Exploring the interplay of chord α and chord μ with pyramidal wavefront aberrometry and ocular biometric indices among pre-operative refractive surgery candidates

Exploring the interplay of chord α and chord μ with pyramidal wavefront aberrometry and ocular biometric indices among pre-operative refractive surgery candidates | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Exploring the interplay of chord α and chord μ with pyramidal wavefront aberrometry and ocular biometric indices among pre-operative refractive surgery candidates Armin Doostparast, Farbod Semnani, Maryam Ghandhari, Amir Hossein Khosronejad, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7456104/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Dec, 2025 Read the published version in International Ophthalmology → Version 1 posted 9 You are reading this latest preprint version Abstract Background To investigate the relationships between chord α and chord µ with age, ocular biometric indices, and wavefront aberrations in pre-operative refractive surgery candidates. Methods This cross-sectional study included 111 right eyes of 111 patients. Ocular biometrics and chord values were measured using the ZEISS IOLMaster 700. Corneal and ocular aberrations were assessed with the PERAMIS pyramidal aberrometer. Data were analyzed using Pearson’s correlation, ANOVA, and simple linear regression to evaluate the interplay between variables. Results A moderate positive correlation was found between chord α and chord µ (r = 0.60, p < 0.001). Chord α demonstrated moderate positive correlations with subjective spherical refraction (r = 0.45) and spherical equivalent (r = 0.41), and moderate negative correlations with anterior chamber depth (r = -0.53) and axial length (r = -0.40) (all p < 0.001). In contrast, correlations involving chord µ were exclusively weak, though it showed significant associations with several higher-order aberrations, including corneal trefoil (r = 0.35) and ocular coma (r = 0.31). Refractive status significantly affected both chord values (p ≤ 0.02), with severely myopic eyes showing the lowest values. Regression analysis identified anterior chamber depth as the strongest anatomical predictor for chord α (R² = 0.28). Conclusion Chord α serves as a more robust indicator of the eye's anatomical characteristics than the more variable chord µ. Our findings underscore the clinical importance of optical decentration in surgical planning, as larger chord values may indicate a greater risk of pre-existing aberrations and potential impacts on visual quality. Chord Alpha Chord Mu Aberrations IOLMaster 700 Peramis Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The human eye relies on the alignment of several optical axes to achieve optimal vision, including the visual, pupillary, and optical axes [ 1 ]. The visual axis, also known as the foveal-fixation axis, connects the fixation point to the fovea and passes through the two nodal points [ 2 ]. Meanwhile, the optical axis is the line passing through and connecting the geometric centers of curvature of the cornea and lens [ 3 ]. The pupillary axis, on the other hand, is the line perpendicular to the local tangent of the cornea reaching the center of the entrance pupil[ 4 ]. Misalignment of these axes affects the visual quality and refractive outcomes[ 5 , 6 ], making their understanding crucial in clinical practice. The angles between the optical and pupillary axes and the visual axis are called angle α and kappa[ 3 ]. Directly reporting angular distances like kappa and α is uncommon in clinical and research settings; thus, modern devices use linear measurements, chord µ and chord α in millimeters. Chord µ is the distance between the pupil center and corneal vertex (also known as the coaxially-sighted corneal light reflex or the first Purkinje image), whereas chord α is the distance between the geometric center of the cornea (center of the white-to-white distance) and corneal vertex[ 7 ]. Angle kappa and alpha have several clinical implications. A large angle kappa may lead to alignment errors during photoablation in laser refractive surgery when the ablation is centered on the pupil center, which carries the risk of under-correction and irregular astigmatism[ 8 ]. Moreover, in light of the growing global burden of presbyopia[ 9 ] and the burgeoning popularity and recent technological advances of multifocal intraocular lenses (MIOL) as corrective measures, patients still report a higher incidence of visual disturbances (like glare, halos, starbursts) and reduced contrast sensitivity with these compared with monofocal lenses[ 10 ]. However, some other studies reported no significant correlation between chord µ and refractive or visual outcomes after ocular surgeries[ 11 – 13 ]. On the other hand, smaller chord α values are predictive of better visual outcomes for both near and distance vision, while larger chord α values could be associated with poorer postoperative visual acuity[ 14 ]. It is also suggested that as angle α increases, there is a significant decline in uncorrected intermediate visual acuity[ 15 ]. Existing research mostly explored the effects of chord µ and α on the visual outcomes, but the relationships between chord µ and α with ocular biometric and topographic characteristics, as well as ocular aberrations, require a more extensive investigation. By recognizing these correlations, clinicians can develop a deeper understanding of eyes more likely to have large or small chord values. This insight raises awareness for specific patient types and enhances understanding of the anatomical factors behind visual axis decentration. For instance, it has been shown that chord µ is associated with spherical equivalent, spherical refraction, and inversely correlated with axial length, asphericity Q front, and keratometry[ 16 ]. Thus, the goal of this study is to evaluate the relationship between chord α and chord µ, with age, ocular biometric indices, and corneal and ocular lower- and higher-order aberrations in candidate patients undergoing refractive surgery. Methods and Materials 2.1. Subjects This cross-sectional study was conducted at Noorafarin Eye Clinic, Mashhad, Iran. The study population included patients who underwent a comprehensive eye examination and imaging between December 2023 and February 2024. All patients provided written informed consent after clearly explaining the study's objectives and procedures. The study received ethical approval from the Research Ethics Office of Mashhad University of Medical Sciences and adhered to the principles of the Declaration of Helsinki. 2.2. Inclusion and Exclusion Criteria Patients aged 35–55 years with healthy, previously unoperated eyes who were scheduled for refractive surgery were included. The preliminary data for this study was collected from healthy individuals chosen to investigate connections with presbyopia, resulting in an age range of 35 to 55 years. Exclusion criteria compromised of the presence of proven or suspected keratoconus, history of dry eye disease, any other corneal diseases, trauma, or previous eye surgeries, poor fixation during imaging, use of rigid contact lenses within the last four weeks, or soft contact lenses within two weeks before imaging, and any other anterior segment abnormalities. 2.3. Imaging Protocol We used the IOL Master 700 (ZEISS, Germany) device to measure topographic indices and ocular biometric data, namely axial length, CCT, anterior chamber (AC) depth, lens thickness, horizontal corneal white-to-white distance, as well as apparent alpha/kappa chords[ 17 , 18 ]. Moreover, the PERAMIS (SCHWIND eye-tech-solutions, Germany) system provided detailed wavefront aberrometry data for the whole eye structure (total ocular aberrations). The ocular aberrations comprise two main components, the corneal and internal aberrations, with the internal referring to the aberrations originating from any structure behind the cornea. The PERAMIS system offers a comprehensive report for these three categories, containing total, higher-order, and lower-order aberrations, as well as the various Zernike coefficients[ 19 ]. To facilitate a deeper evaluation of the HOAs, five Zernike coefficients, namely the vertical and horizontal coma (Z-1/3 and Z1/3), trefoil (Z-3/3 and Z3/3), and spherical (Z0/4) aberrations, were extracted from the PERAMIS reports for the ocular and corneal aberrations. All of the Zernike coefficients are expressed as root mean square (RMS). The data regarding these objective spherical and cylindrical refractions were also extracted from the reports. For each system, three consecutive acquisitions were recorded by the same experienced examiner, and the highest-quality image was selected. All assessments were performed in a dark room under mesopic conditions to eliminate the impact of external light sources. Before each measurement, participants were asked to blink multiple times to stabilize the tear film and were instructed to focus on the fixation target, following the manufacturer’s guidelines. Prior to the installation of each system, the devices were calibrated in accordance with the manufacturer's guidelines. Furthermore, daily calibrations were performed to ensure measurement accuracy. No mydriatic drug was applied to the eyes before imaging. The corrected distance visual acuity was measured by an optometrist using an E chart and was further transformed into the logMAR (Logarithm of the Minimum Angle of Resolution) visual acuity. 2.4. Statistical Analysis Data analysis was performed with Python 3 (Python Software Foundation, USA), utilizing the pingouin and scikit-learn libraries[ 20 , 21 ]. The Seaborn library was further employed for data visualization[ 22 ]. Preprocessing steps included handling missing values and outliers. Missing data, accounting for less than 5% of the dataset, were not uniformly distributed across columns and were therefore filled using the Iterative Imputation function from scikit-learn[ 23 ]. Outliers were identified as data points below the 1st percentile or above the 99th percentile for each variable, and these outliers were adjusted to the 1st and 99th percentiles, respectively. The Shapiro-Wilk test was used to check for a possible violation of the normality assumption. For comparison of the association between refractive status and chords values, the eyes were categorized in sub-groups considering their spherical equivalent values as follows: Severe myopia ( > − 6.00 D), moderate myopia (− 3.00 to − 6.00 D), mild myopia (− 0.50 to − 3.00 D), emmetropia (− 0.50 to 0.50 D), mild hyperopia (0.50 to 2.00 D), and moderate hyperopia (2.00 to 4.00 D). Welch’s One-way analysis of variance (ANOVA) and Games-Howell post-hoc non-parametric tests were utilized to determine any potential differences in these sub-groups[ 24 ]. Pearson’s correlation coefficient and Fisher’s Z-transformation were utilized to assess correlations between variables and to yield more reliable p-values and confidence intervals, respectively[ 25 ]. Strongly associated independent variables were further analyzed using simple linear regression models and visualized in pairwise plots. Results were reported with 95% confidence intervals (CI) and p-values, considering a significance threshold of p < 0.05. Pearson’s r will be interpreted based on the following scale: values between 0 and 0.09 indicate a negligible correlation, 0.10 to 0.39 represent a weak correlation, 0.40 to 0.69 indicate a moderate correlation, 0.70 to 0.89 indicate a strong correlation, and 0.90 to 1.00 indicate a very strong correlation[ 26 ]. Results 3.1. Baseline Characteristics This study included 111 eyes of 111 patients, with an average age of 41.4 ± 5.1 years, representing 34 (31%) men and 77 (69%) women. The mean chord α and µ were 0.43 ± 0.16 and 0.29 ± 0.15, ranging from 0.00 to 0.94 and 0.00 to 0.80, respectively. The mean pupil diameter was 5.38 ± 1.35 mm, ranging from 2.40 to 6.80. The mean subjective spherical refraction and the mean astigmatism were − 1.1 ± 2.5 D and − 1.4 ± 1.3 D for the right eyes, respectively. Eventually, the Best-Corrected Visual acuity was 0.01 ± 0.03 LogMAR. Table 1 summarizes the baseline characteristics of the patients and eyes included. Table 1 Baseline Characteristics Variable Name Mean ± SD Range Age 41.41 ± 5.10 34.10 to 53.90 Subjective refraction sphere (D) -1.10 ± 2.46 -6.50 to 3.98 Subjective refraction cylinder (D) -1.43 ± 1.30 -5.50 to 0.01 Spherical Equivalent (D) -2.20 ± 2.67 -10.42 to 3.33 BCVA (LogMAR) 0.01 ± 0.03 0.00 to 0.15 IOLMaster 700 Pupil Diameter 5.38 ± 1.35 2.40 to 6.80 Peramis Spherical equivalent -2.20 ± 2.67 -10.42 to 3.33 IOL Master 700 Axial Length 23.97 ± 1.19 21.14 to 26.98 IOL Master 700 CCT 538.40 ± 30.61 482.10 to 603.80 IOL Master 700 AC depth 3.36 ± 0.37 2.51 to 4.04 IOL Master 700 lens thickness 4.02 ± 0.33 3.30 to 4.70 IOL Master 700 horizontal White-to-White distance 11.88 ± 0.35 11.02 to 12.87 IOL Master 700 chord mu 0.29 ± 0.15 0.00 to 0.80 IOL Master 700 chord alpha 0.43 ± 0.16 0.00 to 0.94 Peramis Corneal Coma 0.18 ± 0.12 0.02 to 0.63 Peramis Corneal Trefoil 0.19 ± 0.12 0.02 to 0.57 Peramis Corneal SA 0.14 ± 0.11 -0.30 to 0.46 Peramis Corneal HOA 0.35 ± 0.18 0.12 to 1.09 Peramis Ocular Coma 0.15 ± 0.10 0.01 to 0.49 Peramis Ocular Trefoil 0.16 ± 0.11 0.01 to 0.59 Peramis Ocular SA 0.04 ± 0.09 -0.16 to 0.31 Peramis Ocular HOA 0.29 ± 0.14 0.10 to 0.70 BCVA: Best-corrected Visual Acuity, CCT: Central Corneal Thickness, SA: Spherical Aberration, HOA: Higher-order Aberration 3.2. Sub-group analysis based on gender, refractive status, and its severity While gender did not have a significant association with chord α (P = 0.62) or µ (P = 0.52), refractive status was found to have a statistically significant effect on both chord µ (P = 0.02) and chord α (P < 0.001). Details of the refractive status of each subgroup are present in Table 2 . Table 2 Chord µ and α values based on refractive status. Subgroup N Mean SD Min Max Chord µ Severe Myopia 9 0.21 0.07 0.14 0.32 Moderate Myopia 30 0.30 0.19 0.00 0.80 Mild Myopia 46 0.26 0.10 0.10 0.51 Emmetropia 8 0.40 0.10 0.28 0.54 Mild Hyperopia 10 0.33 0.20 0.10 0.71 Moderate Hyperopia 8 0.38 0.10 0.22 0.51 Chord α Severe Myopia 9 0.27 0.16 0.00 0.51 Moderate Myopia 30 0.41 0.16 0.10 0.90 Mild Myopia 46 0.41 0.12 0.10 0.70 Emmetropia 8 0.59 0.13 0.41 0.78 Mild Hyperopia 10 0.51 0.23 0.28 0.94 Moderate Hyperopia 8 0.55 0.15 0.22 0.71 Severely myopic eyes had the lowest values for both measures (0.21 and 0.27, respectively). Pair-wise post-hoc testing confirmed that for chord µ, values were significantly greater in emmetropes and moderate hyperopes when compared to severe myopes (P = 0.01 and P = 0.02, respectively). This pattern was observed for chord α as well, where values were also significantly higher