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Article

High-Order Aberrations: A Key Factor in Accommodative Dysfunctions

Centre of Physics of the Universities of Minho and Porto, University of Minho, 4710-057 Braga, Portugal
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(19), 9119; https://doi.org/10.3390/app14199119
Submission received: 9 September 2024 / Revised: 3 October 2024 / Accepted: 8 October 2024 / Published: 9 October 2024
(This article belongs to the Section Optics and Lasers)

Abstract

:
This study investigated the relationship between high-order aberrations (HOAs) and accommodative dysfunctions by analyzing their changes with accommodation. Understanding this relationship is important for understanding the mechanisms underlying these conditions. Sixty-three subjects were divided into five groups: control, infacility of accommodation (INFA), excess of accommodation (EA), insufficiency of accommodation (INSA), and symptomatic without dysfunction (SWD). Variations in root-mean-square (RMS) of the 3rd, 4th, 5th, and 6th orders and HOAs, and fluctuations of RMS HOAs, were measured using a Shack–Hartmann aberrometer at different accommodative stimuli and during residual accommodation after their removal, in the following order: 0.00 D, 1.00 D, 0.00 D, 2.45 D, 0.00 D, 4.73 D and 0.00 D. The SWD group showed a significant increase in RMS HOAs during accommodation and residual accommodation. In contrast, the EA group showed an improvement in the ocular optical quality at higher stimuli. Different patterns of changes in the 3rd, 4th, 5th, and 6th orders were observed across all groups, and fluctuations of RMS HOAs increased significantly in the SWD group during accommodation and residual accommodation. These distinct patterns of aberration changes in different accommodative dysfunctions suggest a potential link between their underlying mechanisms, providing insights that may aid their earlier diagnosis and improved management.

1. Introduction

Ocular accommodation is the process by which the lens curvature adjusts to achieve a clear image of objects at different distances [1]. During this process, the shape of the lens changes, leading to changes in the ocular aberrations and therefore in the optical quality of the retinal image [2,3,4]. At the same time, ocular aberrations play a significant role in modulating the accommodative response to maintain the best retinal image quality [2,5]. Previous studies using wavefront aberrometry have shown that certain high-order aberrations (HOAs), particularly spherical aberration, change systematically with accommodation and influence the accuracy of the accommodative response [6,7]. For instance, depending on whether the spherical aberration is more positive or negative, the accommodative lag either increases or decreases [2,6,7,8].
The ocular accommodation is sometimes compromised even in young subjects, reducing their ability to focus on objects at different distances or sustain focus for extended periods. While insufficiency of accommodation (INFA) is characterized by a reduced amplitude of accommodation (AA), in excess of accommodation (EA), more accommodation is used than required for a certain stimulus, and infacility of accommodation (INFA) makes it difficult to change the focus between far and near distances [9]. These conditions, called accommodative dysfunctions, are associated with symptoms, such as blurred vision, eye strain, and headaches, and sometimes affect performance at work and school [10,11]. Despite these impacts, the underlying causes of accommodative dysfunctions remain unclear, as not all subjects exposed to similar conditions, such as prolonged near-vision activities, develop accommodative dysfunctions [10].
As mentioned above, there is a close relationship between HOAs and accommodation, and some ocular aberrations have an important impact on the accommodative response [6]. Therefore, the presence of certain aberrations, their signal or how they change during accommodation in certain subjects may lead to dysfunctional accommodative responses. However, this relationship between HOAs and accommodative dysfunctions has not yet been explored. This study seeks to improve the understanding of these conditions, investigating how HOAs change in subjects with accommodative dysfunctions and with symptoms associated with near vision tasks but not yet diagnosed for any accommodative dysfunction. Studying the association between HOAs and accommodative dysfunctions may provide new insights into the underlying mechanisms involved in these conditions and help to understand why some individuals develop accommodative dysfunctions while others do not. Identifying the distinct patterns of aberrations’ changes during accommodation associated with each accommodative dysfunction could also aid in early detection and diagnosis, providing a more targeted approach to managing these conditions.

