). These results suggest that reduced performance in the amblyopia group cannot be attributed to fixation instability. (5) Previous research has indicated that the amblyopic eye exhibits poorer eye-hand coordination compared with healthy controls, whereas the disparity between the fellow eye and the control eye is not significant.⁵¹ Our findings revealed no significant difference in the topological discrimination task between children with amblyopia and their healthy counterparts, suggesting that eye-hand coordination exhibited comparability across both groups and did not exert a discernible disparity within the same age groups. It is widely acknowledged that eye-hand coordination improves with age, which could partially explain why adults outperformed children in our study. 

The global topological properties and local geometric properties differ from the traditional concepts of global and local. Classical global processing refers to the integration of multiple “parts” or elements in time and space. Numerous studies have documented that amblyopia can disrupt global processing, including global shape perception, global motion perception, and global face perception.⁵² The impairment in global processing may stem from abnormalities in the local integration process, which is considered to be associated with the processing in the striate cortex. It could also result from deficiencies in local processing, as global processing involves the handling of local information such as contour integration⁵³ and collinearity detection.⁵⁴ The deficits in local information processing in amblyopia, such as radial deformation⁵⁰ and orientation,⁵⁵ are primarily attributed to the impairment of visual cortex function in patients with amblyopia. Conversely, global topological properties are inherent to the object itself, akin to the color being an intrinsic property of an object. The processing of topological properties is independent from that of other local properties. The designation of topological properties as global stems from its distinct processing compared with other geometric properties, its preferential processing, and its pivotal role in establishing object representations.^25,26,28 In essence, global topological properties and classical global processing represent disparate concepts. Therefore, the observation that global topological processing remains unimpaired in the fellow eye of amblyopic individuals does not contradict the observed impairment in classical global processing associated with amblyopia. 

Another interesting finding is that the fellow eye did not exhibit any impairment in the adult between-group comparison, although noticeable deficits were observed in children, implying that functional impairments in the fellow eye have the potential to undergo spontaneous recovery. Meier and Giaschi⁵⁶ proposed one possible explanation for fellow eye impairment, suggesting that amblyopia hinders the maturation of the fellow eye. They propose that binocular development is disrupted by amblyopia, leading to disturbances in visual function maturation associated with the fellow eye. In this scenario, Meier and Giaschi suggest that the maturation of the fellow eye may be postponed, resulting in deficits among children with amblyopia when compared with control groups. However, as children continue to develop, these visual deficits are likely to naturally resolve and reach full maturity during adulthood. Similarly, a recent study suggests that the disruption in binocular visual experience during developmental stages could potentially give rise to the fellow eye deficit.⁵⁷ Our results provide some support for the hypothesis that amblyopia affects the development of the fellow eye. 

Conclusions

We conducted a systematic investigation into the discrimination of geometric properties in the fellow eye at various functional levels and observed that discrimination of both local geometric properties and color was impaired. However, we found no evidence of any impact on topological property processing. These findings suggest that amblyopia may not affect the subcortical M pathway involved in topological processing. Furthermore, our results indicate that adult amblyopia does not exhibit corresponding deficits, implying that the deficits caused by amblyopia may be attributed to delayed development of the fellow eye. 

Acknowledgments

The authors would like to thank Qiaocan Wu and Haoyun Ma for their help in the data collection. 

Supported by the National Natural Science Foundation of China (32371091), Guangdong Basic and Applied Basic Research Foundation (2024A1515010529), STI2030 – Major Projects (2022ZD0209500), Shenzhen Science and Technology Innovation Commission Sustainable Development Project (KCXFZ20211020163814021), and National Key Research and Development Program of China (2022YFE0132600). 

Disclosure: M. Zhu, None; J. Liang, None; W. Wang, None; H. Deng, None; Y. Huang, None