for both emmetropes and moderate hyperopes against those of severe myopes (P = 0.00 and P = 0.02, respectively). The complete pair-wise comparisons of any possible sub-groups are available for chord α and µ in Tables 3 and 4 , respectively. Moreover, Figs. 1 and 2 illustrate the distribution of chord α and µ values across different refractive states, respectively. Table 3 Differences in Chord α values based on refractive status. Sub-group (S) Comparator (C) Mean(S) Mean(C) Mean difference (mm) Standard error Hedges’ g P value Emmetropia Mild Hyperopia 0.59 0.51 0.07 0.09 0.36 0.95 Emmetropia Mild Myopia 0.59 0.41 0.17 0.05 1.40 0.06 Emmetropia Moderate Hyperopia 0.59 0.55 0.04 0.07 0.27 0.99 Emmetropia Moderate Myopia 0.59 0.41 0.17 0.05 1.10 0.06 Emmetropia Severe Myopia 0.59 0.27 0.32 0.07 2.08 0.00 Mild Hyperopia Mild Myopia 0.51 0.41 0.10 0.07 0.68 0.76 Mild Hyperopia Moderate Hyperopia 0.51 0.55 -0.03 0.09 -0.15 1.00 Mild Hyperopia Moderate Myopia 0.51 0.41 0.10 0.08 0.56 0.78 Mild Hyperopia Severe Myopia 0.51 0.27 0.25 0.09 1.19 0.11 Mild Myopia Moderate Hyperopia 0.41 0.55 -0.13 0.06 -1.04 0.27 Mild Myopia Moderate Myopia 0.41 0.41 0.00 0.03 0.01 1.00 Mild Myopia Severe Myopia 0.41 0.27 0.15 0.06 1.16 0.17 Moderate Hyperopia Moderate Myopia 0.55 0.41 0.13 0.06 0.83 0.31 Moderate Hyperopia Severe Myopia 0.55 0.27 0.28 0.07 1.72 0.02 Moderate Myopia Severe Myopia 0.41 0.27 0.15 0.06 0.91 0.21 *One-way ANOVA test p-value for the presence of differences in chord µ based on subjective refraction status < 0.001, Pair-wise comparisons performed utilizing Games-Howell post hoc non-parametric test, P-values < 0.05 are considered statistically significant. Table 4 Differences in Chord µ values based on refractive status. Sub-group (S) Comparator (C) Mean(S) Mean(C) Mean difference (mm) Standard error Hedges’ g P value Emmetropia Mild Hyperopia 0.40 0.33 0.06 0.07 0.37 0.95 Emmetropia Mild Myopia 0.40 0.26 0.14 0.04 1.36 0.05 Emmetropia Moderate Hyperopia 0.40 0.38 0.02 0.05 0.21 1.00 Emmetropia Moderate Myopia 0.40 0.30 0.10 0.05 0.54 0.40 Emmetropia Severe Myopia 0.40 0.21 0.19 0.04 2.06 0.01 Mild Hyperopia Mild Myopia 0.33 0.26 0.08 0.07 0.60 0.85 Mild Hyperopia Moderate Hyperopia 0.33 0.38 -0.04 0.07 -0.24 0.99 Mild Hyperopia Moderate Myopia 0.33 0.30 0.04 0.07 0.18 1.00 Mild Hyperopia Severe Myopia 0.33 0.21 0.13 0.07 0.76 0.49 Mild Myopia Moderate Hyperopia 0.26 0.38 -0.12 0.04 -1.15 0.10 Mild Myopia Moderate Myopia 0.26 0.30 -0.04 0.04 -0.28 0.89 Mild Myopia Severe Myopia 0.26 0.21 0.05 0.03 0.50 0.51 Moderate Hyperopia Moderate Myopia 0.38 0.30 0.08 0.05 0.42 0.65 Moderate Hyperopia Severe Myopia 0.38 0.21 0.17 0.04 1.85 0.02 Moderate Myopia Severe Myopia 0.30 0.21 0.09 0.04 0.51 0.30 *One-way ANOVA test p-value for the presence of differences in chord µ based on subjective refraction status = 0.02, Pair-wise comparisons performed utilizing Games-Howell post hoc non-parametric test, P-values < 0.05 are considered statistically significant. 3.3. Chord α and µ correlation A moderate positive correlation was found between chord α and chord µ (r = 0.60, 95% CI [0.46, 0.71], p < 0.001), indicating a significant association where larger values of chord α are related to larger values of chord µ. 3.4. Chord α Correlation Analysis The analysis revealed several significant moderate correlations for chord α. These included a positive correlation with subjective spherical refraction (r = 0.45, 95% CI [0.29, 0.59], p < 0.001), and spherical equivalent (r = 0.41, 95% CI [0.24, 0.56], p < 0.001). Moderate negative correlations were observed with anterior chamber depth (r = -0.53, 95% CI [-0.66, -0.39], p < 0.001) and axial length (r = -0.40, 95% CI [-0.55, -0.23], p < 0.001). Moreover, a number of significant weak correlations with chord α were identified. These included positive correlations with corneal trefoil (r = 0.26, 95% CI [0.08, 0.43], p = 0.01) and lens thickness (r = 0.22, 95% CI [0.03, 0.39], p = 0.02). 3.5. Chord µ Correlation Analysis In contrast, the correlations involving chord µ were exclusively weak in magnitude. Significant weak negative correlations were found with anterior chamber depth (r = -0.37, 95% CI [-0.52, -0.19], p < 0.001), axial length (r = -0.25, 95% CI [-0.42, -0.07], p = 0.01), and subjective refractive cylinder (r = -0.22, 95% CI [-0.39, -0.04], p = 0.02). Significant weak positive correlations were observed between chord µ and several aberrometric and refractive parameters. These included corneal trefoil (r = 0.35, 95% CI [0.18, 0.51], p < 0.001), ocular coma (r = 0.31, 95% CI [0.13, 0.47], p < 0.001), subjective spherical refraction (r = 0.31, 95% CI [0.13, 0.47], p < 0.001), ocular trefoil (r = 0.28, 95% CI [0.10, 0.45], p < 0.001), total ocular higher-order aberrations (r = 0.26, 95% CI [0.08, 0.43], p < 0.001), spherical equivalent (r = 0.24, 95% CI [0.05, 0.41], p = 0.01), and lens thickness (r = 0.22, 95% CI [0.03, 0.39], p = 0.02). Pupil diameter and age did not have significant correlations with any of the two chords. The full matrix of correlations and their strengths are depicted in Fig. 3 . 3.6. Regression analysis The regression model indicated that chord α is a significant predictor of chord µ, accounting for 36% of its variance (R² = 0.36, p < 0.001). The model can be expressed by the equation: Chord µ = 0.06 + 0.54 * (Chord α), where for every 1 mm increase in chord α, chord µ is predicted to increase by 0.54 mm. When examining predictors for chord α, several anatomical and refractive parameters showed significant explanatory power. Anterior chamber (AC) depth emerged as the most influential anatomical factor, explaining 28% of the variance in chord α (R² = 0.28, p < 0.001). Subjective spherical refraction accounted for 17% of the variance (R² = 0.17, p < 0.001), while axial length explained 16% (R² = 0.16, p < 0.001). These relationships are defined by the equations: Chord α = 1.21–0.23 * (AC Depth), Chord α = 0.49 + 0.03 * (Spherical Equivalent), and Chord α = 1.76 − 0.06 * (Axial Length), respectively. For chord µ, the predictive power of these same variables was considerably weaker. Besides the strong prediction from chord α, AC depth explained only 13% of the variance in chord µ (p < 0.001), and axial length accounted for a mere 6% (p = 0.01). Figures 4 and 5 depict the regression analysis between various ocular biometric and wave-front characteristics with chord α and µ, respectively. Discussion The longstanding pursuit of emmetropia and satisfactory vision in cataract and refractive surgery necessitates a precise understanding of the eye's optical alignment. As the study of chord µ and chord α has demonstrated its importance in MIOL implantation surgeries[ 27 , 28 ], most studies have used angle kappa and angle α as predictor factors for postoperative visual outcomes, rather than investigating the association between these angles and refractive errors or higher-order aberrations in preoperative patients. A primary finding of this study was a low to moderate and relatively consistent correlation between the magnitudes of both chords and the eye's fundamental biometric architecture. We demonstrate that chord α serves as a more robust indicator of this static, anatomical decentration than the more variable chord µ. Furthermore, our results align with the theoretical expectation that greater decentration correlates with degraded optical quality, evidenced by weak but significant positive correlations between these chords and specific HOAs. Our study acknowledges the previously well-established biometric characteristics of eyes with significant visual axis decentration. In this regard, the moderate positive correlation of chord α with hyperopic spherical equivalent (r = 0.41)[ 6 , 29 ] and its moderate negative correlations with axial length (r = -0.40)[ 6 , 30 , 31 ] and anterior chamber depth (r = -0.53)[ 30 , 31 ] are highly consistent with previous reports. This confirms that shorter, hyperopic eyes with more compact anterior segments are predisposed to larger chord α values. A critical finding of our study, however, is the marked difference in the strength of these correlations compared to chord µ, which were exclusively weak. This disparity strongly supports the growing consensus that chord α, referenced to the stable geometric center of the limbus[ 32 ], is a more reliable surrogate measure for the eye's static anatomical framework than the pupil-referenced chord µ[ 33 ], where the pupil's dynamic nature may render chord µ susceptible to variations in illumination and accommodation[ 30 ] Regarding the interplay of the two chords and refractive status, we found significantly higher chord values in severely myopic and emmetropic eyes compared to the moderate hyperopic patients. A previous study by Basmak et al. reported that chord µ values demonstrated a significant drop toward negative refractive errors in the myopic group. Conversely, a positive correlation was found between chord µ values and positive refractive errors in the hyperopic group[ 8 ]. Moreover, a recent study reported that a large angle kappa predominantly occurs in patients with medium and low myopia, whereas a small angle kappa is primarily associated with severe myopia, as these patients often need to move closer to objects for clear vision[ 34 ]. Correspondingly, the results around axial length are justified. As a surrogate measure of refractive status, several studies have reported a significant inverse relationship between axial length and both angle alpha and angle kappa. In a Korean cohort of 436 eyes, angle kappa correlated negatively with AL (r = − 0.342, p < 0.001)[ 35 ], while a larger study of 8,119 eyes showed that the magnitudes of angle alpha and angle kappa of the right eyes both varied significantly with AL[ 31 ]. Furthermore, comparison of highly myopic eyes (AL > 26 mm) with short eyes (AL < 22 mm) revealed increases of 43.9% in chord mu and 49.7% in chord α in the latter group[ 30 ]. There is a paucity of data and several controversies regarding the relationship between chord α and µ with other ocular biometric indices, namely CCT, WTW distance, and lens thickness. Our study demonstrated a weak positive correlation between both chords and CCT and lens thickness, while there was a negligible inverse correlation with horizontal WTW distance. In line with our results, Velasco-Barona et al. identified a significant inverse correlation between WTW distance and angle alpha (r = -0.359, p = 0.001)[ 6 ]. Similarly, in a post-phacoemulsification population, WTW corneal diameter showed the strongest correlation with change in angle kappa (r = -0.44, p < 0.001), leading to a predictive equation: every 1 mm increment in WTW diameter was associated with a 2.42 scale reduction in angle kappa. However, no significant correlation was found with angle kappa and lens thickness[ 5 ]. Neuman et al. reported a statistically significant, yet negligible to weak, inverse correlation between the chords and both lens thickness and CCT. As both of our studies used IOLMaster 700 for measuring these variables, the discrepancy between our studies could be due to the ethnical differences[ 36 ] or their considerably larger sample size than ours[ 31 ]. In a study of 438 eyes from 219 children (3–15 years) using the IOLMaster 700, neither angle alpha (p = 0.263) nor angle kappa (p = 0.541) correlated with CCT. Both, however, were significantly associated with corneal curvature WTW distance[ 37 ]. Our study did not find a significant correlation between either chord and patient age, which contrasts with some large-scale reports indicating a weak positive correlation. A Korean population study found angle kappa increased with age, particularly in women over 70 years and men in their 50s[ 35 ], which is further accredited by several other studies[ 31 , 38 ]. This discrepancy is likely attributable to the intentionally narrow age range of our cohort (35–55 years), which may have been insufficient to detect the subtle, long-term anatomical changes that manifest across a broader lifespan. The lack of correlation with pupil diameter was expected for chord α[ 30 ], but contradicts some previous studies indicating an increasing trend of chord µ with larger pupil diameters[ 31 ], particularly under pharmacological cycloplegia[ 30 , 39 ]. There is an approximate 0.1 mm increase in chord µ following pharmacological pupillary dilation[ 40 ]. On the other hand, a large-scale study on approximately 1400 eyes reported a nearly similar chord mu for mesopic (0.33 mm ± 0.15 mm) and photopic (0.31 mm ± 0.15 mm) pupils [ 41 ]. By conducting all measurements under standardized dark-room conditions without pharmacological agents, we may have minimized the known confounding effect of pupil dynamics on chord µ measurements. Moreover, the relationship of these chords with gender is highly inconsistent within the literature. While a huge demographic study in the Chinese population showed significantly higher values of chord alpha among females[ 36 ]. Another study by Wang et al. yielded similar results to our study, failing to detect any meaningful correlation between gender and the magnitude of these chords[ 42 ]. The relationship between these chords and higher-order aberrations appears to be complex. Our analysis revealed weak but significant positive correlations between chord µ and total ocular HOAs (r = 0.26), ocular coma (r = 0.31), and both corneal and ocular trefoil. Chord α also showed a positive correlation with corneal trefoil (r = 0.26). This aligns with the theoretical framework where decentration of optical elements induces specific HOAs, particularly coma and trefoil, and could help reconcile the present inconsistencies in linking the chord values with HOAs. These correlations might explain the hypothesized influence of chord α and µ on patient satisfaction and nuanced visual outcomes post-phacoemulsification and use of MIOLs. Recently, a growing body of evidence has linked the alignment of optical axes and their proxies (chord µ and chord α) to both objective and subjective post-operative visual outcomes with MIOLs. A large chord µ may negatively impact objective visual quality parameters, such as the objective scatter index, Strehl ratio, and modulation transfer function cutoff frequency. Additionally, a large chord µ is linked to photic phenomena, including glare, starbursts, and halos, following eye surgery[ 43 – 46 ]. In a study of two aspheric IOLs, a larger angle α was associated with greater higher-order aberrations (HOAs) across all pupil sizes, while a larger angle κ correlated with reduced visual quality, reflected by a lower Strehl ratio and higher internal HOAs[ 47 ]. Cervantes-Coste et al. reported that preoperative angle α was not associated with HOAs and visual acuities measured after surgery. However, they