2. Materials and Methods

2.1. Subjects

Sixty-three healthy subjects were recruited for this study, excluding those with a history of ocular pathology, ocular surgery, orthokeratology or those taking medication that could affect vision, as certain conditions could affect HOAs. They first completed a questionnaire with the CISS (Convergence Insufficiency Symptoms Survey) questions to analyze whether they had symptoms associated with near-vision tasks and to determine whether they were considered symptomatic or asymptomatic according to the criteria of this survey. A score of 21 or more was considered symptomatic [12].
After completing the questionnaire, they underwent an ophthalmic examination, following the procedures reported by Gomes et al. [10], which included the assessment of the following:
  • Objective refraction with static retinoscopy;
  • Subjective refraction was determined for each eye, initiating with the value obtained from objective refraction, and selecting the maximum positive lens power that provided the best visual acuity;
  • Horizontal phoria, measured using the von Graefe technique for both distance and near vision. A phoropter equipped with Risley prisms was used: 12 base-in and 6 base-out for distance vision, and 15 base-in and 9 base-out for near vision. For the distance measurement, a letter column with a visual acuity of 0.8 was used at 6 m, and for near vision, a letter column with the same visual acuity was used at 40 cm.
  • Positive and negative fusional vergences were assessed for both distance and near vision, with the same target used for phoria measurement. Blur, break, and recovery values were recorded.
  • The AA was used with the minus lens method, adding negative lenses in 0.25 D increments until the subject reported that the line of letters before their maximum visual acuity at 40 cm is blurred.
  • The lag of accommodation (LA) with MEM (monocular estimated method) retinoscopy was performed along the horizontal axis, and the plus or minus lens power was estimated to neutralize the movement of the reflex seen through the retinoscope, while the subject read the words of a MEM card.
  • The accommodation facility (AF) at near vision was measured during 1 min and using ±2.00 D flippers, while the subject fixated on a target with letters one line below the subject’s maximum visual acuity.
  • Positive and relative accommodation (PRA and NRA, respectively) was measured, with the subject fixating on a target with letters one line below the subject’s maximum visual acuity placed at 40 cm, and adding negative (for PRA) or positive (for NRA) lenses until the subject reported blurred vision.
The diagnosis of binocular and accommodative dysfunctions was made based on the results obtained in these examinations and according to previously reported criteria [10,13]. Subjects with binocular dysfunctions were not included in the study, and accommodative dysfunctions were classified according to the following criteria [10,13]:
  • INFA: present monocular AF ≤ 6 cpm and binocular ≤ 3 cpm, PRA ≤ 1.25 D and NRA ≤ 1.50 D.
  • EA: present variable VA, variable static retinoscopy/subjective refraction, monocular AF ≤ 6 cpm with difficulty with the lens +2.00 D, and binocular AF ≤ 3 cpm with difficulty with the lens +2.00 D or MEM < +0.25 D or NRA ≤ 1.50 D.
  • INSA: present AA at least 2.00 D below 15 − 0.25 × age15 − 0.25 × age, monocular AF ≤ 6 cpm with difficulty with the lens −2.00 D, and binocular AF ≤ 3 cpm with difficulty with the lens −2.00 or MEM > +0.75 D or PRA ≤ 1.25 D.
Subjects were divided into four groups according to their accommodative dysfunction and symptomatology: a control group of 18 subjects without any accommodative dysfunction, and not considered symptomatic according to the criteria of the CISS survey; 6 subjects with INFA; 9 subjects with EA; 12 subjects with INSA; and 18 subjects without diagnosed accommodative dysfunctions, but symptomatic according to the criteria of the CISS survey (SWD).
The study adhered to the tenets of the Declaration of Helsinki and was approved by the Ethical Subcommittee of Life and Health Sciences of the University of Minho (SECVS 029/2014 (ADENDA), 2 July 2019). All subjects signed an informed consent form in which the procedures were explained.

