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Article

Exploring Changes in Ocular Aberrations for Different Fixation and Accommodation Stimuli

by
María Mechó-García
*,
Rute J. Macedo-de-Araújo
,
Paulo Fernandes
and
José Manuel González-Méijome
Clinical & Experimental Optometry Research Lab, Physics Center of Minho, and Porto Universities (CF-UM-UP), School of Sciences, University of Minho, 4710-057 Braga, Portugal
*
Author to whom correspondence should be addressed.
Photonics 2024, 11(11), 1090; https://doi.org/10.3390/photonics11111090
Submission received: 2 October 2024 / Revised: 14 November 2024 / Accepted: 18 November 2024 / Published: 20 November 2024
(This article belongs to the Special Issue Novel Techniques and Applications of Ophthalmic Optics)
Browse Figures
Versions Notes

Abstract

:
Background: Given the lack of standardization in stimulus types for assessing accommodation, we aimed to evaluate accommodative response (AR) and Zernike coefficients using four different stimuli. Methods: Sixteen healthy subjects aged 22–32 years participated. Four black transilluminated stimuli (Snellen 6/12 “E”, 6/6 “e”, Maltese Cross 6/12 “X”, 6/6 “x”) were used to stimulate accommodation from 0 D to 5 D, in 1 D increments, using the irx3 aberrometer. From the results, AR was calculated with Seidel defocus and the change in Zernike coefficient value between the non-accommodative state and the fully accommodative state (5 D) was determined. Results: Larger pupils were observed with stimulus “E” (p-value < 0.05). The mean AR at the maximum accommodative level (5 D) for the different stimuli was −1.88 ± 1.00 for “E”, −2.60 ± 1.44 for “X”, −2.00 ± 1.32 for “e”, and −2.40 ± 1.27 for “x”. No statistically significant differences were found between AR and Zernike coefficients with the four different accommodative stimuli (p-value > 0.05, one-way ANOVA). Conclusions: The study evaluated accommodative stimulus design and size on AR and Zernike coefficients and found no significant differences. However, stimuli with higher spatial frequencies (“e” and “E”) provided larger ARs compared to the other stimuli.

1. Introduction

Accommodation refers to the eye’s ability to enhance optical power for sustaining a sharp image on the retina. The accommodative amplitude (AA) is the difference between the nearest and the farthest point at which the eye can maintain a clear image; it decreases steadily from approximately 15 diopters during early childhood to 1 diopter by the age of 60 [1].
During accommodation, changes in lens shape introduce changes in higher-order aberrations (HOA) [2,3,4,5,6], mainly spherical aberration [7,8], particularly as the eye shifts focus to near objects. Simultaneously, the pupils constrict to reduce the negative impact of these aberrations and enhance the depth of focus, which helps maintain clear vision [9,10,11,12]. However, the exact relationship between aberrations and pupil size is dynamic and varies with lighting conditions, age [4,13], and the degree of accommodation [2,5].
Several factors can influence the accommodative response (AR). One of the main responses to accommodation is the blur [14]. However, other cues may influence AR. It has been suggested that optical cues, such as chromatic aberration [15,16,17,18] or monochromatic HOA), especially spherical aberration [7,19,20,21,22], play a role in determining the direction of accommodation. In addition, non-optical cues such as pupil size [9], proximity, or apparent distance and retinal image characteristics such as spatial frequency of the stimulus [22,23], contrast [24,25], luminance [26], depth of focus [12], or stimulus size [12,26] can also influence accommodation.
The AR represents the final adjustment made in response to a change in stimulus vergence and results from the proximal, tonic, vergence, and reflex accommodation [27]. Theoretically, AR can be calculated from the inverse of distance (in meters) from the object that acts as the accommodative stimulus. Nevertheless, this does not work for practical purposes, so, the difference or delay between theoretical and real accommodation is called accommodative lag. Measuring accommodative lag is essential to assess and correct visual problems, ensure accurate vision, and avoid eye fatigue [28]. However, a key challenge lies in the lack of standardized procedures for selecting the fixation stimulus during clinical assessments. Several authors [29,30,31] advocate for using stimuli that mimic real-world reading conditions, as AR tends to be more accurate with increased cognitive demand. Schmid et al. [32] found that smaller letters (corresponding to higher visual acuity) resulted in better accommodation accuracy as measured by retinoscopy and autorefraction, compared to larger letters (lower visual acuity) that produced higher lag. Tan and O’Leary [30] investigated AR using a Snellen chart with varying letter sizes (subtended arcminutes: 1, 1.5, 2, 3, 4, 5, and 10). They found no significant differences in AR, whether measured monocularly or binocularly, across these different stimulus sizes. Conversely, Day et al. [33] reported an increase in accommodation microfluctuations at low and high spatial frequencies (0.5 and 16 cycles per degree (cpd)), with the smallest microfluctuations occurring at mid-spatial frequencies (2 and 4 cpd). Kruger and Pola [34] explored the impact of stimulus size and blur on the AR using a Maltese cross target. They manipulated the object size and blur inversely (larger size with less blur, smaller size with more blur). Their findings suggest that blur is most effective in stimulating accommodation at low spatial frequencies. On the other hand, Taylor et al. [35] report differences obtained with myopes and emmetropes. In both groups, some participants responded more accurately to the higher spatial-frequency targets, while others performed best with targets at intermediate frequencies. However, there is no agreement among the various studies mentioned above, leaving a gap in understanding this issue objectively.
Since accurate and objective assessment of AR is crucial, the present study aims to investigate potential variations in subjects’ AR and ocular wavefront data elicited by different types and sizes of accommodative stimuli.