found that postoperative angle α had a negative impact on intermediate vision. Lee et al. conducted a retrospective study on patients with quadrifocal intraocular lenses (IOLs). They found that a smaller chord α was associated with better far and near visual outcomes, whereas larger chord α values correlated with poorer postoperative visual acuity[ 14 ]. The corneal HOAs had a significant negative correlation with postoperative angle α, in contrast to the internal HOAs, which showed a weaker, but still significant correlation[ 48 ]. Although Fu et al. did not identify any correlations between chord α and postoperative visual parameters, they observed that the majority of patients with a chord α exceeding 0.5 mm experienced disturbing visual symptoms[ 49 ]. Moreover, a chord α value exceeding 0.4 mm correlates with poorer objective visual quality under scotopic conditions following extended depth of focus (EDOF) IOL implantation, and it also increases the risk of halos and glare post-surgery[ 45 ]. This study benefits from the use of high-resolution instrumentation, combining swept-source OCT biometry with pyramidal aberrometry, particularly useful in assessing the relationship of the chords with total ocular aberrations and their sub-categories. Nevertheless, several limitations must be acknowledged. The IOL Master 700 measures the apparent chord µ, which is larger than the actual one, as it sees the picture of the pupil through the cornea and is thus subject to the corneal magnification[ 18 ]. This could affect the results. The cross-sectional design precludes any inference of causality, and the sample size, while adequate for correlational analysis, may limit the broader generalizability of our findings. We only used the data of the right eye, which ignores previously proven inherent differences of the eyes regarding laterality and dominance[ 31 , 36 ]. The most significant limitation is the absence of postoperative data. While our preoperative findings provide a detailed characterization of the baseline optical system, longitudinal follow-up is essential to determine the ultimate predictive power of these correlations on surgical outcomes. Conclusions In summary, this study highlights chord α as a reliable anatomical marker, closely linked to the biometric structure of hyperopic eyes and more stable than chord µ. Although its association with higher-order aberrations is modest, it underscores the role of optical decentration in visual quality and may harbor considerable clinical implications. Larger chord values may indicate a higher risk of pre-existing aberrations and impaired optical balance, warranting cautious surgical planning. Declarations Disclosure of financial and proprietary interests for all authors: In accordance with ethical standards and transparency practices, all authors involved in this study have disclosed their financial and proprietary interests. Each author has provided a detailed account of any potential conflicts of interest or explicitly stated that they have no such interests to declare. Acknowledgements The authors have no acknowledgements to declare. Funding The authors received no financial support for the research, authorship, and/or publication of this article. Competing Interests The authors have no competing interests to declare. Authors’ contributions Armin Doostparast was responsible for conceptualization, methodology, formal analysis, data visualization, table preparation, project administration, and drafting of the original manuscript, as well as its review and editing. Farbod Semnani was involved in conceptualization, methodology, formal analysis, drafting, and reviewing the manuscript. Maryam Ghandhari, Amir Hossein Khosronejad, Mohammad Mirzaei, and Amirhossein Amiriani contributed to data preparation, project administration, and manuscript drafting. Alireza Eslampoor contributed to conceptualization, methodology, provision of resources, supervision, and critical review and editing. All authors reviewed and approved the final version of the manuscript. *Armin Doostparast and Farbod Semnani contributed equally to this work as co–first authors. Ethics approval The study was approved by the Research Ethics Office of Mashhad University of Medical Sciences (Ethics ID: IR.MUMS.MEDICAL.REC.1403.238). All procedures strictly adhered to the tenets of the Declaration of Helsinki. All participants provided written informed consent. Consent for publication Not applicable. Availability of data and materials The data of the study are available from the corresponding author upon reasonable request. References Doane JF, Cavanaugh TB. Optical Zone Centration for Keratorefractive Surgery. Ophthalmology. 1994;101:215–6. Rodrigues PF, Moscovici BK, Lamazales L, Freitas MMS, Gomes JÁP, Nosé W, et al. Measurement of the visual axis through two different methods: quantification and differences for measuring chord µ. Arq Bras Oftalmol [Internet]. 2023 [cited 2025 Aug 7];87:e2022-0035. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC11619329/ Mosquera SA, Verma S, McAlinden C. Centration axis in refractive surgery. Eye and Vision [Internet]. 2015 [cited 2025 Aug 7];2:4. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC4655455/ Evans T, Rubin A. Linear optics of the eye and optical systems: a review of methods and applications. BMJ Open Ophthalmol [Internet]. 2022 [cited 2025 Aug 7];7. Available from: https://bmjophth.bmj.com/content/7/1/e000932 Umesh Y, Saolapurkar K, Joshi P, Singh D. Measurement of change in angle kappa and its correlation with ocular biometric parameters pre- and post-phacoemulsification. Indian J Ophthalmol [Internet]. 2023 [cited 2025 Aug 7];71:535. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC10228972/ Velasco-Barona C, Corredor-Ortega C, Avendaño-Domnguez A, Cervantes-Coste G, Cantú-Treviño MP, Gonzalez-Salinas R. Impact of correlation of angle α with ocular biometry variables. J Cataract Refract Surg [Internet]. 2021 [cited 2025 Aug 20];47:1279–84. Available from: https://pubmed.ncbi.nlm.nih.gov/34544085/ A M, R Ž, K Y, A G. Chord mu and chord alpha as postoperative predictors in multifocal intraocular lens implantation. Graefes Arch Clin Exp Ophthalmol [Internet]. 2024 [cited 2025 Aug 7];262. Available from: https://pubmed.ncbi.nlm.nih.gov/37278907/ Basmak H, Sahin A, Yildirim N, Papakostas TD, Kanellopoulos AJ. Measurement of angle kappa with synoptophore and Orbscan II in a normal population. Journal of Refractive Surgery [Internet]. 2007 [cited 2025 Aug 8];23:456–60. Available from: https://pubmed.ncbi.nlm.nih.gov/17523505/ Fricke TR, Tahhan N, Resnikoff S, Papas E, Burnett A, Ho SM, et al. Global Prevalence of Presbyopia and Vision Impairment from Uncorrected Presbyopia: Systematic Review, Meta-analysis, and Modelling. Ophthalmology [Internet]. 2018 [cited 2025 Aug 8];125:1492–9. Available from: https://pubmed.ncbi.nlm.nih.gov/29753495/ Salerno L, Tiveron M, Alió J. Multifocal intraocular lenses: Types, outcomes, complications and how to solve them. Taiwan J Ophthalmol [Internet]. 2017 [cited 2025 Aug 8];7:179. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC5747227/ Velasco-Barona C, Corredor-Ortega C, Mendez-Leon A, Casillas-Chavarín NL, Valdepeña-López Velarde D, Cervantes-Coste G, et al. Influence of angle and higher-order aberrations on visual quality employing two diffractive trifocal IOLs. J Ophthalmol [Internet]. 2019 [cited 2025 Aug 8];2019. Available from: https://pubmed.ncbi.nlm.nih.gov/31885892/ Liu Y, Gao Y, Liu R, Hu C, Ma B, Miao J, et al. Influence of angle kappa-customized implantation of rotationally asymmetric multifocal intraocular lens on visual quality and patient satisfaction. Acta Ophthalmol [Internet]. 2020 [cited 2025 Aug 8];98:e734–42. Available from: https://pubmed.ncbi.nlm.nih.gov/31981307/ Garzón N, García-Montero M, López-Artero E, Albarrán-Diego C, Pérez-Cambrodí R, Illarramendi I, et al. Influence of angle on visual and refractive outcomes after implantation of a diffractive trifocal intraocular lens. J Cataract Refract Surg [Internet]. 2020 [cited 2025 Aug 7];46:721–7. Available from: https://pubmed.ncbi.nlm.nih.gov/32358267/ Lee CY, Huang JY, Sun CC, Yang SF, Chen HC, Lin HY. Correlation and predictability of ocular aberrations and the visual outcome after quadrifocal intraocular lens implantation: A retrospective longitudinal study. BMC Ophthalmol [Internet]. 2019 [cited 2025 Aug 8];19. Available from: https://pubmed.ncbi.nlm.nih.gov/31426784/ Kim DR, Yoon YC, Whang WJ, Hwang HS, Na KS. Ocular parameters associated with visual performance of enhanced monofocal intraocular lens. BMC Ophthalmol [Internet]. 2024 [cited 2025 Aug 8];24. Available from: https://pubmed.ncbi.nlm.nih.gov/38369454/ Gharieb Ibrahim HM, Gharieb HM, Othman IS. Angle κ Measurement and Its Correlation with Other Ocular Parameters in Normal Population by a New Imaging Modality. Optometry and Vision Science [Internet]. 2022 [cited 2025 Aug 8];99:580–8. Available from: https://pubmed.ncbi.nlm.nih.gov/35657347/ Klaproth O. ZEISS IOLMaster 700. Essentials in Ophthalmology [Internet]. 2024 [cited 2025 Aug 9];297–306. Available from: https://link.springer.com/chapter/10.1007/978-3-031-50666-6_17 Holladay JT. Apparent chord mu and actual chord mu and their clinical value. J Cataract Refract Surg [Internet]. 2019 [cited 2025 Aug 9];45:1198–9. Available from: https://pubmed.ncbi.nlm.nih.gov/31371009/ SCHWIND PERAMIS: Topographer and aberrometer [Internet]. [cited 2025 Aug 9]. Available from: https://www.eye-tech-solutions.com/en/products/diagnostic-systems/schwind-peramis Pedregosa FABIANPEDREGOSA F, Michel V, Grisel OLIVIERGRISEL O, Blondel M, Prettenhofer P, Weiss R, et al. Scikit-learn: Machine Learning in Python. The Journal of Machine Learning Research [Internet]. 2011 [cited 2025 Aug 9];12:2825–30. Available from: https://dl.acm.org/doi/pdf/10.5555/1953048.2078195 Vallat R. Pingouin: statistics in Python. J Open Source Softw [Internet]. 2018 [cited 2025 Aug 9];3:1026. Available from: https://joss.theoj.org/papers/10.21105/joss.01026 Waskom ML. seaborn: statistical data visualization. J Open Source Softw [Internet]. 2021 [cited 2025 Aug 9];6:3021. Available from: https://joss.theoj.org/papers/10.21105/joss.03021 IterativeImputer — scikit-learn 1.7.1 documentation [Internet]. [cited 2025 Aug 9]. Available from: https://scikit-learn.org/stable/modules/generated/sklearn.impute.IterativeImputer.html Agbangba CE, Sacla Aide E, Honfo H, Glèlè Kakai R. On the use of post-hoc tests in environmental and biological sciences: A critical review. Heliyon [Internet]. 2024 [cited 2025 Aug 20];10:e25131. Available from: https://www.sciencedirect.com/science/article/pii/S2405844024011629 Welz T, Doebler P, Pauly M. Fisher transformation based confidence intervals of correlations in fixed- and random-effects meta-analysis. British Journal of Mathematical and Statistical Psychology [Internet]. 2022 [cited 2025 Aug 19];75:1–22. Available from: https://pubmed.ncbi.nlm.nih.gov/33934346/ Schober P, Schwarte LA. Correlation coefficients: Appropriate use and interpretation. Anesth Analg [Internet]. 2018 [cited 2025 Aug 19];126:1763–8. Available from: https://journals.lww.com/anesthesia-analgesia/fulltext/2018/05000/correlation_coefficients__appropriate_use_and.50.aspx Karhanová M, Pluháček F, Mlčák P, Vláčil O, Šín M, Marešová K. The importance of angle kappa evaluation for implantation of diffractive multifocal intra-ocular lenses using pseudophakic eye model. Acta Ophthalmol [Internet]. 2015 [cited 2025 Aug 20];93:e123–8. Available from: https://pubmed.ncbi.nlm.nih.gov/25160117/ Prakash G, Prakash DR, Agarwal A, Kumar DA, Jacob S. Predictive factor and kappa angle analysis for visual satisfactions in patients with multifocal IOL implantation. Eye [Internet]. 2011 [cited 2025 Aug 20];25:1187–93. Available from: https://pubmed.ncbi.nlm.nih.gov/21681216/ Bteich Y, Ibrahim H, Barake K, Khalil J, Assaf JF, Reinstein DZ, et al. Distribution of Angle Alpha and Angle Kappa Chord Magnitude and Axes in Myopic and Hyperopic Refractive Surgery Candidates. Journal of Refractive Surgery [Internet]. 2025 [cited 2025 Aug 20];41:e585–93. Available from: https://pubmed.ncbi.nlm.nih.gov/40488487/ Stern B, Chowers I, Ben-Eli H. Effect of mydriasis on chord mu value in cataract surgery candidates. Eur J Ophthalmol [Internet]. 2024 [cited 2025 Aug 20];34:759–65. Available from: https://journals.sagepub.com/doi/10.1177/11206721231207470 Neuman G, Abulafia A, Wasser L, Zadok D. Distribution of angle alpha and angle kappa offsets among adult candidates for cataract surgery. Graefe’s Archive for Clinical and Experimental Ophthalmology [Internet]. 2024 [cited 2025 Aug 20];263:157. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC11807017/ Miháltz K, Vécsei-Marlovits PV. The impact of visual axis position on the optical quality after implantation of multifocal intraocular lenses with different asphericity values. Graefe’s Archive for Clinical and Experimental Ophthalmology [Internet]. 2021 [cited 2025 Aug 20];259:673–83. Available from: https://pubmed.ncbi.nlm.nih.gov/33471202/ Montrimas A, Žemaitienė R, Yao K, Grzybowski A. Chord mu and chord alpha as postoperative predictors in multifocal intraocular lens implantation. Graefe’s Archive for Clinical and Experimental Ophthalmology [Internet]. 2024 [cited 2025 Aug 20];262:367–80. Available from: https://pubmed.ncbi.nlm.nih.gov/37278907/ Ding Y, Zhang Z, Min X, Xia X, Hu S. Changes of angle Kappa and corneal morphology changes in myopic patients after Sub-Bowman-Keratomileusis. Journal of Central South University (Medical Sciences) [Internet]. 2021 [cited 2025 Aug 20];46:162–8. Available from: https://pubmed.ncbi.nlm.nih.gov/33678653/ Choi SR ang, Kim US amuel. The Correlation between Angle Kappa and Ocular Biometry in Koreans. Korean J Ophthalmol [Internet]. 2013 [cited 2025 Aug 20];27:421. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC3849305/ Hua Z, Zeng Q, Zhang L, Shen J, Yang J. Distribution of Angle Alpha in a Large Population in Eastern China: An Analysis of the 30705 Eyes Using the Ray Tracing Aberrometer. Clin Ophthalmol [Internet]. 2025 [cited 2025 Aug 25];19:753. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC11889998/ Ye Y, Zhao Y, Zhang Z, Wei R, Xian Y, Huang Y, et al. Correlation analysis of angles κ and α with the refraction and anterior segment parameters in children. BMC Ophthalmol [Internet]. 2024 [cited 2025 Aug 20];24:143. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC10976721/ Chen XN, Xiong YY, Wei J, Luo B, Gao YL. Alpha and Kappa angle on postoperative visual quality in cataract surgery. Int J Ophthalmol [Internet]. 2025 [cited 2025 Aug 20];18:1023. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC12120454/ Sella R, Shouchane-Blum K, Reitblat O, Bahar I. The association between pupil diameter and apparent chord mu length value. Invest Ophthalmol Vis Sci. 2022;63:1698-F0016-1698 – F0016. Shouchane-Blum K, Reitblat O, Dadon J, Bahar I, Sella R. Evaluating Changes in Apparent Chord Mu after Pharmacological Pupil Dilatation. Ophthalmic Res [Internet]. 2023 [cited 2025 Aug 20];66:921–7. Available from: https://pubmed.ncbi.nlm.nih.gov/37231882/ Wang Q, Stoakes IM, Moshirfar M, Harvey DH, Hoopes PC. Assessment of Pupil Size and Angle Kappa in Refractive Surgery: A Population-Based Epidemiological Study in Predominantly American Caucasians. Cureus [Internet]. 2023 [cited 2025 Aug 20];15. Available from: https://pubmed.ncbi.nlm.nih.gov/37638275/ Wang R, Long T, Gu X, Ma T. Changes in angle kappa and angle alpha before and after cataract surgery. J Cataract Refract Surg [Internet]. 2020 [cited 2025 Aug 25];46:365–71. Available from: https://pubmed.ncbi.nlm.nih.gov/32050219/ Park CY, Oh SY, Chuck RS. Measurement of angle kappa and centration in refractive surgery. Curr Opin Ophthalmol [Internet]. 2012 [cited 2025 Aug 7];23:269–75. Available from: https://pubmed.ncbi.nlm.nih.gov/22569467/ Fu Y, Kou J, Chen D, Wang D, Zhao Y, Hu M, et al. Influence of angle kappa and angle alpha on visual quality after implantation of multifocal intraocular lenses. J Cataract Refract Surg [Internet]. 2019 [cited 2025 Aug 7];45:1258–64. Available from: https://pubmed.ncbi.nlm.nih.gov/31326223/ Qi Y, Lin J, Leng L, Zhao G, Wang Q, Li C, et al. Role of angle κ in visual quality in patients with a trifocal diffractive intraocular lens. J Cataract Refract Surg [Internet]. 2018 [cited 2025 Aug 7];44:949–54. Available from: https://pubmed.ncbi.nlm.nih.gov/30033112/ Tchah H, Nam K, Yoo A. Predictive factors for photic phenomena after refractive, rotationally asymmetric, multifocal intraocular lens implantation. Int J Ophthalmol [Internet]. 2017 [cited 2025 Aug 7];10:241–5. Available from: https://pubmed.ncbi.nlm.nih.gov/28251083/ Thakur A, Adiga S, Malhotra C, Sachdeva K, Singh S, Jain AK. Effect of decentration on the quality of vision in two aspheric posterior chamber intraocular lenses: A contralateral eye study. Indian J Ophthalmol [Internet]. 2024 [cited 2025 Aug 20];72:558–64. Available from: https://pubmed.ncbi.nlm.nih.gov/38189441/ Cervantes-Coste G, Tapia A, Corredor-Ortega C, Osorio M, Valdez R, Massaro M, et al. The Influence of Angle Alpha, Angle Kappa, and Optical Aberrations on Visual Outcomes after the Implantation of a High-Addition Trifocal IOL. J Clin Med [Internet]. 2022 [cited 2025 Aug 20];11. Available from: https://pubmed.ncbi.nlm.nih.gov/35160346/ Fu Y, Kou J, Chen D, Wang D, Zhao Y, Hu M, et al. Influence of angle kappa and angle alpha on visual quality after implantation of multifocal intraocular lenses. J Cataract Refract Surg [Internet]. 2019 [cited 2025 Aug 20];45:1258–64. Available from: https://pubmed.ncbi.nlm.nih.gov/31326223/ Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 17 Dec, 2025 Read the published version in International Ophthalmology → Version 1 posted Editorial decision: Revision requested 13 Oct, 2025 Reviews received at journal 13 Oct, 2025 Reviews received at journal 06 Oct, 2025 Reviewers agreed at journal 23 Sep, 2025 Reviewers agreed at journal 22 Sep, 2025 Reviewers invited by journal 09 Sep, 2025 Editor assigned by journal 05 Sep, 2025 Submission checks completed at journal 05 Sep, 2025 First submitted to journal 25 Aug, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7456104","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":505405720,"identity":"e0272005-5760-44d9-930d-8fb5cfc30628","order_by":0,"name":"Armin Doostparast","email":"","orcid":"","institution":"Mashhad University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Armin","middleName":"","lastName":"Doostparast","suffix":""},{"id":505405721,"identity":"d6694d34-6b22-47aa-b19c-22c6e39f5657","order_by":1,"name":"Farbod Semnani","email":"","orcid":"","institution":"National Center for Health Insurance Research","correspondingAuthor":false,"prefix":"","firstName":"Farbod","middleName":"","lastName":"Semnani","suffix":""},{"id":505405722,"identity":"d3dcb0a3-567a-434b-87f5-f4f41ea8c2b1","order_by":2,"name":"Maryam Ghandhari","email":"","orcid":"","institution":"Mashhad University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Maryam","middleName":"","lastName":"Ghandhari","suffix":""},{"id":505405723,"identity":"00582ae5-4c2c-43a6-95df-df7183770b38","order_by":3,"name":"Amir Hossein Khosronejad","email":"","orcid":"","institution":"Mazandaran University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Amir","middleName":"Hossein","lastName":"Khosronejad","suffix":""},{"id":505405724,"identity":"f5c9f5c0-ea45-4a0f-b66f-ee975f9a88df","order_by":4,"name":"Mohammad Mirzaei","email":"","orcid":"","institution":"Mashhad University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"","lastName":"Mirzaei","suffix":""},{"id":505405725,"identity":"cbe92864-568f-43c6-8bbf-27533b5bc357","order_by":5,"name":"Amirhossein Amiriani","email":"","orcid":"","institution":"Mashhad University of Medical Sciences","correspondingAuthor":false,"prefix":"","firstName":"Amirhossein","middleName":"","lastName":"Amiriani","suffix":""},{"id":505405726,"identity":"640de962-c847-4d4f-a75b-bc48c338d485","order_by":6,"name":"Alireza Eslampoor","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVRIiWNgGAWjYBACezBZAOV9AGI2dgJaDBtApAGEwzgDpIWZgBaDA0hamHnAJCEttw8wPvxhYBdtzt587LPNr23yfMwMjB8+5uDRci6B2ZjHIDl3Z8+x5Nm5fbcN25gZmCVnbsOj5QwDmzSDAXPuhhs5xsy5PbcZgVrYmHnxa2H/+cOgHqLFsue2PTFa2Bh4DA5DtDD8uJ1IUIthD2OzNI/BcbBfGHsbbie3MTM24/WLPQ/zwY8/Kqpzt7M3H2b48ee27fz25oMfPuLRAoy/BogLwew2JBGCABKbf4hTPApGwSgYBSMLAADFPk1B18VRrQAAAABJRU5ErkJggg==","orcid":"","institution":"Mashhad University of Medical Sciences","correspondingAuthor":true,"prefix":"","firstName":"Alireza","middleName":"","lastName":"Eslampoor","suffix":""}],"badges":[],"createdAt":"2025-08-25 17:38:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7456104/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7456104/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10792-025-03893-9","type":"published","date":"2025-12-17T15:58:02+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":90485742,"identity":"f222b858-2e18-43f0-9150-0a198c27f5f4","added_by":"auto","created_at":"2025-09-03 08:49:59","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":381720,"visible":true,"origin":"","legend":"\u003cp\u003eThe distribution of chord alpha values among different refractive states. Box plots represent median (Inter-quartile range) and 95% confidence intervals. Black dots represent the mean of the values. Red dots represent the outlier values.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-7456104/v1/de0a24b5a93e0e25da77734c.png"},{"id":90485743,"identity":"fb532804-edc8-4cb2-b2c5-f797b15a958f","added_by":"auto","created_at":"2025-09-03 08:49:59","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":402384,"visible":true,"origin":"","legend":"\u003cp\u003eThe distribution of chord mu values among different refractive states. Box plots represent median (Inter-quartile range) and 95% confidence intervals. Black dots represent the mean of the values. Red dots represent the outlier values.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-7456104/v1/d64fdd180f6260b9f51841b3.png"},{"id":90485749,"identity":"53165dcb-887b-47de-b33d-f72423741eb3","added_by":"auto","created_at":"2025-09-03 08:49:59","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":907973,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation matrix.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-7456104/v1/3a794e48e2a199e889238fba.png"},{"id":90485747,"identity":"2901aee8-20e0-4d12-bd32-8c563142adb8","added_by":"auto","created_at":"2025-09-03 08:49:59","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":4197357,"visible":true,"origin":"","legend":"\u003cp\u003eRegression plots regarding the correlations of chord alpha with several refractive and biometric characteristics of the eye. Circles with black and grey borders represent male and female patients, respectively. Blue: myopia, Green: Emmetropia, Coral: Hyperopia\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-7456104/v1/298855cbbf7a8097e82ebfc4.png"},{"id":90487413,"identity":"8fe8e5ed-f749-4999-b5cc-9b5377a9d851","added_by":"auto","created_at":"2025-09-03 09:05:59","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":4148749,"visible":true,"origin":"","legend":"\u003cp\u003eRegression plots regarding the correlations of chord mu with several refractive and biometric characteristics of the eye. Circles with black and grey borders represent male and female patients, respectively. Blue: myopia, Green: Emmetropia, Coral: Hyperopia\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-7456104/v1/eb6326b6007e22815df200d5.png"},{"id":98814978,"identity":"56c84f4f-3ca2-43d1-8b36-a800a871873a","added_by":"auto","created_at":"2025-12-22 16:13:11","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10800223,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7456104/v1/c07d3bb4-bcef-48ea-9a46-99bc16cfaf36.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Exploring the interplay of chord α and chord μ with pyramidal wavefront aberrometry and ocular biometric indices among pre-operative refractive surgery candidates","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe human eye relies on the alignment of several optical axes to achieve optimal vision, including the visual, pupillary, and optical axes [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. The visual axis, also known as the foveal-fixation axis, connects the fixation point to the fovea and passes through the two nodal points [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Meanwhile, the optical axis is the line passing through and connecting the geometric centers of curvature of the cornea and lens [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The pupillary axis, on the other hand, is the line perpendicular to the local tangent of the cornea reaching the center of the entrance pupil[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Misalignment of these axes affects the visual quality and refractive outcomes[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], making their understanding crucial in clinical practice.\u003c/p\u003e\u003cp\u003eThe angles between the optical and pupillary axes and the visual axis are called angle α and kappa[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Directly reporting angular distances like kappa and α is uncommon in clinical and research settings; thus, modern devices use linear measurements, chord \u0026micro; and chord α in millimeters. Chord \u0026micro; is the distance between the pupil center and corneal vertex (also known as the coaxially-sighted corneal light reflex or the first Purkinje image), whereas chord α is the distance between the geometric center of the cornea (center of the white-to-white distance) and corneal vertex[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eAngle kappa and alpha have several clinical implications. A large angle kappa may lead to alignment errors during photoablation in laser refractive surgery when the ablation is centered on the pupil center, which carries the risk of under-correction and irregular astigmatism[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Moreover, in light of the growing global burden of presbyopia[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] and the burgeoning popularity and recent technological advances of multifocal intraocular lenses (MIOL) as corrective measures, patients still report a higher incidence of visual disturbances (like glare, halos, starbursts) and reduced contrast sensitivity with these compared with monofocal lenses[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. However, some other studies reported no significant correlation between chord \u0026micro; and refractive or visual outcomes after ocular surgeries[\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eOn the other hand, smaller chord α values are predictive of better visual outcomes for both near and distance vision, while larger chord α values could be associated with poorer postoperative visual acuity[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. It is also suggested that as angle α increases, there is a significant decline in uncorrected intermediate visual acuity[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eExisting research mostly explored the effects of chord \u0026micro; and α on the visual outcomes, but the relationships between chord \u0026micro; and α with ocular biometric and topographic characteristics, as well as ocular aberrations, require a more extensive investigation. By recognizing these correlations, clinicians can develop a deeper understanding of eyes more likely to have large or small chord values. This insight raises awareness for specific patient types and enhances understanding of the anatomical factors behind visual axis decentration. For instance, it has been shown that chord \u0026micro; is associated with spherical equivalent, spherical refraction, and inversely correlated with axial length, asphericity Q front, and keratometry[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThus, the goal of this study is to evaluate the relationship between chord α and chord \u0026micro;, with age, ocular biometric indices, and corneal and ocular lower- and higher-order aberrations in candidate patients undergoing refractive surgery.\u003c/p\u003e"},{"header":"Methods and Materials","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Subjects\u003c/h2\u003e\u003cp\u003eThis cross-sectional study was conducted at Noorafarin Eye Clinic, Mashhad, Iran. The study population included patients who underwent a comprehensive eye examination and imaging between December 2023 and February 2024. All patients provided written informed consent after clearly explaining the study's objectives and procedures. The study received ethical approval from the Research Ethics Office of Mashhad University of Medical Sciences and adhered to the principles of the Declaration of Helsinki.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Inclusion and Exclusion Criteria\u003c/h2\u003e\u003cp\u003ePatients aged 35\u0026ndash;55 years with healthy, previously unoperated eyes who were scheduled for refractive surgery were included. The preliminary data for this study was collected from healthy individuals chosen to investigate connections with presbyopia, resulting in an age range of 35 to 55 years. Exclusion criteria compromised of the presence of proven or suspected keratoconus, history of dry eye disease, any other corneal diseases, trauma, or previous eye surgeries, poor fixation during imaging, use of rigid contact lenses within the last four weeks, or soft contact lenses within two weeks before imaging, and any other anterior segment abnormalities.