2.2. Set-Up and Experimental Procedure

An adaptive optical system with an in-house Hartmann–Shack aberrometer (Thorlabs WF150-7AR), previously developed in the Centre of Physics of the University of Minho, was used to measure ocular aberrations in real-time while inducing accommodation (Figure 1). The accommodation was stimulated with negative lenses (−1.00 D, −2.50 D and −5.00 D) allocated to a motorized system (SML). The aberrometer had a resolution of 1280 × 1024 and 39 × 31, operating at a frequency of 10 Hz. The super-luminescent diode (SLD) used to generate the optical beam had a power of 10 µW (L8414-04, Hamamatsu, Shizuoka, Japan) at the eye, with a spectral maximum at 830 nm. The beam within the wavefront sensor was approximately 4 mm, with an effective diameter of 2 mm used to measure ocular aberrations.
The subject’s eye was aligned with the system and stabilized using a chin and forehead support unit, The target was a white cross on a black background, simulated to be at a far distance (≈6 m), and subjects were instructed to keep it in focus as best as possible. Subject refractive error, including sphere and astigmatism, was fully corrected with lenses during the measurements. Each subject underwent different cycles of accommodation and disaccommodation. Disaccommodation is defined as the relaxation of the ocular accommodative system after a stimulus, involving the relaxation of the ciliary muscle and a decrease in the lens power, and residual accommodation refers to the accommodation remaining even after it has attempted to shift its focus back to a resting state following an accommodative stimulus. Given the 20 mm distance from the lens to the eye and the simulated far target conditions, accommodation was stimulated in the following sequence: 0.00 D, 1.00 D, 0.00 D, 2.45 D, 0.00 D, 4.73 D, 0.00 D. Each lens was placed in front of the subject’s eye for approximately 5 s, resulting in about 50 measurements for each accommodation stimulus.

2.3. Data Analysis

Zernike coefficients up to the 6th order were exported and analyzed for a 2.5 mm pupil radius. The root mean square (RMS) of the total HOAs and the 3rd, 4th, 5th and 6th orders were calculated by the following formula [14]:
R M S = ( Z n m ) 2 ,
where n is the order and m is the frequency.
To analyze the magnitude of microfluctuations of the ocular optical quality during the different accommodative responses and the residual accommodation, the RMS deviation of HOAs was obtained using the following formula [15,16]:
R M S d e v i a t i o n = 1 n ( x i x ¯ ) 2 ,
where n is the number of measurements of RMS HOAs over a period of time, x i are the RMS HOAs at each time and x ¯ are the average RMS HOAs over the same period. This parameter indicates the average level of fluctuations in micrometres (µm) around the mean RMS HOAs over a specific period. The difference between the accommodated state and the initial relaxed state of these two parameters (RMS HOAs and RMS deviation) was calculated by subtracting the value of the corresponding accommodative state from the value of the initial state.
The normality of the data were assessed using the Shapiro–Wilk test. For comparing means between groups, one-way ANOVA was employed for parametric data, while the Kruskal–Wallis test was used for non-parametric data. To compare differences between the initial accommodative state and subsequent stimuli, repeated-measures ANOVA was used for parametric data, and Friedman’s test was utilized for non-parametric data.