2. Materials and Methods

2.1. Subjects

This study included 16 young subjects (11 females and 5 males) with a mean age of 27.31 ± 3.48 years and a range of 22 to 32 years.
To ensure participant eligibility and maintain ethical guidelines, this study adhered to the tenets of the Declaration of Helsinki and received approval from the Ethics Subcommittee for Life and Health Sciences of the University of Minho (Ref. 081/2022). All participants signed informed consent forms after receiving a full explanation of the study’s purpose.
Participants with the following criteria were excluded: accommodative and/or binocular vision disorders, corrected visual acuity (VA) worse than 0.0 LogMAR (measured with an EDTRS chart), cylinder higher than −1 D, rigid gas permeable contact lens wear within the last month, prior cataract or refractive surgery, pregnancy, or taking medications that could affect accommodation.
Additionally, no mydriatic [36,37] or cycloplegic [38] drugs were administered to maintain the accommodation as close as possible to the physiological conditions of the subjects.

2.2. Materials

The standard sensory dominance test [39] was performed by using a +1.5 D positive blur in one eye while both eyes remained open and focused on a distant visual acuity chart (ETDRS chart). The dominant eye was identified based on the participant’s perceived discomfort with the induced defocus, while the non-dominant eye was the one in which the defocus was most easily suppressed.
The irx3 aberrometer (Imagine Eyes, Orsay, France) was used to measure ocular aberrations with the accommodation based on the Hartmann–Shack principle. The instrument has a Badal internal system to change the vergence of the target stimulus in the form of a transilluminated black 6/12 “E” Snellen letter subtending about 0.70 × 1.00 degrees approximately 1.43 cpd with a luminance of 85 cd/m2. The software enables the customization of the Badal system movement, allowing for adjustments based on predefined refractive errors and targeted step changes in accommodative demand. Three additional stimuli were then designed: an “e” corresponding to a Snellen 6/6 acuity and approximately 3 cpd, a “X” Maltese Cross corresponding to 6/12 acuity and approximately an average of 1.43 cpd, and a “x” Maltese Cross corresponding to 6/6 acuity and approximately an average of 3 cpd (Figure 1). The Maltese cross has areas of high and low spatial frequency simultaneously. The high frequencies are found at the edges and corners, where contrast changes are abrupt, while the wider areas of the arms of the cross contain lower spatial frequencies, due to the more gradual transitions, and are useful precisely because of this combination of frequencies.
Wavefront aberrations were assessed monocularly, while the contralateral eye was occluded. Measurements were made in both eyes of each subject. As there was no relationship between accommodative response and ocular dominance, only the right eyes of the subjects were considered for the analysis.
Subsequently, wavefront measurements were obtained under different accommodative demands for each stimulus. No refractive corrections were worn during the aberrometric measurement sessions. The spherical equivalent (SE) of each subject was obtained using the nebulization technique [2,40], by placing the stimulus 1 D beyond the far point (measured by Zernike refraction), thus allowing each individual’s natural refraction to capture the less accommodated state of the eye. Starting from this SE value, the Wi (Ti), with i = 1 to i ≤ 6, six accommodative steps were obtained by stimulating accommodation from 0 to 5 D, in steps of 1 D (Figure 2). The four conditions (different stimuli, presented in Figure 1) and eye (right or left) for each subject. Each axial change in target position took 2 s to allow the subject to accommodate.