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Imaging Protocol\u003c/h2\u003e\u003cp\u003eWe used the IOL Master 700 (ZEISS, Germany) device to measure topographic indices and ocular biometric data, namely axial length, CCT, anterior chamber (AC) depth, lens thickness, horizontal corneal white-to-white distance, as well as \u003cem\u003eapparent\u003c/em\u003e alpha/kappa chords[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Moreover, the PERAMIS (SCHWIND eye-tech-solutions, Germany) system provided detailed wavefront aberrometry data for the whole eye structure (total ocular aberrations). The ocular aberrations comprise two main components, the corneal and internal aberrations, with the internal referring to the aberrations originating from any structure behind the cornea. The PERAMIS system offers a comprehensive report for these three categories, containing total, higher-order, and lower-order aberrations, as well as the various Zernike coefficients[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. To facilitate a deeper evaluation of the HOAs, five Zernike coefficients, namely the vertical and horizontal coma (Z-1/3 and Z1/3), trefoil (Z-3/3 and Z3/3), and spherical (Z0/4) aberrations, were extracted from the PERAMIS reports for the ocular and corneal aberrations. All of the Zernike coefficients are expressed as root mean square (RMS). The data regarding these objective spherical and cylindrical refractions were also extracted from the reports.\u003c/p\u003e\u003cp\u003eFor each system, three consecutive acquisitions were recorded by the same experienced examiner, and the highest-quality image was selected. All assessments were performed in a dark room under mesopic conditions to eliminate the impact of external light sources. Before each measurement, participants were asked to blink multiple times to stabilize the tear film and were instructed to focus on the fixation target, following the manufacturer\u0026rsquo;s guidelines. Prior to the installation of each system, the devices were calibrated in accordance with the manufacturer's guidelines. Furthermore, daily calibrations were performed to ensure measurement accuracy. No mydriatic drug was applied to the eyes before imaging. The corrected distance visual acuity was measured by an optometrist using an E chart and was further transformed into the logMAR (Logarithm of the Minimum Angle of Resolution) visual acuity.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Statistical Analysis\u003c/h2\u003e\u003cp\u003eData analysis was performed with Python 3 (Python Software Foundation, USA), utilizing the pingouin and scikit-learn libraries[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. The Seaborn library was further employed for data visualization[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. Preprocessing steps included handling missing values and outliers. Missing data, accounting for less than 5% of the dataset, were not uniformly distributed across columns and were therefore filled using the Iterative Imputation function from scikit-learn[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Outliers were identified as data points below the 1st percentile or above the 99th percentile for each variable, and these outliers were adjusted to the 1st and 99th percentiles, respectively. The Shapiro-Wilk test was used to check for a possible violation of the normality assumption. For comparison of the association between refractive status and chords values, the eyes were categorized in sub-groups considering their spherical equivalent values as follows: Severe myopia (\u0026thinsp;\u0026gt;\u0026thinsp;\u0026minus;\u0026thinsp;6.00 D), moderate myopia (\u0026minus;\u0026thinsp;3.00 to \u0026minus;\u0026thinsp;6.00 D), mild myopia (\u0026minus;\u0026thinsp;0.50 to \u0026minus;\u0026thinsp;3.00 D), emmetropia (\u0026minus;\u0026thinsp;0.50 to 0.50 D), mild hyperopia (0.50 to 2.00 D), and moderate hyperopia (2.00 to 4.00 D). Welch\u0026rsquo;s One-way analysis of variance (ANOVA) and Games-Howell post-hoc non-parametric tests were utilized to determine any potential differences in these sub-groups[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Pearson\u0026rsquo;s correlation coefficient and Fisher\u0026rsquo;s Z-transformation were utilized to assess correlations between variables and to yield more reliable p-values and confidence intervals, respectively[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Strongly associated independent variables were further analyzed using simple linear regression models and visualized in pairwise plots. Results were reported with 95% confidence intervals (CI) and p-values, considering a significance threshold of p\u0026thinsp;\u0026lt;\u0026thinsp;0.05. Pearson\u0026rsquo;s r will be interpreted based on the following scale: values between 0 and 0.09 indicate a negligible correlation, 0.10 to 0.39 represent a weak correlation, 0.40 to 0.69 indicate a moderate correlation, 0.70 to 0.89 indicate a strong correlation, and 0.90 to 1.00 indicate a very strong correlation[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Baseline Characteristics\u003c/h2\u003e\u003cp\u003eThis study included 111 eyes of 111 patients, with an average age of 41.4\u0026thinsp;\u0026plusmn;\u0026thinsp;5.1 years, representing 34 (31%) men and 77 (69%) women. The mean chord α and \u0026micro; were 0.43\u0026thinsp;\u0026plusmn;\u0026thinsp;0.16 and 0.29\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15, ranging from 0.00 to 0.94 and 0.00 to 0.80, respectively. The mean pupil diameter was 5.38\u0026thinsp;\u0026plusmn;\u0026thinsp;1.35 mm, ranging from 2.40 to 6.80. The mean subjective spherical refraction and the mean astigmatism were \u0026minus;\u0026thinsp;1.1\u0026thinsp;\u0026plusmn;\u0026thinsp;2.5 D and \u0026minus;\u0026thinsp;1.4\u0026thinsp;\u0026plusmn;\u0026thinsp;1.3 D for the right eyes, respectively. Eventually, the Best-Corrected Visual acuity was 0.01\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03 LogMAR. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e summarizes the baseline characteristics of the patients and eyes included.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eBaseline Characteristics\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVariable Name\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMean\u0026thinsp;\u0026plusmn;\u0026thinsp;SD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRange\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAge\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e41.41\u0026thinsp;\u0026plusmn;\u0026thinsp;5.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e34.10 to 53.90\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSubjective refraction sphere (D)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e-1.10\u0026thinsp;\u0026plusmn;\u0026thinsp;2.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-6.50 to 3.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSubjective refraction cylinder (D)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e-1.43\u0026thinsp;\u0026plusmn;\u0026thinsp;1.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-5.50 to 0.01\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpherical Equivalent (D)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e-2.20\u0026thinsp;\u0026plusmn;\u0026thinsp;2.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-10.42 to 3.33\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBCVA (LogMAR)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.01\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00 to 0.15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOLMaster 700 Pupil Diameter\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e5.38\u0026thinsp;\u0026plusmn;\u0026thinsp;1.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.40 to 6.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Spherical equivalent\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e-2.20\u0026thinsp;\u0026plusmn;\u0026thinsp;2.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-10.42 to 3.33\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 Axial Length\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e23.97\u0026thinsp;\u0026plusmn;\u0026thinsp;1.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e21.14 to 26.98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 CCT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e538.40\u0026thinsp;\u0026plusmn;\u0026thinsp;30.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e482.10 to 603.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 AC depth\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e3.36\u0026thinsp;\u0026plusmn;\u0026thinsp;0.37\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.51 to 4.04\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 lens thickness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e4.02\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.30 to 4.70\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 horizontal White-to-White distance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e11.88\u0026thinsp;\u0026plusmn;\u0026thinsp;0.35\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e11.02 to 12.87\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 chord mu\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.29\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00 to 0.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIOL Master 700 chord alpha\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.43\u0026thinsp;\u0026plusmn;\u0026thinsp;0.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00 to 0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Corneal Coma\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.18\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.02 to 0.63\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Corneal Trefoil\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.19\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.02 to 0.57\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Corneal SA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.30 to 0.46\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Corneal HOA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.35\u0026thinsp;\u0026plusmn;\u0026thinsp;0.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.12 to 1.09\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Ocular Coma\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.01 to 0.49\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Ocular Trefoil\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.16\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.01 to 0.59\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Ocular SA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.16 to 0.31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePeramis Ocular HOA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c2\"\u003e\u003cp\u003e0.29\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.10 to 0.70\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"3\"\u003eBCVA: Best-corrected Visual Acuity, CCT: Central Corneal Thickness, SA: Spherical Aberration, HOA: Higher-order Aberration\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Sub-group analysis based on gender, refractive status, and its severity\u003c/h2\u003e\u003cp\u003eWhile gender did not have a significant association with chord α (P\u0026thinsp;=\u0026thinsp;0.62) or \u0026micro; (P\u0026thinsp;=\u0026thinsp;0.52), refractive status was found to have a statistically significant effect on both chord \u0026micro; (P\u0026thinsp;=\u0026thinsp;0.02) and chord α (P\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Details of the refractive status of each subgroup are present in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eChord \u0026micro; and α values based on refractive status.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSubgroup\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMin\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMax\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003eChord \u0026micro;\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eSevere Myopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.32\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eModerate Myopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMild Myopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eEmmetropia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.54\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMild Hyperopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eModerate Hyperopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e\u003cp\u003e\u003cb\u003eChord α\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eSevere Myopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eModerate Myopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.90\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMild Myopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.70\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eEmmetropia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eMild Hyperopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cb\u003eModerate Hyperopia\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.71\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eSeverely myopic eyes had the lowest values for both measures (0.21 and 0.27, respectively). Pair-wise post-hoc testing confirmed that for chord \u0026micro;, values were significantly greater in emmetropes and moderate hyperopes when compared to severe myopes (P\u0026thinsp;=\u0026thinsp;0.01 and P\u0026thinsp;=\u0026thinsp;0.02, respectively). This pattern was observed for chord α as well, where values were also significantly higher for both emmetropes and moderate hyperopes against those of severe myopes (P\u0026thinsp;=\u0026thinsp;0.00 and P\u0026thinsp;=\u0026thinsp;0.02, respectively). The complete pair-wise comparisons of any possible sub-groups are available for chord α and \u0026micro; in Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, respectively. Moreover, Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrate the distribution of chord α and \u0026micro; values across different refractive states, respectively.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDifferences in Chord α values based on refractive status.