3. Results

Sixty-three subjects (42 female and 21 male), with a mean age of 21.12 years, participated in this study and were divided into four groups according to their accommodative dysfunction and symptomatology. The number of subjects in each group who participated in this study, their average age, and mean spherical equivalent (SE) are presented in Table 1. It also includes the results of accommodative exams conducted during the initial visual exam: AA, LA, and AF. Additionally, Table 1 also provides the mean CISS score. Subjects with INSA had significantly lower AA and AF than the control group (p < 0.001 for both exams) but higher LA (p = 0.02) and score (p = 0.03). Subjects with EA had significantly lower AF (p < 0.001) and LA (p = 0.02) and subjects with INFA had lower AF (p < 0.001) when compared to the control group. On the other hand, subjects’ SWD had no significant differences in AA (p > 0.05), LA (p > 0.05) and AF (p > 0.05) but significantly higher scores (p < 0.001) than the control group.
The results of changes in HOA RMS for each stimulus are illustrated in Figure 2. The SWD group showed a significantly higher increase (p = 0.011) in the RMS HOAs (0.166 ± 0.197 μm) than the control group (−0.066 ± 0.286 μm) for the 2.45 D stimulus. They also presented a higher increase than the EA (−0.087 ± 0.188 μm; p = 0.003) and INSA (−0.032 ± 0.211 μm; p = 0.039) groups for the 4.73 D stimulus. In addition, a statistically significant change of 0.179 ± 0.168 μm (p = 0.002) was observed for the 4.73 D stimulus when compared to the initial state.
When observing the data collected after disaccommodation, the SWD group presented a RMS HOA value statistically higher than the initial after removing the 1.00 D (0.061 ± 0.131 μm; p = 0.033) and 4.73D (0.104 ± 0.187 μm; p = 0.002) stimuli. On the other hand, the subjects with EA displayed a decrease in RMS HOAs when disaccommodated after the 4.73 D stimulus (−0.01 ± 0.09 μm; p = 0.043). Other subjects displayed no significant changes.
Figure 3 presents the variations in RMS, from the 3rd to 6th orders with accommodation, and the differences between the initial relaxed state and the residual accommodation after removing the stimulus are shown in Table 2. Regarding the changes with accommodation, the control group suffered significant changes in 4th-order RMS at 2.45 D (p = 0.02) and 5th-order RMS (p = 0.049) at 4.73 D, the INFA group in 3rd-order RMS at 4.73 D (p = 0.025), the EA group in 4th- and 6th-order RMS at both 2.45 D (4th-order, p = 0.032; 6th-order, p = 0.014) and 4.73 D (4th-order, p = 0.047; 6th-order, p = 0.048), and SWD in 3rd-order RMS at 2.45 D (p = 0.002) and 4.73 D (p = 0.002), and in 5th-order RMS at 2.45 D (p = 0.01) and 4.73D (p = 0.004). In addition, the increase in 3rd-order RMS at 2.45 D (p = 0.003) and 4.73 D (p = 0.025) in the SWD group was significantly higher than the variation in the control group.
Regarding the residual accommodation, subjects from the SWD group had a significantly higher 3rd-order RMS after the 1.00 D stimuli were removed compared to the initial state (p = 0.045). For the other stimulus and groups, all orders returned to their initial value after disaccommodation and with no differences compared to the control group (Table 2).
Fluctuations in the RMS HOAs were also analyzed and their changes with different stimuli compared to the initial state are shown in Figure 4. The control group suffered a significant increase in microfluctutions at the 2.45 D stimulus (0.053 ± 0.201; p = 0.04) and SWD at 1.00 D (0.134 ± 0.125; p < 0.001) and 2.45 D (0.171 ± 0.245; p < 0.001), whereas the INFA group significantly decreased at the 1.00D stimulus (−0.010 ± 0.172; p = 0.03). Regarding this parameter for the residual accommodation state, a significant increase in the microfluctuations of RMS HOAs was observed in the control group after disaccommodating 1.00 D (0.104 ± 0.115; p = 0.046) and 2.45 D (0.053 ± 0.201; p = 0.04), as well as in the EA group after the 4.73 D (0.077 ± 0.069; p = 0.03) stimulus was removed and in the SWD after the 2.45 D (0.104 ± 0.116; p < 0.001) and 4.73 D (0.183 ± 0.145; p < 0.001) stimuli were removed.