2.3. Data Analysis

Ocular aberrations were measured for a maximum round pupil, in the pupil plane, in the form of Zernike coefficients, C m n , where n represents the radial order of the polynomials and m denotes the azimuthal frequency as defined by the ANSI standards [41,42]. The wavefront data were fitted with an 8th order Zernike expansion and exported for further analysis. Since accommodation affects pupil diameter [43,44,45], wavefronts were rescaled according to the selected pupil size, using the method described by Schwiegerling [46] and corrected by Visser et al. [47], with a fixed entrance pupil size depending on the accommodative vergence, taking into account a physiological approach. The fixed entrance pupil size was chosen as the minimum pupil diameter of all subjects in each accommodative vergence. Specific diameter pupil sizes (mm) were assigned for the wavefront rescale for each accommodative demand 4.64 mm for 0 D, 4.44 mm for 1 D, 4.22 mm for 2 D, 4.08 for 3 D, 3.88 mm for 4 D, and 3.60 mm for 5 D.
AR for each target vergence was calculated using the Paraxial curvature matching method (Seidel defocus) adapted from those used in determining objective refractions by Thibos et al. and other authors [3,48,49].
The AR was calculated from the Seidel defocus (M) (Equation (1)), for each vergence and analyzed only up to 2 D due to the inter-subject variability at the maximum accommodation level (5 D). Subsequently, the value of the stimulus target (ST) can be seen in Figure 2 (Equation (2)) for each subject and was extracted from the obtained M to normalize the M values.
M ( i ) = C 2 0 i 4 3 − C 4 0 i 12 5 − C 6 0 24 7 r ( i ) 2 ,
C(2,0) is the second-order Zernike coefficient for the defocus, C(4,0) is the fourth-order Zernike coefficient for primary spherical aberration, C(6,0) is the sixth-order Zernike coefficient for the secondary spherical aberration, and r is the radius.
A R ( i ) = M ( i ) − S T ( i ) ,
M is the Seidel defocus, and the ST is the position of the stimulus target in the aberrometer when performing the measurements.
The magnitude of the change (in D) between the AR value in the non-accommodative state and the AR value in the maximally accommodative state (5 D) was determined using Equation (3), and the results are represented in Figure 3.
D A R ( D ) = A R max ⁡ a c   − A R n o n   a c ,
To characterize the wavefront for each accommodative demand across all stimuli, individual assessment focused on the Zernike coefficients (C(4,0), C(6,0), C(3,−1), and C(3,1)) was also performed.
The magnitude of the change (μm) between the Zernike coefficient C m n value in the non-accommodative state and the value in the maximally accommodative state (5 D) was determined using Equation (4).
D A R ( μ m ) = C m n m a x − a c − C m n n o n − a c ,

2.4. Statistical Analysis

Statistical analysis was performed using SPSS version 29.0 for Windows (IBM Corp, Armonk, NY, USA). Descriptive statistics, utilizing the mean for central tendency and standard deviation (SD) for variability, were employed. Analysis of variance (ANOVA) was applied to assess potential differences among multiple groups (different stimuli and different target vergences). To minimize Type I error due to multiple comparisons, a Bonferroni correction was applied. The evaluation of results was based on 95% confidence intervals (CI), with the statistical significance level set at p-value < 0.05.

3. Results

In total, 16 participants were enrolled in the present study: 8 emmetropes, 7 myopes, and 1 hyperope (11 women and 5 men) with a mean ± SD age of 27.31 ± 3.48 years. The mean spherical equivalent refraction was −0.98 ± 1.53 for right eyes (RE) and −0.95 ± 1.44 for left eyes (LE); no statistically significant differences were found. Refractive error was defined as hyperopes (SE > +0.50 D), emmetropes (−0.50 ≤ SE ≤ +0.50 D), and myopes (SE < −0.50 D).

3.1. Pupil Size

Natural pupil size showed significant variability with accommodation. On average, the higher pupil diameters were noted in response to the “E” Snellen corresponding to a 0.5 visual acuity (VA) (Figure 3). The pupil diameters obtained during measurements with the designed stimuli were, on average, 0.25 mm lower than the pupillary diameters associated with the Snellen “E” with a visual acuity of 0.5. It should be noted that the analysis of variance showed no significant differences for the “E” (p-value > 0.05, one-way ANOVA, Table 1), while significant differences were observed for the other three accommodative stimuli (p-value < 0.05, one-way ANOVA, Table 1). Despite this, a consistent trend indicates a reduction in pupil diameter by 0.75 mm with increased accommodative demand across all stimuli (see Figure 3 and Table 1).
Therefore, specific diameter pupil sizes (mm) were assigned for the wavefront rescale for each accommodative demand: 4.64 mm for 0 D, 4.44 mm for 1 D, 4.22 mm for 2 D, 4.08 mm for 3 D, 3.88 mm for 4 D, and 3.60 mm for 5 D.

3.2. Ocular Dominance

The analysis of AR with the different accommodative stimuli revealed that in 56.25% of the cases, the AR was higher in the sensorial dominant eye, whereas in 43.75%, it was higher in the non-dominant eye, but no statistically significant differences were found between the dominant and non-dominant eye. In that case, it was decided to include only the right eye of the subjects for the analysis.