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSub-group (S)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eComparator (C)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean(S)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMean(C)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMean difference (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eStandard error\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eHedges\u0026rsquo; g\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eP value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.78\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-1.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.02\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.91\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"8\"\u003e*One-way ANOVA test p-value for the presence of differences in chord \u0026micro; based on subjective refraction status\u0026thinsp;\u0026lt;\u0026thinsp;0.001, Pair-wise comparisons performed utilizing Games-Howell post hoc non-parametric test, P-values\u0026thinsp;\u0026lt;\u0026thinsp;0.05 are considered statistically significant.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDifferences in Chord \u0026micro; values based on refractive status.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSub-group (S)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eComparator (C)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean(S)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMean(C)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eMean difference (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eStandard error\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eHedges\u0026rsquo; g\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eP value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.37\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.95\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.36\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEmmetropia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e2.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.85\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-0.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e1.00\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.49\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-1.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.10\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e-0.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.89\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMild Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModerate Hyperopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e1.85\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModerate Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSevere Myopia\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.51\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"8\"\u003e*One-way ANOVA test p-value for the presence of differences in chord \u0026micro; based on subjective refraction status\u0026thinsp;=\u0026thinsp;0.02, Pair-wise comparisons performed utilizing Games-Howell post hoc non-parametric test, P-values\u0026thinsp;\u0026lt;\u0026thinsp;0.05 are considered statistically significant.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Chord α and \u0026micro; correlation\u003c/h2\u003e\u003cp\u003eA moderate positive correlation was found between chord α and chord \u0026micro; (r\u0026thinsp;=\u0026thinsp;0.60, 95% CI [0.46, 0.71], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), indicating a significant association where larger values of chord α are related to larger values of chord \u0026micro;.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.4. Chord α Correlation Analysis\u003c/h2\u003e\u003cp\u003eThe analysis revealed several significant moderate correlations for chord α. These included a positive correlation with subjective spherical refraction (r\u0026thinsp;=\u0026thinsp;0.45, 95% CI [0.29, 0.59], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), and spherical equivalent (r\u0026thinsp;=\u0026thinsp;0.41, 95% CI [0.24, 0.56], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Moderate negative correlations were observed with anterior chamber depth (r = -0.53, 95% CI [-0.66, -0.39], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) and axial length (r = -0.40, 95% CI [-0.55, -0.23], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001).\u003c/p\u003e\u003cp\u003eMoreover, a number of significant weak correlations with chord α were identified. These included positive correlations with corneal trefoil (r\u0026thinsp;=\u0026thinsp;0.26, 95% CI [0.08, 0.43], p\u0026thinsp;=\u0026thinsp;0.01) and lens thickness (r\u0026thinsp;=\u0026thinsp;0.22, 95% CI [0.03, 0.39], p\u0026thinsp;=\u0026thinsp;0.02).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e\u003cem\u003e3.5. Chord\u003c/em\u003e \u0026micro; \u003cem\u003eCorrelation Analysis\u003c/em\u003e\u003c/h2\u003e\u003cp\u003eIn contrast, the correlations involving chord \u0026micro; were exclusively weak in magnitude. Significant weak negative correlations were found with anterior chamber depth (r = -0.37, 95% CI [-0.52, -0.19], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), axial length (r = -0.25, 95% CI [-0.42, -0.07], p\u0026thinsp;=\u0026thinsp;0.01), and subjective refractive cylinder (r = -0.22, 95% CI [-0.39, -0.04], p\u0026thinsp;=\u0026thinsp;0.02).\u003c/p\u003e\u003cp\u003eSignificant weak positive correlations were observed between chord \u0026micro; and several aberrometric and refractive parameters. These included corneal trefoil (r\u0026thinsp;=\u0026thinsp;0.35, 95% CI [0.18, 0.51], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), ocular coma (r\u0026thinsp;=\u0026thinsp;0.31, 95% CI [0.13, 0.47], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), subjective spherical refraction (r\u0026thinsp;=\u0026thinsp;0.31, 95% CI [0.13, 0.47], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), ocular trefoil (r\u0026thinsp;=\u0026thinsp;0.28, 95% CI [0.10, 0.45], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), total ocular higher-order aberrations (r\u0026thinsp;=\u0026thinsp;0.26, 95% CI [0.08, 0.43], p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), spherical equivalent (r\u0026thinsp;=\u0026thinsp;0.24, 95% CI [0.05, 0.41], p\u0026thinsp;=\u0026thinsp;0.01), and lens thickness (r\u0026thinsp;=\u0026thinsp;0.22, 95% CI [0.03, 0.39], p\u0026thinsp;=\u0026thinsp;0.02). Pupil diameter and age did not have significant correlations with any of the two chords. The full matrix of correlations and their strengths are depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.6. Regression analysis\u003c/h2\u003e\u003cp\u003eThe regression model indicated that chord α is a significant predictor of chord \u0026micro;, accounting for 36% of its variance (R\u0026sup2; = 0.36, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). The model can be expressed by the equation: Chord \u0026micro;\u0026thinsp;=\u0026thinsp;0.06\u0026thinsp;+\u0026thinsp;0.54 * (Chord α), where for every 1 mm increase in chord α, chord \u0026micro; is predicted to increase by 0.54 mm.\u003c/p\u003e\u003cp\u003eWhen examining predictors for chord α, several anatomical and refractive parameters showed significant explanatory power. Anterior chamber (AC) depth emerged as the most influential anatomical factor, explaining 28% of the variance in chord α (R\u0026sup2; = 0.28, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Subjective spherical refraction accounted for 17% of the variance (R\u0026sup2; = 0.17, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), while axial length explained 16% (R\u0026sup2; = 0.16, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). These relationships are defined by the equations: Chord α\u0026thinsp;=\u0026thinsp;1.21\u0026ndash;0.23 * (AC Depth), Chord α\u0026thinsp;=\u0026thinsp;0.49\u0026thinsp;+\u0026thinsp;0.03 * (Spherical Equivalent), and Chord α\u0026thinsp;=\u0026thinsp;1.76\u0026thinsp;\u0026minus;\u0026thinsp;0.06 * (Axial Length), respectively.\u003c/p\u003e\u003cp\u003eFor chord \u0026micro;, the predictive power of these same variables was considerably weaker. Besides the strong prediction from chord α, AC depth explained only 13% of the variance in chord \u0026micro; (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), and axial length accounted for a mere 6% (p\u0026thinsp;=\u0026thinsp;0.01). Figures\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e depict the regression analysis between various ocular biometric and wave-front characteristics with chord α and \u0026micro;, respectively.\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe longstanding pursuit of emmetropia and satisfactory vision in cataract and refractive surgery necessitates a precise understanding of the eye's optical alignment. As the study of chord \u0026micro; and chord α has demonstrated its importance in MIOL implantation surgeries[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e], most studies have used angle kappa and angle α as predictor factors for postoperative visual outcomes, rather than investigating the association between these angles and refractive errors or higher-order aberrations in preoperative patients. A primary finding of this study was a low to moderate and relatively consistent correlation between the magnitudes of both chords and the eye's fundamental biometric architecture. We demonstrate that chord α serves as a more robust indicator of this static, anatomical decentration than the more variable chord \u0026micro;. Furthermore, our results align with the theoretical expectation that greater decentration correlates with degraded optical quality, evidenced by weak but significant positive correlations between these chords and specific HOAs.\u003c/p\u003e\u003cp\u003eOur study acknowledges the previously well-established biometric characteristics of eyes with significant visual axis decentration. In this regard, the moderate positive correlation of chord α with hyperopic spherical equivalent (r\u0026thinsp;=\u0026thinsp;0.41)[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] and its moderate negative correlations with axial length (r = -0.40)[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] and anterior chamber depth (r = -0.53)[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] are highly consistent with previous reports. This confirms that shorter, hyperopic eyes with more compact anterior segments are predisposed to larger chord α values. A critical finding of our study, however, is the marked difference in the strength of these correlations compared to chord \u0026micro;, which were exclusively weak. This disparity strongly supports the growing consensus that chord α, referenced to the stable geometric center of the limbus[\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], is a more reliable surrogate measure for the eye's static anatomical framework than the pupil-referenced chord \u0026micro;[\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], where the pupil's dynamic nature may render chord \u0026micro; susceptible to variations in illumination and accommodation[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003cp\u003eRegarding the interplay of the two chords and refractive status, we found significantly higher chord values in severely myopic and emmetropic eyes compared to the moderate hyperopic patients. A previous study by Basmak et al. reported that chord \u0026micro; values demonstrated a significant drop toward negative refractive errors in the myopic group. Conversely, a positive correlation was found between chord \u0026micro; values and positive refractive errors in the hyperopic group[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Moreover, a recent study reported that a large angle kappa predominantly occurs in patients with medium and low myopia, whereas a small angle kappa is primarily associated with severe myopia, as these patients often need to move closer to objects for clear vision[\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Correspondingly, the results around axial length are justified. As a surrogate measure of refractive status, several studies have reported a significant inverse relationship between axial length and both angle alpha and angle kappa. In a Korean cohort of 436 eyes, angle kappa correlated negatively with AL (r\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.342, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001)[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], while a larger study of 8,119 eyes showed that the magnitudes of angle alpha and angle kappa of the right eyes both varied significantly with AL[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Furthermore, comparison of highly myopic eyes (AL\u0026thinsp;\u0026gt;\u0026thinsp;26 mm) with short eyes (AL\u0026thinsp;\u0026lt;\u0026thinsp;22 mm) revealed increases of 43.9% in chord mu and 49.7% in chord α in the latter group[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThere is a paucity of data and several controversies regarding the relationship between chord α and \u0026micro; with other ocular biometric indices, namely CCT, WTW distance, and lens thickness. Our study demonstrated a weak positive correlation between both chords and CCT and lens thickness, while there was a negligible inverse correlation with horizontal WTW distance. In line with our results, Velasco-Barona et al. identified a significant inverse correlation between WTW distance and angle alpha (r = -0.359, p\u0026thinsp;=\u0026thinsp;0.001)[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Similarly, in a post-phacoemulsification population, WTW corneal diameter showed the strongest correlation with change in angle kappa (r = -0.44, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), leading to a predictive equation: every 1 mm increment in WTW diameter was associated with a 2.42 scale reduction in angle kappa. However, no significant correlation was found with angle kappa and lens thickness[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Neuman et al. reported a statistically significant, yet negligible to weak, inverse correlation between the chords and both lens thickness and CCT. As both of our studies used IOLMaster 700 for measuring these variables, the discrepancy between our studies could be due to the ethnical differences[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] or their considerably larger sample size than ours[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. In a study of 438 eyes from 219 children (3\u0026ndash;15 years) using the IOLMaster 700, neither angle alpha (p\u0026thinsp;=\u0026thinsp;0.263) nor angle kappa (p\u0026thinsp;=\u0026thinsp;0.541) correlated with CCT. Both, however, were significantly associated with corneal curvature WTW distance[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eOur study did not find a significant correlation between either chord