4. Discussion

Accommodative dysfunctions affect a significant number of subjects, leading to symptoms and affecting performance when working and studying. Despite the wide range of prevalences, insufficiency of accommodation is the accommodative dysfunction with the highest prevalence reported in the literature, affecting between 2% and 61.7% of the population [17]. In the present study, insufficiency of accommodation was also the most prevalent accommodative dysfunction.
Given the close relationship between ocular aberrations and accommodation, this study aimed to investigate how wavefront aberrations change during accommodation and disaccommodation for different accommodative dysfunctions. Several studies reported that the RMS HOA value tends to maintain or decrease its value up to around 3.00 D of accommodation [2,4,18]. Marcos et al. [4] found the maximum optical quality at around 2.50 D of accommodation. As a result of this accommodative demand, the RMS HOAs increase. In our study, a slight decrease in RMS HOAs was observed in the control group, reaching the best optical quality at 2.45 D of accommodation and increasing at 4.73 D. The same tendency was observed in subjects with INFA, with the 3rd-order aberrations responsible for this increase in the 4.73 D stimulus.
The changes within the INSA group were not significant in any order, neither during accommodation nor residual accommodation. Changes in ocular aberrations during accommodation have been reported as a mechanism to control the direction of the accommodative response [2,5]. If subjects do not have significant changes in ocular aberrations, the accommodative process may be affected and they may have lower accommodative responses.
After analyzing each RMS order, a statistically significant decrease was observed in the 4th and 6th orders in subjects with EA. Subjects with high accommodative responses may benefit from improved ocular optical quality. As the accommodative system adjusts to achieve the best retinal image quality, these subjects may over-accommodate, leading to excessive accommodation. The SWD group experienced an increase in RMS HOA for the 2.45 D and 4.73 D stimuli. This decline in ocular optical quality may explain the symptoms reported by these subjects, as the retinal image is more degraded, resulting in blurred vision, headache, or eye strain. The SWD group demonstrated difficulty in returning to their initial state after accommodation, with poorer ocular optical quality than before. This difficulty may be attributed to the challenges in returning to the initial accommodative state, as the crystalline lens is primarily responsible for most of the ocular aberration changes during accommodation due to its biometric changes [19,20,21]. The pattern of changes in ocular aberrations appears to change differently among the groups of accommodative dysfunctions. The visual system may interpret different blur patterns caused by changes in ocular aberrations, impacting accommodation accuracy. The shape and morphology of the crystalline lens, especially in the nucleus thickness [22], change during accommodation [23,24], and the way they change may be different in some individuals, resulting in distinct changes in ocular aberrations and consequently affecting the accommodative response. On the other hand, these differences found in the changes in ocular aberrations with accommodation may be a consequence of the accommodative dysfunctions. As the structure of the lens defines its physiological function [23], it would also be interesting to study the lens capsule and its epithelial cells, as well as the lens fibres and the zonules of these subjects.
The SWD group exhibited noticeable instability in optical quality, with a significant increase in the microfluctuations of the RMS HOAs during and after accommodation, i.e., in residual accommodation. This may indicate the instability of the accommodative response in these subjects, as well as the difficulty in reaching the relaxed state of accommodation and its stabilization after an accommodative demand. This instability of the ocular optical quality during the residual accommodation is greater than the accommodative demand induced before. These findings may be due to an attempt of the visual system to find the best retinal image quality or be related to the morphological characteristics of the lens. Furthermore, the characteristics of the ciliary body may also be related, as its thickness was related to the microfluctuations of accommodation, which were higher for thinner ciliary bodies [25].
Clinical special attention should be given to patients with these features and symptoms, even if they show no alterations on clinical examination. The implementation of vision therapy exercises may improve their AF and stability, increasing the control of accommodation and reducing the symptoms [26,27]. Furthermore, the manipulation of spherical aberration has been shown to modify the accommodative response after 3 months of wearing custom-designed soft contact lenses with modified spherical aberration [28]. In addition, the manipulation of spherical aberration influences the depth of focus [29,30] and thus allows clear vision over a range of distances without the further adjustment of the accommodative system. Therefore, optical solutions based on spherical aberration manipulation may benefit these patients and those with accommodative dysfunctions to improve dynamic accommodative accuracy.
It is important to note that the small sample size of subjects with each accommodative dysfunction, as well as the difference compared to the control group, could have influenced the statistical significance of the results found. This could be considered a limitation of the study. However, given the differences in the prevalence of accommodative dysfunction in the general population and the randomized selection of subjects, an unequal sample size was expected.

5. Conclusions

This study showed the different patterns of changes in ocular aberrations during accommodation and their stability in various accommodative dysfunctions. These findings suggest that these changes may impact the accuracy and stability of the accommodative response. Subjects with different accommodative dysfunctions demonstrated specific patterns of alterations in their optical quality, which may explain their accommodative behaviour. Subjects with EA benefit from having high accommodative responses, as the optical quality increases. In contrast, the absence of changes in subjects with INSA may lead to a lack of cues to control the direction of the accommodative response. Recognizing these patterns may help in understanding the causes of accommodative dysfunctions. Moreover, it can assist in identifying individuals who are at risk of developing accommodative dysfunctions before they show symptoms, potentially enabling earlier intervention and management by eye care professionals. Additionally, those with symptoms but without accommodative dysfunctions previously diagnosed by clinical exams (SWD) show a significant decrease in their ocular optical quality and an increase in their instability, both during and after the accommodative stimuli, which may contribute to the symptoms and may evolve into an accommodative dysfunction.
These findings offer valuable clinical insights into the connection between accommodative dysfunctions and the optical quality of the eye. Understanding this relationship could help in the early detection of accommodative dysfunctions, even without obvious clinical signs. This knowledge could lead to timely interventions involving personalized visual therapy or optical solutions, aimed at enhancing accommodative control and reducing symptoms.
It is recommended that future research includes follow-up studies to assess changes in study parameters during visual therapy and their effectiveness in improving accommodative dysfunctions. Additionally, it would be valuable to utilize adaptive optics to manipulate wavefront aberrations and assess their impact on the accommodative response of subjects with accommodative dysfunctions. These studies would offer valuable insights and have implications for future research.