3.3. Intrasubject Accommodative Response for Different Accommodative Stimuli

The individual differences in AR between stimuli are shown in Figure 4. Higher differences in AR were observed for lower VA stimuli compared to higher VA stimuli, suggesting higher AR with lower VA stimuli (6/12).
Considering the inter-subject variability in AR values at the maximum accommodation level (5 D) across the different stimuli (−1.88 ± 1.00 for “E”, −2.60 ± 1.44 for “X”, −2.00 ± 1.32 for “e”, and −2.40 ± 1.27 for “x”), the AR was subsequently analyzed only up to 2 D (Figure 5).
When comparing the “e” and “x” stimuli (6/12 Snellen), neither showed a higher AR. Notably, 6 subjects exhibited a higher AR with the “e” stimulus, while 10 subjects showed a higher AR with stimulus “x” (Figure 4D). Similarly, when comparing “E” and “X”, 6/12 VA (Figure 4A), there was no consistently higher AR for either stimulus.
Due to the increased standard deviation with higher accommodative demands for all stimuli (SD > 1.0) in the AR measured at 5 D, only lower accommodative demands (up to 2 D) were analyzed and are presented in Figure 5, for each stimulus. The results showed a normal distribution for all stimuli (p-value > 0.05). The mean and SD AR for 1 D were 0.66 ± 0.24 for “E”, 0.67 ± 0.35 for “e”, 0.68 ± 0.29 for “X”, and 0.63 ± 0.39 for “x”. The mean and SD AR for 2 D were 0.70 ± 0.54 for “E”, 0.94 ± 0.50 for “e”, 0.85 ± 0.25 for “X”, and 0.90 ± 0.55 for “x”. On average, stimulus “e” presented a higher AR, but the consistency of the AR was higher with stimulus “E”.
No significant difference were found between the four accommodative stimuli in both 1 D and 2 D. For 1 D accommodative vergence it was, p-value = 0.889, one-way ANOVA. For 2 D p-value = 0.778, one-way ANOVA.

3.4. Spherical Aberration Effect in Each Accommodative Stimulus

The substantial variations observed in AR (Figure 5) motivated the analysis of potential changes in both primary and secondary spherical aberration magnitudes across different stimuli. This aimed to elucidate whether the aberrations themselves contribute to the observed variability in AR.
The mean and SD of primary and secondary spherical aberration (C(4,0) and C(6,0)) subjects were analyzed for each accommodative demand and accommodative stimulus and are shown in Figure 6A the C(4,0) and Figure 6B the C(6,0).
For C(4,0), the values decreased with increased accommodative demand, transitioning from positive to negative. The “E” stimulus resulted in the most negative values on average, while the “e” stimulus showed the most positive values at 5D of accommodation. Variability in the data was higher at lower accommodative demands but became more consistent as accommodative demand increased. In contrast, secondary aberration C(6,0) lacked clear trends, with the average values close to zero for all the accommodative stimuli across the different accommodative demands.
No s significant differences were found between the different accommodative demands among the four accommodative stimuli in C(4,0) ANOVA: 0 D (p-value = 0.872), 1 D (p-value = 0.972), 2 D (p-value = 0.836), 3 D (p-value = 0.893), 4 D (p-value = 0.574), and 5 D (p-value = 0.293). Also, no significant differences were found in C(6,0), the p-values for the various demands were as follows: 0 D (p-value = 0.135), 1 D (p-value = 0.908), 2 D (p-value = 0.642), 3 D (p-value = 0.857), 4 D (p-value = 0.158), and 5 D (p-value = 0.197).
Figure 7 shows the difference in C(4,0) between the unaccommodated state and at the maximum accommodation (5 D) for each participant and stimulus. As expected from Figure 6A, almost all accommodative stimuli exhibit negative differences, which indicate a decrease in the spherical aberration value during accommodation. Interestingly, two myopic participants (numbers 13 and 16) showed positive differences, suggesting an increase in aberration with accommodation.
Furthermore, the magnitude of the differences between accommodative stimuli varies across participants (Figure 7). This variability highlights a lack of consistent response patterns in how C(4,0) changes with different stimuli.