and patient age, which contrasts with some large-scale reports indicating a weak positive correlation. A Korean population study found angle kappa increased with age, particularly in women over 70 years and men in their 50s[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], which is further accredited by several other studies[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. This discrepancy is likely attributable to the intentionally narrow age range of our cohort (35\u0026ndash;55 years), which may have been insufficient to detect the subtle, long-term anatomical changes that manifest across a broader lifespan. The lack of correlation with pupil diameter was expected for chord α[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], but contradicts some previous studies indicating an increasing trend of chord \u0026micro; with larger pupil diameters[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], particularly under pharmacological cycloplegia[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. There is an approximate 0.1 mm increase in chord \u0026micro; following pharmacological pupillary dilation[\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. On the other hand, a large-scale study on approximately 1400 eyes reported a nearly similar chord mu for mesopic (0.33 mm\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15 mm) and photopic (0.31 mm\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15 mm) pupils [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. By conducting all measurements under standardized dark-room conditions without pharmacological agents, we may have minimized the known confounding effect of pupil dynamics on chord \u0026micro; measurements. Moreover, the relationship of these chords with gender is highly inconsistent within the literature. While a huge demographic study in the Chinese population showed significantly higher values of chord alpha among females[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Another study by Wang et al. yielded similar results to our study, failing to detect any meaningful correlation between gender and the magnitude of these chords[\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe relationship between these chords and higher-order aberrations appears to be complex. Our analysis revealed weak but significant positive correlations between chord \u0026micro; and total ocular HOAs (r\u0026thinsp;=\u0026thinsp;0.26), ocular coma (r\u0026thinsp;=\u0026thinsp;0.31), and both corneal and ocular trefoil. Chord α also showed a positive correlation with corneal trefoil (r\u0026thinsp;=\u0026thinsp;0.26). This aligns with the theoretical framework where decentration of optical elements induces specific HOAs, particularly coma and trefoil, and could help reconcile the present inconsistencies in linking the chord values with HOAs. These correlations might explain the hypothesized influence of chord α and \u0026micro; on patient satisfaction and nuanced visual outcomes post-phacoemulsification and use of MIOLs.\u003c/p\u003e\u003cp\u003eRecently, a growing body of evidence has linked the alignment of optical axes and their proxies (chord \u0026micro; and chord α) to both objective and subjective post-operative visual outcomes with MIOLs. A large chord \u0026micro; may negatively impact objective visual quality parameters, such as the objective scatter index, Strehl ratio, and modulation transfer function cutoff frequency. Additionally, a large chord \u0026micro; is linked to photic phenomena, including glare, starbursts, and halos, following eye surgery[\u003cspan additionalcitationids=\"CR44 CR45\" citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. In a study of two aspheric IOLs, a larger angle α was associated with greater higher-order aberrations (HOAs) across all pupil sizes, while a larger angle κ correlated with reduced visual quality, reflected by a lower Strehl ratio and higher internal HOAs[\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. Cervantes-Coste et al. reported that preoperative angle α was not associated with HOAs and visual acuities measured after surgery. However, they found that postoperative angle α had a negative impact on intermediate vision. Lee et al. conducted a retrospective study on patients with quadrifocal intraocular lenses (IOLs). They found that a smaller chord α was associated with better far and near visual outcomes, whereas larger chord α values correlated with poorer postoperative visual acuity[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. The corneal HOAs had a significant negative correlation with postoperative angle α, in contrast to the internal HOAs, which showed a weaker, but still significant correlation[\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. Although Fu et al. did not identify any correlations between chord α and postoperative visual parameters, they observed that the majority of patients with a chord α exceeding 0.5 mm experienced disturbing visual symptoms[\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. Moreover, a chord α value exceeding 0.4 mm correlates with poorer objective visual quality under scotopic conditions following extended depth of focus (EDOF) IOL implantation, and it also increases the risk of halos and glare post-surgery[\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThis study benefits from the use of high-resolution instrumentation, combining swept-source OCT biometry with pyramidal aberrometry, particularly useful in assessing the relationship of the chords with total ocular aberrations and their sub-categories. Nevertheless, several limitations must be acknowledged. The IOL Master 700 measures the \u003cem\u003eapparent\u003c/em\u003e chord \u0026micro;, which is larger than the actual one, as it sees the picture of the pupil through the cornea and is thus subject to the corneal magnification[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. This could affect the results. The cross-sectional design precludes any inference of causality, and the sample size, while adequate for correlational analysis, may limit the broader generalizability of our findings. We only used the data of the right eye, which ignores previously proven inherent differences of the eyes regarding laterality and dominance[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. The most significant limitation is the absence of postoperative data. While our preoperative findings provide a detailed characterization of the baseline optical system, longitudinal follow-up is essential to determine the ultimate predictive power of these correlations on surgical outcomes.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn summary, this study highlights chord α as a reliable anatomical marker, closely linked to the biometric structure of hyperopic eyes and more stable than chord \u0026micro;. Although its association with higher-order aberrations is modest, it underscores the role of optical decentration in visual quality and may harbor considerable clinical implications. Larger chord values may indicate a higher risk of pre-existing aberrations and impaired optical balance, warranting cautious surgical planning.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDisclosure of financial and proprietary interests for all authors:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn accordance with ethical standards and transparency practices, all authors involved in this study have disclosed their financial and proprietary interests. Each author has provided a detailed account of any potential conflicts of interest or explicitly stated that they have no such interests to declare.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no acknowledgements to declare.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors received no financial support for the research, authorship, and/or publication of this article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no competing interests to declare.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eArmin Doostparast was responsible for conceptualization, methodology, formal analysis, data visualization, table preparation, project administration, and drafting of the original manuscript, as well as its review and editing. Farbod Semnani was involved in conceptualization, methodology, formal analysis, drafting, and reviewing the manuscript. Maryam Ghandhari, Amir Hossein Khosronejad, Mohammad Mirzaei, and Amirhossein Amiriani contributed to data preparation, project administration, and manuscript drafting. Alireza Eslampoor contributed to conceptualization, methodology, provision of resources, supervision, and critical review and editing. All authors reviewed and approved the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003e*Armin Doostparast and Farbod Semnani contributed equally to this work as co\u0026ndash;first authors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study was approved by the Research Ethics Office of Mashhad University of Medical Sciences (Ethics ID: IR.MUMS.MEDICAL.REC.1403.238). All procedures strictly adhered to the tenets of the Declaration of Helsinki. All participants provided written informed consent.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data of the study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eDoane JF, Cavanaugh TB. Optical Zone Centration for Keratorefractive Surgery. Ophthalmology. 1994;101:215\u0026ndash;6. \u003c/li\u003e\n\u003cli\u003eRodrigues PF, Moscovici BK, Lamazales L, Freitas MMS, Gomes J\u0026Aacute;P, Nos\u0026eacute; W, et al. Measurement of the visual axis through two different methods: quantification and differences for measuring chord \u0026micro;. Arq Bras Oftalmol [Internet]. 2023 [cited 2025 Aug 7];87:e2022-0035. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC11619329/\u003c/li\u003e\n\u003cli\u003eMosquera SA, Verma S, McAlinden C. Centration axis in refractive surgery. Eye and Vision [Internet]. 2015 [cited 2025 Aug 7];2:4. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC4655455/\u003c/li\u003e\n\u003cli\u003eEvans T, Rubin A. Linear optics of the eye and optical systems: a review of methods and applications. BMJ Open Ophthalmol [Internet]. 2022 [cited 2025 Aug 7];7. Available from: https://bmjophth.bmj.com/content/7/1/e000932\u003c/li\u003e\n\u003cli\u003eUmesh Y, Saolapurkar K, Joshi P, Singh D. Measurement of change in angle kappa and its correlation with ocular biometric parameters pre- and post-phacoemulsification. Indian J Ophthalmol [Internet]. 2023 [cited 2025 Aug 7];71:535. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC10228972/\u003c/li\u003e\n\u003cli\u003eVelasco-Barona C, Corredor-Ortega C, Avenda\u0026ntilde;o-Domnguez A, Cervantes-Coste G, Cant\u0026uacute;-Trevi\u0026ntilde;o MP, Gonzalez-Salinas R. Impact of correlation of angle \u0026alpha; with ocular biometry variables. J Cataract Refract Surg [Internet]. 2021 [cited 2025 Aug 20];47:1279\u0026ndash;84. Available from: https://pubmed.ncbi.nlm.nih.gov/34544085/\u003c/li\u003e\n\u003cli\u003eA M, R Ž, K Y, A G. Chord mu and chord alpha as postoperative predictors in multifocal intraocular lens implantation. Graefes Arch Clin Exp Ophthalmol [Internet]. 2024 [cited 2025 Aug 7];262. Available from: https://pubmed.ncbi.nlm.nih.gov/37278907/\u003c/li\u003e\n\u003cli\u003eBasmak H, Sahin A, Yildirim N, Papakostas TD, Kanellopoulos AJ. Measurement of angle kappa with synoptophore and Orbscan II in a normal population. Journal of Refractive Surgery [Internet]. 2007 [cited 2025 Aug 8];23:456\u0026ndash;60. Available from: https://pubmed.ncbi.nlm.nih.gov/17523505/\u003c/li\u003e\n\u003cli\u003eFricke TR, Tahhan N, Resnikoff S, Papas E, Burnett A, Ho SM, et al. Global Prevalence of Presbyopia and Vision Impairment from Uncorrected Presbyopia: Systematic Review, Meta-analysis, and Modelling. Ophthalmology [Internet]. 2018 [cited 2025 Aug 8];125:1492\u0026ndash;9. Available from: https://pubmed.ncbi.nlm.nih.gov/29753495/\u003c/li\u003e\n\u003cli\u003eSalerno L, Tiveron M, Ali\u0026oacute; J. Multifocal intraocular lenses: Types, outcomes, complications and how to solve them. Taiwan J Ophthalmol [Internet]. 2017 [cited 2025 Aug 8];7:179. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC5747227/\u003c/li\u003e\n\u003cli\u003eVelasco-Barona C, Corredor-Ortega C, Mendez-Leon A, Casillas-Chavar\u0026iacute;n NL, Valdepe\u0026ntilde;a-L\u0026oacute;pez Velarde D, Cervantes-Coste G, et al. Influence of angle and higher-order aberrations on visual quality employing two diffractive trifocal IOLs. J Ophthalmol [Internet]. 2019 [cited 2025 Aug 8];2019. Available from: https://pubmed.ncbi.nlm.nih.gov/31885892/\u003c/li\u003e\n\u003cli\u003eLiu Y, Gao Y, Liu R, Hu C, Ma B, Miao J, et al. Influence of angle kappa-customized implantation of rotationally asymmetric multifocal intraocular lens on visual quality and patient satisfaction. Acta Ophthalmol [Internet]. 2020 [cited 2025 Aug 8];98:e734\u0026ndash;42. Available from: https://pubmed.ncbi.nlm.nih.gov/31981307/\u003c/li\u003e\n\u003cli\u003eGarz\u0026oacute;n N, Garc\u0026iacute;a-Montero M, L\u0026oacute;pez-Artero E, Albarr\u0026aacute;n-Diego C, P\u0026eacute;rez-Cambrod\u0026iacute; R, Illarramendi I, et al. Influence of angle on visual and refractive outcomes after implantation of a diffractive trifocal intraocular lens. J Cataract Refract Surg [Internet]. 2020 [cited 2025 Aug 7];46:721\u0026ndash;7. Available from: https://pubmed.ncbi.nlm.nih.gov/32358267/\u003c/li\u003e\n\u003cli\u003eLee CY, Huang JY, Sun CC, Yang SF, Chen HC, Lin HY. Correlation and predictability of ocular aberrations and the visual outcome after quadrifocal intraocular lens implantation: A retrospective longitudinal study. BMC Ophthalmol [Internet]. 2019 [cited 2025 Aug 8];19. Available from: https://pubmed.ncbi.nlm.nih.gov/31426784/\u003c/li\u003e\n\u003cli\u003eKim DR, Yoon YC, Whang WJ, Hwang HS, Na KS. Ocular parameters associated with visual performance of enhanced monofocal intraocular lens. BMC Ophthalmol [Internet]. 2024 [cited 2025 Aug 8];24. Available from: https://pubmed.ncbi.nlm.nih.gov/38369454/\u003c/li\u003e\n\u003cli\u003eGharieb Ibrahim HM, Gharieb HM, Othman IS. Angle \u0026kappa; Measurement and Its Correlation with Other Ocular Parameters in Normal Population by a New Imaging Modality. Optometry and Vision Science [Internet]. 2022 [cited 2025 Aug 8];99:580\u0026ndash;8. Available from: https://pubmed.ncbi.nlm.nih.gov/35657347/\u003c/li\u003e\n\u003cli\u003eKlaproth O. ZEISS IOLMaster 700. Essentials in Ophthalmology [Internet]. 2024 [cited 2025 Aug 9];297\u0026ndash;306. Available from: https://link.springer.com/chapter/10.1007/978-3-031-50666-6_17\u003c/li\u003e\n\u003cli\u003eHolladay JT. Apparent chord mu and actual chord mu and their clinical value. J Cataract Refract Surg [Internet]. 