Author Contributions

Conceptualization, S.F.; Methodology, J.G. and S.F.; Validation, S.F.; Formal analysis, J.G.; Investigation, J.G.; Writing—original draft, J.G.; Writing—review & editing, S.F.; Supervision, S.F.; Project administration, S.F. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. The author J.G. is also supported by the PhD grant 2020.08737.BD from FCT.

Institutional Review Board Statement

The study adhered to the tenets of the Declaration of Helsinki and was approved by the Ethical Subcommittee of Life and Health Sciences of the University of Minho (SECVS 029/2014 (ADENDA), 2 July 2019.

Informed Consent Statement

All subjects signed an informed consent form with an explanation of the procedures.

Data Availability Statement

The raw data supporting the conclusions of this article will be made available by the authors on request.

Conflicts of Interest

There are no conflicts of interest to declare.

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Figure 1. Schematic representation of the experimental set-up. SML: Motorized System of Lens.
Figure 1. Schematic representation of the experimental set-up. SML: Motorized System of Lens.
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Figure 2. Differences between the root mean square (RMS) of high-order aberrations (HOAs) for accommodation (on the (left))/residual accommodation (on the (right)) and the initial state across different groups (lines represent standard deviation). SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.
Figure 2. Differences between the root mean square (RMS) of high-order aberrations (HOAs) for accommodation (on the (left))/residual accommodation (on the (right)) and the initial state across different groups (lines represent standard deviation). SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.
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Figure 3. Differences between the root mean square (RMS) of high-order aberrations (HOAs) for accommodation (on the (left))/residual accommodation (on the (right)) and the initial state across different groups (lines represent standard deviation). SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.
Figure 3. Differences between the root mean square (RMS) of high-order aberrations (HOAs) for accommodation (on the (left))/residual accommodation (on the (right)) and the initial state across different groups (lines represent standard deviation). SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.
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Figure 4. Differences between the fluctuations of the root mean square (RMS) of high-order aberrations (HOAs) for accommodation (on the (left))/residual accommodation (on the (right)) and the initial state across different groups (lines represent standard deviation). SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.
Figure 4. Differences between the fluctuations of the root mean square (RMS) of high-order aberrations (HOAs) for accommodation (on the (left))/residual accommodation (on the (right)) and the initial state across different groups (lines represent standard deviation). SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.
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Table 1. Characteristics (mean ± standard deviation) of the subjects in each group.