3.5. Coma Effect in Each Accommodative Stimulus

Figure 8 shows the difference in vertical coma C(3,−1) (Figure 8A) and horizontal coma C(3,1) (Figure 8B) at all accommodation demands for each participant and accommodative stimuli. No clear changes in coma were observed for any stimulus across different accommodative demands.
One-way ANOVA showed no significant differences in C(3,−1) nor C(3,1) between each accommodative demand. The p-values for the different accommodative demands were as follows: for the C(3,−1), 0 D (p-value = 0.891), 1 D (p-value = 0.852), 2 D (p-value = 0.768), 3 D (p-value = 0.922), 4 D (p = 0995), and 5 D (p-value = 0.982); for the C(3,1), 0 D (p-value = 0.976), 1 D (p-value = 0.980), 2 D (p-value = 1.000), 3 D (p-value = 0.603), 4 D (p-value = 0.708), and 5 D (p-value = 0.860).
Figure 9 presents the magnitude of the difference in C(3,−1) (Figure 9A) and C(3,1) (Figure 9B) between the unaccommodated eye and the eye at its maximum accommodative demand of 5 D for each subject with each accommodative stimuli presented.
The changes in coma coefficients for each stimulus varied considerably within and between participants. The presence of this variability makes it difficult to discern any definitive trend.