2019 [cited 2025 Aug 9];45:1198\u0026ndash;9. Available from: https://pubmed.ncbi.nlm.nih.gov/31371009/\u003c/li\u003e\n\u003cli\u003eSCHWIND PERAMIS: Topographer and aberrometer [Internet]. [cited 2025 Aug 9]. Available from: https://www.eye-tech-solutions.com/en/products/diagnostic-systems/schwind-peramis\u003c/li\u003e\n\u003cli\u003ePedregosa FABIANPEDREGOSA F, Michel V, Grisel OLIVIERGRISEL O, Blondel M, Prettenhofer P, Weiss R, et al. Scikit-learn: Machine Learning in Python. The Journal of Machine Learning Research [Internet]. 2011 [cited 2025 Aug 9];12:2825\u0026ndash;30. Available from: https://dl.acm.org/doi/pdf/10.5555/1953048.2078195\u003c/li\u003e\n\u003cli\u003eVallat R. Pingouin: statistics in Python. J Open Source Softw [Internet]. 2018 [cited 2025 Aug 9];3:1026. Available from: https://joss.theoj.org/papers/10.21105/joss.01026\u003c/li\u003e\n\u003cli\u003eWaskom ML. seaborn: statistical data visualization. J Open Source Softw [Internet]. 2021 [cited 2025 Aug 9];6:3021. Available from: https://joss.theoj.org/papers/10.21105/joss.03021\u003c/li\u003e\n\u003cli\u003eIterativeImputer \u0026mdash; scikit-learn 1.7.1 documentation [Internet]. [cited 2025 Aug 9]. Available from: https://scikit-learn.org/stable/modules/generated/sklearn.impute.IterativeImputer.html\u003c/li\u003e\n\u003cli\u003eAgbangba CE, Sacla Aide E, Honfo H, Gl\u0026egrave;l\u0026egrave; Kakai R. On the use of post-hoc tests in environmental and biological sciences: A critical review. Heliyon [Internet]. 2024 [cited 2025 Aug 20];10:e25131. Available from: https://www.sciencedirect.com/science/article/pii/S2405844024011629\u003c/li\u003e\n\u003cli\u003eWelz T, Doebler P, Pauly M. Fisher transformation based confidence intervals of correlations in fixed- and random-effects meta-analysis. British Journal of Mathematical and Statistical Psychology [Internet]. 2022 [cited 2025 Aug 19];75:1\u0026ndash;22. Available from: https://pubmed.ncbi.nlm.nih.gov/33934346/\u003c/li\u003e\n\u003cli\u003eSchober P, Schwarte LA. Correlation coefficients: Appropriate use and interpretation. Anesth Analg [Internet]. 2018 [cited 2025 Aug 19];126:1763\u0026ndash;8. Available from: https://journals.lww.com/anesthesia-analgesia/fulltext/2018/05000/correlation_coefficients__appropriate_use_and.50.aspx\u003c/li\u003e\n\u003cli\u003eKarhanov\u0026aacute; M, Pluh\u0026aacute;ček F, Mlč\u0026aacute;k P, Vl\u0026aacute;čil O, \u0026Scaron;\u0026iacute;n M, Mare\u0026scaron;ov\u0026aacute; K. The importance of angle kappa evaluation for implantation of diffractive multifocal intra-ocular lenses using pseudophakic eye model. Acta Ophthalmol [Internet]. 2015 [cited 2025 Aug 20];93:e123\u0026ndash;8. Available from: https://pubmed.ncbi.nlm.nih.gov/25160117/\u003c/li\u003e\n\u003cli\u003ePrakash G, Prakash DR, Agarwal A, Kumar DA, Jacob S. Predictive factor and kappa angle analysis for visual satisfactions in patients with multifocal IOL implantation. Eye [Internet]. 2011 [cited 2025 Aug 20];25:1187\u0026ndash;93. Available from: https://pubmed.ncbi.nlm.nih.gov/21681216/\u003c/li\u003e\n\u003cli\u003eBteich Y, Ibrahim H, Barake K, Khalil J, Assaf JF, Reinstein DZ, et al. Distribution of Angle Alpha and Angle Kappa Chord Magnitude and Axes in Myopic and Hyperopic Refractive Surgery Candidates. Journal of Refractive Surgery [Internet]. 2025 [cited 2025 Aug 20];41:e585\u0026ndash;93. Available from: https://pubmed.ncbi.nlm.nih.gov/40488487/\u003c/li\u003e\n\u003cli\u003eStern B, Chowers I, Ben-Eli H. Effect of mydriasis on chord mu value in cataract surgery candidates. Eur J Ophthalmol [Internet]. 2024 [cited 2025 Aug 20];34:759\u0026ndash;65. Available from: https://journals.sagepub.com/doi/10.1177/11206721231207470\u003c/li\u003e\n\u003cli\u003eNeuman G, Abulafia A, Wasser L, Zadok D. Distribution of angle alpha and angle kappa offsets among adult candidates for cataract surgery. Graefe\u0026rsquo;s Archive for Clinical and Experimental Ophthalmology [Internet]. 2024 [cited 2025 Aug 20];263:157. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC11807017/\u003c/li\u003e\n\u003cli\u003eMih\u0026aacute;ltz K, V\u0026eacute;csei-Marlovits PV. The impact of visual axis position on the optical quality after implantation of multifocal intraocular lenses with different asphericity values. Graefe\u0026rsquo;s Archive for Clinical and Experimental Ophthalmology [Internet]. 2021 [cited 2025 Aug 20];259:673\u0026ndash;83. Available from: https://pubmed.ncbi.nlm.nih.gov/33471202/\u003c/li\u003e\n\u003cli\u003eMontrimas A, Žemaitienė R, Yao K, Grzybowski A. Chord mu and chord alpha as postoperative predictors in multifocal intraocular lens implantation. Graefe\u0026rsquo;s Archive for Clinical and Experimental Ophthalmology [Internet]. 2024 [cited 2025 Aug 20];262:367\u0026ndash;80. Available from: https://pubmed.ncbi.nlm.nih.gov/37278907/\u003c/li\u003e\n\u003cli\u003eDing Y, Zhang Z, Min X, Xia X, Hu S. Changes of angle Kappa and corneal morphology changes in myopic patients after Sub-Bowman-Keratomileusis. Journal of Central South University (Medical Sciences) [Internet]. 2021 [cited 2025 Aug 20];46:162\u0026ndash;8. Available from: https://pubmed.ncbi.nlm.nih.gov/33678653/\u003c/li\u003e\n\u003cli\u003eChoi SR ang, Kim US amuel. The Correlation between Angle Kappa and Ocular Biometry in Koreans. Korean J Ophthalmol [Internet]. 2013 [cited 2025 Aug 20];27:421. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC3849305/\u003c/li\u003e\n\u003cli\u003eHua Z, Zeng Q, Zhang L, Shen J, Yang J. Distribution of Angle Alpha in a Large Population in Eastern China: An Analysis of the 30705 Eyes Using the Ray Tracing Aberrometer. Clin Ophthalmol [Internet]. 2025 [cited 2025 Aug 25];19:753. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC11889998/\u003c/li\u003e\n\u003cli\u003eYe Y, Zhao Y, Zhang Z, Wei R, Xian Y, Huang Y, et al. Correlation analysis of angles \u0026kappa; and \u0026alpha; with the refraction and anterior segment parameters in children. BMC Ophthalmol [Internet]. 2024 [cited 2025 Aug 20];24:143. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC10976721/\u003c/li\u003e\n\u003cli\u003eChen XN, Xiong YY, Wei J, Luo B, Gao YL. Alpha and Kappa angle on postoperative visual quality in cataract surgery. Int J Ophthalmol [Internet]. 2025 [cited 2025 Aug 20];18:1023. Available from: https://pmc.ncbi.nlm.nih.gov/articles/PMC12120454/\u003c/li\u003e\n\u003cli\u003eSella R, Shouchane-Blum K, Reitblat O, Bahar I. The association between pupil diameter and apparent chord mu length value. Invest Ophthalmol Vis Sci. 2022;63:1698-F0016-1698 \u0026ndash; F0016. \u003c/li\u003e\n\u003cli\u003eShouchane-Blum K, Reitblat O, Dadon J, Bahar I, Sella R. Evaluating Changes in Apparent Chord Mu after Pharmacological Pupil Dilatation. Ophthalmic Res [Internet]. 2023 [cited 2025 Aug 20];66:921\u0026ndash;7. Available from: https://pubmed.ncbi.nlm.nih.gov/37231882/\u003c/li\u003e\n\u003cli\u003eWang Q, Stoakes IM, Moshirfar M, Harvey DH, Hoopes PC. Assessment of Pupil Size and Angle Kappa in Refractive Surgery: A Population-Based Epidemiological Study in Predominantly American Caucasians. Cureus [Internet]. 2023 [cited 2025 Aug 20];15. Available from: https://pubmed.ncbi.nlm.nih.gov/37638275/\u003c/li\u003e\n\u003cli\u003eWang R, Long T, Gu X, Ma T. Changes in angle kappa and angle alpha before and after cataract surgery. J Cataract Refract Surg [Internet]. 2020 [cited 2025 Aug 25];46:365\u0026ndash;71. Available from: https://pubmed.ncbi.nlm.nih.gov/32050219/\u003c/li\u003e\n\u003cli\u003ePark CY, Oh SY, Chuck RS. Measurement of angle kappa and centration in refractive surgery. Curr Opin Ophthalmol [Internet]. 2012 [cited 2025 Aug 7];23:269\u0026ndash;75. Available from: https://pubmed.ncbi.nlm.nih.gov/22569467/\u003c/li\u003e\n\u003cli\u003eFu Y, Kou J, Chen D, Wang D, Zhao Y, Hu M, et al. Influence of angle kappa and angle alpha on visual quality after implantation of multifocal intraocular lenses. J Cataract Refract Surg [Internet]. 2019 [cited 2025 Aug 7];45:1258\u0026ndash;64. Available from: https://pubmed.ncbi.nlm.nih.gov/31326223/\u003c/li\u003e\n\u003cli\u003eQi Y, Lin J, Leng L, Zhao G, Wang Q, Li C, et al. Role of angle \u0026kappa; in visual quality in patients with a trifocal diffractive intraocular lens. J Cataract Refract Surg [Internet]. 2018 [cited 2025 Aug 7];44:949\u0026ndash;54. Available from: https://pubmed.ncbi.nlm.nih.gov/30033112/\u003c/li\u003e\n\u003cli\u003eTchah H, Nam K, Yoo A. Predictive factors for photic phenomena after refractive, rotationally asymmetric, multifocal intraocular lens implantation. Int J Ophthalmol [Internet]. 2017 [cited 2025 Aug 7];10:241\u0026ndash;5. Available from: https://pubmed.ncbi.nlm.nih.gov/28251083/\u003c/li\u003e\n\u003cli\u003eThakur A, Adiga S, Malhotra C, Sachdeva K, Singh S, Jain AK. Effect of decentration on the quality of vision in two aspheric posterior chamber intraocular lenses: A contralateral eye study. Indian J Ophthalmol [Internet]. 2024 [cited 2025 Aug 20];72:558\u0026ndash;64. Available from: https://pubmed.ncbi.nlm.nih.gov/38189441/\u003c/li\u003e\n\u003cli\u003eCervantes-Coste G, Tapia A, Corredor-Ortega C, Osorio M, Valdez R, Massaro M, et al. The Influence of Angle Alpha, Angle Kappa, and Optical Aberrations on Visual Outcomes after the Implantation of a High-Addition Trifocal IOL. J Clin Med [Internet]. 2022 [cited 2025 Aug 20];11. Available from: https://pubmed.ncbi.nlm.nih.gov/35160346/\u003c/li\u003e\n\u003cli\u003eFu Y, Kou J, Chen D, Wang D, Zhao Y, Hu M, et al. Influence of angle kappa and angle alpha on visual quality after implantation of multifocal intraocular lenses. J Cataract Refract Surg [Internet]. 2019 [cited 2025 Aug 20];45:1258\u0026ndash;64. Available from: https://pubmed.ncbi.nlm.nih.gov/31326223/\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"international-ophthalmology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"inte","sideBox":"Learn more about [International Ophthalmology](https://www.springer.com/journal/10792)","snPcode":"10792","submissionUrl":"https://submission.nature.com/new-submission/10792/3","title":"International Ophthalmology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Chord Alpha, Chord Mu, Aberrations, IOLMaster 700, Peramis","lastPublishedDoi":"10.21203/rs.3.rs-7456104/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7456104/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground\u003c/h2\u003e\u003cp\u003eTo investigate the relationships between chord α and chord \u0026micro; with age, ocular biometric indices, and wavefront aberrations in pre-operative refractive surgery candidates.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eThis cross-sectional study included 111 right eyes of 111 patients. Ocular biometrics and chord values were measured using the ZEISS IOLMaster 700. Corneal and ocular aberrations were assessed with the PERAMIS pyramidal aberrometer. Data were analyzed using Pearson\u0026rsquo;s correlation, ANOVA, and simple linear regression to evaluate the interplay between variables.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eA moderate positive correlation was found between chord α and chord \u0026micro; (r\u0026thinsp;=\u0026thinsp;0.60, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Chord α demonstrated moderate positive correlations with subjective spherical refraction (r\u0026thinsp;=\u0026thinsp;0.45) and spherical equivalent (r\u0026thinsp;=\u0026thinsp;0.41), and moderate negative correlations with anterior chamber depth (r = -0.53) and axial length (r = -0.40) (all p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). In contrast, correlations involving chord \u0026micro; were exclusively weak, though it showed significant associations with several higher-order aberrations, including corneal trefoil (r\u0026thinsp;=\u0026thinsp;0.35) and ocular coma (r\u0026thinsp;=\u0026thinsp;0.31). Refractive status significantly affected both chord values (p\u0026thinsp;\u0026le;\u0026thinsp;0.02), with severely myopic eyes showing the lowest values. Regression analysis identified anterior chamber depth as the strongest anatomical predictor for chord α (R\u0026sup2; = 0.28).\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e\u003cp\u003eChord α serves as a more robust indicator of the eye's anatomical characteristics than the more variable chord \u0026micro;. Our findings underscore the clinical importance of optical decentration in surgical planning, as larger chord values may indicate a greater risk of pre-existing aberrations and potential impacts on visual quality.\u003c/p\u003e","manuscriptTitle":"Exploring the interplay of chord α and chord μ with pyramidal wavefront aberrometry and ocular biometric indices among pre-operative refractive surgery candidates","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-03 08:49:54","doi":"10.21203/rs.3.rs-7456104/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-13T19:40:57+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-13T16:01:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-06T10:08:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"314759870864517983951020454150637961302","date":"2025-09-23T20:51:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"15565405094289665056405553222409154051","date":"2025-09-22T05:05:53+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-09-09T20:01:33+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-05T07:57:25+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-05T07:56:43+00:00","index":"","fulltext":""},{"type":"submitted","content":"International Ophthalmology","date":"2025-08-25T17:32:11+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"international-ophthalmology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"inte","sideBox":"Learn more about [International Ophthalmology](https://www.springer.com/journal/10792)","snPcode":"10792","submissionUrl":"https://submission.nature.com/new-submission/10792/3","title":"International Ophthalmology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"9aa5ac94-96aa-4171-8953-6e8ee2cc7043","owner":[],"postedDate":"September 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-12-22T16:08:42+00:00","versionOfRecord":{"articleIdentity":"rs-7456104","link":"https://doi.org/10.1007/s10792-025-03893-9","journal":{"identity":"international-ophthalmology","isVorOnly":false,"title":"International Ophthalmology"},"publishedOn":"2025-12-17 15:58:02","publishedOnDateReadable":"December 17th, 2025"},"versionCreatedAt":"2025-09-03 08:49:54","video":"","vorDoi":"10.1007/s10792-025-03893-9","vorDoiUrl":"https://doi.org/10.1007/s10792-025-03893-9","workflowStages":[]},"version":"v1","identity":"rs-7456104","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7456104","identity":"rs-7456104","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}