Table 1. Characteristics (mean ± standard deviation) of the subjects in each group.
NAge (Years)SE (D)AA (D)LA (D)AF (cpm)Score
Control1823.9 ± 3.05 ⁺0.02 ± 0.30 ⁺9.60 ± 1.01 ⁺,*0.57 ± 0.22 ⁺,*14.3 ± 4.9 ⁺,*12.6 ± 4.3 ⁺,*,†
SWD1823.2 ± 3.28 ⁺−0.72 ± 1.61 ⁺10.01 ± 2.11 ⁺0.56 ± 0.20 ⁺13.7 ± 4.7 ⁺27.3 ± 2.7 *
INFA624.4 ± 5.03 ⁺−0.29 ± 1.32 ⁺8.04 ± 2.64 ⁺0.63 ± 0.38 ⁺3.5 ± 1.9 *19.0 ± 12.3 ⁺,
EA922.9 ± 3.37 ⁺0.32 ± 0.43 ⁺8.75 ± 1.78 ⁺0.38 ± 0.18 *1.1 ± 2.2 *12.2 ± 6.5 ⁺,
INSA1221.3 ± 4.13 ⁺−0.52 ± 2.81 ⁺5.71 ± 1.29 *0.92 ± 0.33 *7.8 ± 4.5 *20.5 ± 11.4
p ⁺ > 0.05⁺ > 0.05* <0.001
⁺ > 0.05
* 0.02
⁺ > 0.05
* < 0.001
⁺ > 0.05
* < 0.001; 0.03
⁺ > 0.05
N: number of subjects; cpm: cycles per minute; SE: spherical equivalent; AA: amplitude of accommodation; LA: lag of accommodation; AF: accommodation facility; SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation.*,,† Comparison to the control group. The ± errors indicate the standard deviation from the mean.
Table 2. Changes in RMS of 3rd, 4th, 5th and 6th orders during residual accommodation.
Table 2. Changes in RMS of 3rd, 4th, 5th and 6th orders during residual accommodation.
Residual Accommodation
0.00 D (1.00 D)0.00D (2.45 D)0.00 D (4.73 D)0.00 D (1.00 D)0.00D (2.45 D)0.00 D (4.73 D)
3rd-order5th-order
Control−0.051 ± 0.216 *0.025 ± 0.201 *0.019 ± 0.193 *−0.011 ± 0.063 *0.010 ± 0.043 *0.005 ± 0.068 *
INFA−0.021 ± 0.151 *−0.015 ± 0.07 *−0.0001 ± 0.100 *−0.001 ± 0.024 *0.015 ± 0.034 *0.026 ± 0.057 *
EA0.033 ± 0.091 *0.024 ± 0.120 *−0.0001 ± 0.104 *0.022 ± 0.051 *0.002 ± 0.030 *0.024 ± 0.060 *
INSA−0.004 ± 0.137 *−0.018 ± 0.105 *−0.046 ± 0.221 *−0.005 ± 0.055 *0.001 ± 0.029 *−0.010 ± 0.096 *
SWD0.052 ± 0.122 0.045 ± 0.117 *0.080 ± 0.139 *0.010 ± 0.043 *0.022 ± 0.058 *0.020 ± 0.046 *
p 0.045; * >0.05* >0.05* >0.05* >0.05* >0.05* >0.05
4th-order6th-order
Control−0.024 ± 0.100−0.006 ± 0.095−0.029 ± 0.059−0.011 ± 0.032 *−0.003 ± 0.024 *−0.0001 ± 0.030 *
INFA−0.044 ± 0.133−0.066 ± 0.171−0.007 ± 0.069−0.010 ± 0.031 *−0.011 ± 0.040 *0.016 ± 0.021 *
EA−0.008 ± 0.117−0.007 ± 0.1070.016 ± 0.032−0.007 ± 0.032 *−0.006 ± 0.019 *0.013 ± 0.023 *
INSA−0.012 ± 0.0430.005 ± 0.054−0.017 ± 0.094−0.010 ± 0.026 *−0.004 ± 0.032 *−0.006 ± 0.031 *
SWD0.003 ± 0.0420.017 ± 0.1030.041 ± 0.1290.004 ± 0.027 *0.005 ± 0.028 *0.002 ± 0.032 *
p* >0.05* >0.05* >0.05* >0.05* >0.05* >0.05
SWD: symptomatic without dysfunction; INFA: infacility of accommodation; EA: excess of accommodation; INSA: insufficiency of accommodation. *,† Comparison to the initial state. The ± errors indicate the standard deviation from the mean.
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Gomes, J.; Franco, S. High-Order Aberrations: A Key Factor in Accommodative Dysfunctions. Appl. Sci. 2024, 14, 9119. https://doi.org/10.3390/app14199119

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Gomes J, Franco S. High-Order Aberrations: A Key Factor in Accommodative Dysfunctions. Applied Sciences. 2024; 14(19):9119. https://doi.org/10.3390/app14199119

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Gomes, Jessica, and Sandra Franco. 2024. "High-Order Aberrations: A Key Factor in Accommodative Dysfunctions" Applied Sciences 14, no. 19: 9119. https://doi.org/10.3390/app14199119

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