4. Discussion

The present study explored the impact of different accommodative stimuli in the AR and pupil size, revealing significant insights that both align with and extend existing knowledge. By systematically examining the variations in AR and Zernike coefficients across four distinct stimulus designs, the present findings underscore the complex interplay between stimulus characteristics and the eye’s accommodative mechanisms. Particularly, the observed influence of stimulus design on pupil size elucidates a crucial aspect of visual perception that has broader implications for understanding the physiological basis of accommodation. This discussion aims to contextualize the results within the framework of current research, exploring the physiological, clinical, and practical implications of the present findings.
The present study revealed a significant difference in accommodative stimulus design on pupil size (Figure 3). The measurements with the “E” stimulus consistently elicited a larger pupil diameter compared to the other three stimuli. This finding likely relates to the luminance reaching the participants’ eyes. The larger “E” letter blocks a greater portion of the bright background, resulting in a decrease in overall target luminance. This aligns with previous research by Marthur et al. [44], Atchison et al. [50], and Watson et al. [51] who reported a similar relationship between target luminance and pupil size. In simpler terms, the smaller stimuli (“e”, “x”) and “X” allowed more light to reach the eye due to their smaller size or design. This increased luminance triggered pupil constriction, resulting in smaller pupil diameters for these stimuli suggesting that both stimulus size and luminance play a role in the pupil size response.
Since pupil diameter naturally fluctuates and responds to accommodation demand (decreasing pupil diameter with increasing accommodation demand, Figure 3), a standardized procedure to normalize all wavefronts to a consistent pupil size for each accommodative vergence was implemented [46,47]. The normalization process resulted in an average reduction in pupil diameter of 0.75 mm for the “E” stimulus and a 1.00 mm decrease for the remaining three accommodative stimuli (Figure 3). An analysis of variance revealed a statistically significant difference (p-value < 0.05) in pupil diameter across all the stimuli (except “E” where p-value = 0.068, one-way ANOVA). The present study observed a smaller reduction in pupil diameter (0.75–1.00 mm) compared to Lara et al. [40] who reported a 1.74 mm reduction. This difference is likely due to the higher accommodative demand used in their study (twice the demand in our study, 10 D), thereby elucidating the augmented reduction reported in their findings.
The results of ocular dominance with the subjects’ maximum AR aim to investigate any potential alignment between ocular dominance and increased accommodative capability. Contrary to expectations, it was found that ocular dominance and greater AR are not necessarily linked. Prior studies, such as that conducted by Ibi [52], suggest that the dominant eye typically maintains a tonic state and assumes a primary role in far-tonic accommodation during binocular viewing. Additionally, Momemi-Moghaddam et al. [53] reported superior AA and AF in the dominant eye, as determined by the hole-in-the-card method, in young healthy adults. Although the observed differences were deemed clinically insignificant (i.e., <0.50 D), it is noteworthy that in the current study, these differences between the eyes are more pronounced, with an 87.5% prevalence of larger differences in maximal accommodative demand. Due to the lack of consistent results regarding the value of the AR and ocular dominance, only the right eyes of the 16 subjects were analyzed in this study.
The subjects were individually analyzed to observe the intrasubject difference between the four different stimuli (Table S1 in Supplementary Materials). The difference between the AR in the four accommodative stimuli presents larger differences between “e” and “x”, comparing the “E” and “X”, and 62.5% of the subjects exhibited a greater AR with the “E” stimulus.
Considering the high variability (>SD) for higher accommodative demands, the AR was subsequently analyzed only up to 2 D (Figure 5). The AR results between subjects were more stable for the “E” stimulus, but higher AR was obtained with the “e”. No statistically significant difference (p-value > 0.05; one-way ANOVA) between the four accommodative stimuli in both 1 D and 2 D were found.
The phenomenon produced can be seen in Figure 10, illustrating five levels of defocusing (from 0 D to 5 D) to stimuli (“E” and “X”). The letter “E” contains spatial frequencies; inducing blur in this stimulus requires more effort on the part of the observer to perceive it. As the size of the letters decreases, the spatial frequency increases, placing greater demands on the visual system. For this reason, with the stimulus “E”, the AR was lower (Figure 5) than with the stimulus “e” (Figure 5), since the smaller stimulus requires more visual demand from the subject. In contrast, the stimulus “X” remains distinguishable from the aforementioned stimulus, even under a 5 D blur. Consequently, the pre-eminent criterion relating to AR may not be met if the patient perceives the ability to discriminate the “X” without requiring further effort to improve clarity and without considering that he or she must keep the edges sharp. Both the large and small letters provided have sharp edges and should provide good accommodation stimulus. Defocus affects the detection of smaller letters more than for larger ones. Consequently, smaller letters demand greater accommodation accuracy to be resolved [32].
The result of a more stable AR (<SD) in the “E” may be because the pupil size obtained with this stimulus was larger, so the depth of focus [12] will be shorter and therefore the range where the stimulus will be sharp was smaller and more precise concerning the other three accommodative stimuli.
A primary limitation of this study remains the low AR, which should be considered in the final conclusions and in future research with a larger sample to further support the results obtained. A factor contributing to the variability in the results in the AR may be the speed at which the stimulus was presented, only lasting 2 s to achieve sharpness. Although another study [54] had utilized a similar representation time for the stimuli, the nature of the accommodative stimulus being a balloon could potentially influence the response or the time needed to focus on details. Clufflin et al. also reported an increase in AR phase lag when tracking a sinusoidally moving accommodative stimulus [14]. Furthermore, it can be seen how subjects respond differently between eyes. In this experiment, each eye was stimulated separately, with the contralateral eye covered, and stimulation was performed first in the right and left eye. This alternating stimulation method could be a contributing factor to the different responses observed between the two eyes. Furthermore, while this method has been commonly used to stimulate accommodation, it is possible that, despite the subjects having accommodative capacity, the Badal method—similar to using a negative lens—did not provide sufficient accommodative cues for some individuals in the study. This variability implies that while the method may be effective for some individuals, it may not produce consistent responses across a broader population. This finding suggests that future studies could benefit from a more tailored approach, possibly adjusting the stimulus to individual accommodative characteristics. Furthermore, understanding the underlying causes of this variability is essential, as it may lead to improved methodologies that ensure more reliable stimulation of accommodation across diverse subjects. Another limitation of the study is that only the spherical equivalent was corrected, and subjects with astigmatism up to −1.00 diopter were included in the sample. This could impact the accuracy of the accommodative response, as uncorrected or partially corrected astigmatism may blur certain spatial frequencies and reduce the overall visual acuity, potentially affecting the outcomes.
Over the past years, researchers have explored additional cues that could influence AR, diverging from the conventional emphasis on refractive error. Traditionally, studies centered around the assumption that myopic refractive errors were linked to increased lag [55,56,57]. Contrary to this assumption, the observed pattern did not align with a higher lag in subjects who took part in the study.
In addition to refractive errors, Zernike coefficients also play a significant role in accommodation. Authors such as López-Gil et al. [8] explain that changes in the lens with accommodation lead to alterations in C(4,0) resulting in a 19% decrease contributed by the front surface of the lens, while the change in C(6,0) due to the same surface contributes a 4% increase. Therefore, the study analyzed different Zernike coefficients that vary with accommodation (C(4,0), C(6,0), C(3,−1), and C(3,1)) to find out if they were related to the AR. A decrease in C(4,0) with increasing accommodative demand was observed with all the stimuli presented (Figure 5A), as also reported by authors such as Del Águila-Carrasco et al. [6], López-Gil et al. [2], Ninomiya et al. [58], and Cheng et al. [5], but no statistically significant differences were found between the four different accommodative stimuli (p-value > 0.05, one-way ANOVA). Comatic Zernike coefficients also displayed no change in response to accommodative stimuli (Figure 8), a result consistent with the finding reported by authors [5,40] who described non-systematic changes with accommodation, and no statistically significant differences were found between the different accommodative stimuli (p-value > 0.05, one-way ANOVA).

5. Conclusions

In conclusion, the present study assessed the impact of accommodative stimulus design and size on objective accommodation response (AR), providing valuable insights for clinical evaluation. No statistically significant differences were found in AR or the Zernike coefficients (C(4,0), C(6,0), C(3,−1), and C(3,1)) across the different stimuli. However, the study observed that stimuli with higher spatial frequencies, such as “E”, were more effective in eliciting higher AR. The “e” stimulus, being smaller, promoted greater accommodation, while the “E” stimulus was more stable due to its larger wavefront, making it better suited for larger pupil sizes and more accurate due to its shorter depth of focus.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/photonics11111090/s1, Table S1: Accommodative response values for each subject for each accommodative stimulus target.

Author Contributions

Conceptualization, J.M.G.-M., P.F. and M.M.-G.; methodology, J.M.G.-M., P.F. and M.M.-G.; software, M.M.-G.; formal analysis, M.M.-G. and P.F.; investigation, J.M.G.-M., P.F. and M.M.-G.; resources, J.M.G.-M., P.F. and M.M.-G.; data curation, M.M.-G.; writing—original draft preparation, M.M.-G.; writing—review and editing, J.M.G.-M., P.F., R.J.M.-d.-A. and M.M.-G.; visualization, J.M.G.-M., P.F., R.J.M.-d.-A. and M.M.-G.; supervision, J.M.G.-M. and P.F.; project administration, J.M.G.-M.; funding acquisition, J.M.G.-M. All authors have read and agreed to the published version of the manuscript.

Funding

This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 956720.

Institutional Review Board Statement

The study was conducted in accordance with the Declaration of Helsinki and approved by the Ethics Subcommittee for Life and Health Sciences of the University of Minho (Ref. 081/2022).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The datasets generated and analyzed during the study are available from the corresponding authors upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Photonics 11 01090 g001
Figure 1. Accommodative targets were used in this study. The “E” Snellen (A) 12/6 (up) and (C) 6/6 (down), and the Maltese Cross “X” (B) 12/6 (up) and (D) 6/6 (down).
Figure 1. Accommodative targets were used in this study. The “E” Snellen (A) 12/6 (up) and (C) 6/6 (down), and the Maltese Cross “X” (B) 12/6 (up) and (D) 6/6 (down).
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Figure 2. Schematic representation of the Badal system and Hartmann–Shack system, present in the aberrometer. From the Hartmann–Shack system, a map of the wavefront of each accommodative demand and the values of each Zernike coefficient can be obtained. In this case, the subject was emmetropic (0 D), and the stimulus “E” of VA 0.5 was presented.
Figure 2. Schematic representation of the Badal system and Hartmann–Shack system, present in the aberrometer. From the Hartmann–Shack system, a map of the wavefront of each accommodative demand and the values of each Zernike coefficient can be obtained. In this case, the subject was emmetropic (0 D), and the stimulus “E” of VA 0.5 was presented.
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Figure 3. Changes in pupil diameter as a function of different accommodative demands, for each of the stimuli presented.
Figure 3. Changes in pupil diameter as a function of different accommodative demands, for each of the stimuli presented.
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Figure 4. Difference in AR between different stimuli. (A) The difference between “E” and “X”, (B) the difference between “E” and “e”, (C) the difference between “X” and “x”, and (D) the difference between “e” and “x”.
Figure 4. Difference in AR between different stimuli. (A) The difference between “E” and “X”, (B) the difference between “E” and “e”, (C) the difference between “X” and “x”, and (D) the difference between “e” and “x”.
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Figure 5. Individual ARs for each stimulus. The plots depict the AR to different stimuli ((A)—“E”, (B)—“e”, (C)—“X”, (D)—“x”) across varied accommodative targets, including demands at 1 D and 2 D. The solid lines represent the mean response, while vertical lines indicate the SD. The dashed line in each subplot represents the expected AR (1:1) for reference.
Figure 5. Individual ARs for each stimulus. The plots depict the AR to different stimuli ((A)—“E”, (B)—“e”, (C)—“X”, (D)—“x”) across varied accommodative targets, including demands at 1 D and 2 D. The solid lines represent the mean response, while vertical lines indicate the SD. The dashed line in each subplot represents the expected AR (1:1) for reference.
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Figure 6. This figure illustrates the accommodative demands for each of the six studied accommodative demands associated with four different stimuli, primary (A) and secondary (B) spherical aberration. The bar chart displays the mean spherical aberration values, while the error bars represent the variability in the data. The whiskers extend to the minimum and maximum values within the dataset, providing insights into the range of spherical aberration values behaviors observed across the diverse stimuli.
Figure 6. This figure illustrates the accommodative demands for each of the six studied accommodative demands associated with four different stimuli, primary (A) and secondary (B) spherical aberration. The bar chart displays the mean spherical aberration values, while the error bars represent the variability in the data. The whiskers extend to the minimum and maximum values within the dataset, providing insights into the range of spherical aberration values behaviors observed across the diverse stimuli.
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Figure 7. The bar chart illustrates, for each subject and each accommodative stimulus (“E”, “e”, “X” and “x”), the difference in C(4,0) values between the unaccommodated eye and the eye stimulated to the maximum accommodation of 5 D. Each bar represents an individual subject’s difference.
Figure 7. The bar chart illustrates, for each subject and each accommodative stimulus (“E”, “e”, “X” and “x”), the difference in C(4,0) values between the unaccommodated eye and the eye stimulated to the maximum accommodation of 5 D. Each bar represents an individual subject’s difference.
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Figure 8. This figure illustrates the accommodative demands for each of the six studied accommodative demands associated with four different stimuli, vertical (A) and horizontal (B) coma. The bar chart displays the mean ARs, while the error bars represent the variability in the data. The whiskers extend to the minimum and maximum values within the dataset, providing insights into the range of accommodative behaviors observed across the diverse stimuli.
Figure 8. This figure illustrates the accommodative demands for each of the six studied accommodative demands associated with four different stimuli, vertical (A) and horizontal (B) coma. The bar chart displays the mean ARs, while the error bars represent the variability in the data. The whiskers extend to the minimum and maximum values within the dataset, providing insights into the range of accommodative behaviors observed across the diverse stimuli.
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Figure 9. The bar chart illustrates, for each subject and each accommodative stimulus (“E”, “e”, “X” and “x”), the difference in C(3,−1) (A) and C(3,1) (B) values between the unaccommodated eye and the eye stimulated to the maximum accommodation of 5D. Each bar represents an individual subject’s difference for each accommodative stimulus.
Figure 9. The bar chart illustrates, for each subject and each accommodative stimulus (“E”, “e”, “X” and “x”), the difference in C(3,−1) (A) and C(3,1) (B) values between the unaccommodated eye and the eye stimulated to the maximum accommodation of 5D. Each bar represents an individual subject’s difference for each accommodative stimulus.
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Figure 10. Visual representation illustrating the impact of defocusing on stimuli “X” (up) and “E” (down). Five levels of defocusing from 1 D to 5 D in steps of 1 D.
Figure 10. Visual representation illustrating the impact of defocusing on stimuli “X” (up) and “E” (down). Five levels of defocusing from 1 D to 5 D in steps of 1 D.
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Table 1. Mean and SD of the pupil size in each accommodative state for accommodation stimulus. Analysis of variance (one-way ANOVA) results with Bonferroni correction.
Table 1. Mean and SD of the pupil size in each accommodative state for accommodation stimulus. Analysis of variance (one-way ANOVA) results with Bonferroni correction.
“E”“X”“e”“x”
Mean SDMean SDMean SDMean SD
0 D6.520.946.220.946.270.896.190.88
1 D6.410.996.021.056.220.936.120.99
2 D6.291.116.091.096.121.005.981.02
3 D6.211.035.871.125.930.975.881.06
4 D6.091.065.571.085.690.875.711.05
5 D5.781.015.280.955.320.955.330.93
ANOVA0.068<0.001 *0.003 *0.008 *
0.005 (0 D vs. 5 D)0.001 (0 D vs. 5 D)0.010 (0 D vs. 5 D)
Bonferroni 0.030 (2 D vs. 5 D)0.003 (1 D vs. 5 D)0.023 (1 D vs. 5 D)
0.012 (2 D vs. 5 D)
* Denote statistically significant differences with one-way ANOVA (p-value < 0.05). Bonferroni correction was applied to control for multiple comparisons. Only the interactions that remained statistically significant after the correction are reported in the last line of the table.
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Mechó-García, M.; Macedo-de-Araújo, R.J.; Fernandes, P.; González-Méijome, J.M. Exploring Changes in Ocular Aberrations for Different Fixation and Accommodation Stimuli. Photonics 2024, 11, 1090. https://doi.org/10.3390/photonics11111090

AMA Style

Mechó-García M, Macedo-de-Araújo RJ, Fernandes P, González-Méijome JM. Exploring Changes in Ocular Aberrations for Different Fixation and Accommodation Stimuli. Photonics. 2024; 11(11):1090. https://doi.org/10.3390/photonics11111090

Chicago/Turabian Style

Mechó-García, María, Rute J. Macedo-de-Araújo, Paulo Fernandes, and José Manuel González-Méijome. 2024. "Exploring Changes in Ocular Aberrations for Different Fixation and Accommodation Stimuli" Photonics 11, no. 11: 1090. https://doi.org/10.3390/photonics11111090

APA Style

Mechó-García, M., Macedo-de-Araújo, R. J., Fernandes, P., & González-Méijome, J. M. (2024). Exploring Changes in Ocular Aberrations for Different Fixation and Accommodation Stimuli. Photonics, 11(11), 1090. https://doi.org/10.3390/photonics11111090

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