Clinical and simulated impact of intraocular lens tilt and decentration: from real-world data to optical simulation

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We included 105 eyes implanted with a monofocal aspheric IOL and measured their positioning using a tomographic device. With the clinical data we reconstruct each eye in Zemax optical software and evaluate four scenarios: aligned, decentered, tilted, and combined decentration and tilt. For each case, we calculated wavefront aberrations, three objective refractions, and predicted visual acuity from the intersection of the MTF and a threshold function. The average IOL tilt was 5.19 ± 1.28° and decentration was 0.25 ± 0.13 mm. Coma RMS increased from 0.00 µm in the aligned model to 0.26 ± 0.09 µm in the most altered scenario (p < 0.001), and VSX decreased from 0.80 ± 0.11 to 0.35 ± 0.17. Despite this optical degradation, BCVA remained unaffected, with a mean of 0.00 ± 0.05 LogMAR, and no significant correlation was found with tilt or decentration. The best agreement between simulated and clinical refraction was observed when both tilt and decentration were included. These results suggest that moderate IOL misalignment degrades optical quality without compromising visual acuity in monofocal IOLs, but further studies are needed for multifocal designs. Health sciences/Diseases Health sciences/Health care Health sciences/Medical research Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction The influence of intraocular lens (IOL) tilt on postoperative refraction was clinically described during the development of the first IOL power calculation formulas 1 – 3 . Later, this issue and the consequences of IOL misalignment were elegantly explained using paraxial optics 4 – 6 . As newer formulas and toric IOLs were developed and residual refraction improved, this topic gained even more importance 7 , 8 . The sensitivity of multifocal and extended depth of focus (EDOF) IOLs to misalignment prompted researchers to investigate the topic using optical bench setups 8 , 9 and ocular wavefront measurements 10 , 11 . More recently, ray-tracing software has been used to simulate synthetic ocular models to evaluate IOL tilt and decentration 12 , 13 . Scheimpflug imaging and anterior segment optical coherence tomography (AS-OCT) have enabled clinical evaluation of IOL tilt and decentration. Studies report mean tilt values between 2° and 5°, depending on factors such as axial length, IOL haptics, capsular tension ring use, and preoperative crystalline lens tilt 14 , 15 . These factors also influence the sagittal and meridional displacement of the IOL, with typical decentration values around 0.2–0.3 mm 16 . Both tilt and decentration can impair visual quality by inducing high-order aberrations (HOAs), and in more extreme cases, may reduce visual acuity (VA). Some studies suggest that decentration has a more significant impact on vision than tilt, although both are influenced by IOL design 17 , 18 . The visual impact of decentering a spherical IOL is less pronounced than with aspheric designs; however, tilt appears to affect both types similarly 19 , 20 . IOL tilt is more strongly correlated with coma-like aberrations, while both tilt and decentration contribute to induced astigmatism 21 , 22 . As premium IOLs evolve rapidly, more sophisticated designs demand a deeper understanding of ocular optics. While optical bench simulations have provided valuable insights into IOL misalignment, and clinical studies have documented its effects on visual acuity, few studies have combined both perspectives to assess the impact on ocular aberrations comprehensively. The purpose of this study is to replicate ocular parameters using optical simulation software to evaluate changes in synthetic ocular aberrations due to IOL tilt and decentration, and to correlate these findings with clinical outcomes. Methods Settings This cross-sectional study was conducted at Fundación Jiménez Díaz University Hospital between November 2023 and June 2024. The local institutional review board (Comité de Etica de la Investigación Fundación Jiménez Diaz. Code: PIC204-24) approved the study protocol, which complies with the tenets of the Declaration of Helsinki. Informed consent was obtained from all subjects following an explanation of the nature and possible consequences of the study. Patient eligibility Patients who underwent uneventful cataract surgery of both eyes and implanted with Clareon® CNAT0 with a minimum follow-up of 3 months were included. The exclusion criteria comprehend amblyopia, retinal or corneal or any other ocular disease that could affect the patient’s vision performance. Also, any patient with history of ocular surgery such as refractive surgery or interventions that could affect the capsule-bag integrity like Nd-YAG capsulotomy was excluded. Measurement protocol Subjective refraction to obtain the best corrected visual acuity (BCVA) was performed by the same experienced optometrist (ASL) using EDTRS chart. One drop of tropicamide (1%) was instilled for the next measurements. Postoperative biometry using IOL-Master 700 (Carl Zeiss Meditec, AG, Jenna, Germany, version 1.90.33.04) was used to acquire axial length. Patients anterior segment was measured with AS-OCT CASIA II (TOMEY corp, Nagoya, Japan, version 50.6B.07) using the cataract protocol examination. Only measurements labeled as OK by the instrument were included in this study. IOL edge detection was performed by a researcher (GVR) using the semi-trace method included in the AS-OCT software. IOL parametrization The anterior radii of curvature and central thickness of each implanted IOL were measured using the AS-OCT software. Although the software also reports the posterior radius of curvature, accurate identification of the posterior IOL surface was often impaired by the proximity of the posterior capsule, leading to acquisition errors. To address this limitation, it was assumed that the labeled paraxial power of IOL matched its nominal value. Based on this assumption and using the refractive index provided by the manufacturer (Nd = 1.55, at 35 ºC), the posterior radius of curvature was calculated such that the combination of anterior radius, central thickness, and material index would result in the labeled paraxial power. Each IOL’s anterior surface was then modeled as a fourth-order even asphere, excluding the 2nd-order term. The conic constant (𝑘) and fourth-order aspheric coefficient (𝑎₄) were optimized in Zemax OpticStudio to ensure that the IOL corrected − 0.20 µm of fourth-order corneal spherical aberration (Zernike term) in a physiological model eye, assuming a 6.0 mm entrance pupil. Synthetic eye model and simulating different scenarios Ansys Zemax OpticStudio (v 22.1) was used to build the eye model. Coordinates breaks were used to include pupil decentration, IOL tilt and decentration and corneal angle shift of the principal axes (Z-axis tilt). The anterior and posterior corneal surface were included as a biconic surface with data from IOL Master 700 principal meridians (setting conic constant to zero). The iris was represented by a stop surface of pupil’s patient diameter and situated 0.75 millimeters before the IOL anterior surface. IOL anterior surface was described as a fourth order even asphere and a posterior standard surface, adhering to the data collected by de AS-OCT and the IOL power labelled by manufacturer. The system setting was adjusted for a wavelength of 550 nm with no field modification. The selected pupil for the analysis was 4 mm. The corneal index used in this model 1.3752 and 1.336 for the aqueous and vitreous humors. More information is available in Fig. 1 . Four scenarios were simulated using this eye model. The first situation was with the IOL totally aligned. In the second one, the measured IOL decentration (AS-OCT) was introduced, then the IOL tilt was set and finally the IOL decentration was set to zero. Therefore, four scenarios were evaluated as “Aligned”, “Decentration”, “Decentration + tilt” and “Tilted” respectively. The wavefront phase and its associated Zernike coefficients values (up to sixth order) were collected for each situation. Objective synthetic refraction A total of three refractions for each of the described scenarios were obtained for each patient derived from the synthetic ocular wavefront. Two objective refractions were directly obtained from the Zernike coefficient values: minimum root min square (MinRMS) and paraxial curvature matching (PCM) 23 . Another refraction was calculated by maximizing the retinal image quality weighted by a neural function 24 . The selected metric was the visual strehl in the special domain (VSX). This was performed using an iterative process of testing lenses with the aberration map and maximizing the metric value. The following equation describes how we calculate this metric: $$\:VSX=\:\frac{\iint\:PSF\:\left(x,y\right)*iCSF\:\left(x,y\right)\:dxdy}{\iint\:{PSF}_{DL}\:\left(x,y\right)*iCSF\:\left(x,y\right)dxdy}$$ Where PSF is the point spread function and the iCSF is the inverse fourier transform of the contrast sensitivity function (CSF) 25 . The optimizing process was carried out testing a combination of sphero-cylindrical lenses with a range from − 3 to 3 D in steps of 0.25 D. The step for the refractive axis was 5º, from 0 to 175 degrees. These values were converted into power vectors (M,J0 and J45) and finally into their equivalent Zernike coefficients Z (2,0), Z (2,-2) and Z (2,2). These variables were converted into wavefront error in microns and added to the original ocular wavefront calculating the new value of the VSX. We selected the sphero-cylindrical prescription that maximize the VSX value. Evaluating the synthetic eye model: To assess the consistency of the eye model, the predicted visual (VA pred ) acuity was estimated by identifying the intersection between the radial modulation transfer function (MTFr) and the contrast sensitivity threshold 26 , for this purpose we choose the Mannos and Sakrison threshold curve 27 . Additionally, the objective prescriptions were derived from the scenario IOL decentration and tilt, which replicates the actual clinical setting in the synthetic eye model. This comparison was evaluated twofold, with the subtraction (subjective prescription – objective prescription) and by the Bland-Altman agreement analysis method. Impact IOL tilt and decentration in visual performance We evaluated this subject with two different approaches; On one hand variables derived from the synthetic eye and on the other hand clinical variables measurements. The synthetic eye model allows the statistical comparison of the image quality metrics such as VSX or the optical aberrations (RMS astigmatism and RMS Coma) for the different simulated scenarios (Aligned’, ’Decentration’, Tilt’ and Decentration and tilt’). These variables changes were assessed using the Anova statistical tests, a p-value < 0.05 was considered statistically significant. The image quality metrics obtained for each scenario were compared using the Wilcoxon signed-ranked test and box and whiskers plots analysis. Concerning the clinical measurements, we studied the IOL positioning (tilt and decentration) and BCVA. First, we performed a partial correlation analysis to determine the relationship between IOL tilt, decentration and BCVA. But also, we explore the BCVA differences between patients with high IOL tilt (more than third quartile) or decentration to those that presented low values (less than first quartile) of these variables. For that purpose, we used Mann-Whitney U test with the mentioned statistical threshold. Results A total of 105 right eyes from 105 participants (53% females and 47% males) were included in this study. The mean patients age was 73.35 ± 8.39 years old and follow-up period was 9.41 ± 4.54 months after cataract surgery. A statistical summary of the main clinical variables is presented in Table 1 . The main modulus of the vectors tilt and decentration were 5.19 ± 1.28° and 0.25 ± 0.13 mm, respectively. The study of the IOL tilt revealed a tendency, the nasal-superior IOL edge was shifted towards the cornea compared to the temporal edge. The maximum value for tilt was 9.3º (eye 12) and decentration was 0.83 mm (eye 36). Table 1 Summarize the results for the demographic and clinical variables. Category Parameter Values Demographic Number of patients (M-F) 105 (49–56) Number of eyes (R-L) 105 (105-0) Biometrical data Anterior corneal radius (mm) 7.72 ± 0.08 Posterior corneal radius (mm) 6.52 ± 0.21 Corneal central thickness (µm) 543.03 ± 31.35 Anterior chamber depth (mm) 4.64 ± 0.25 Pupil decentration [X,Y] (mm) [-0.26 ± 0.21, -0.10 ± 0.22] Axial length (mm) 23.57 ± 1.09 IOL power (D) 21.22 ± 3.25 IOL decentration [X,Y] (mm) [-0.11 ± 0.19, 0.03 ± 0.18] IOL tilt [X,Y] (mm) [-4.77 ± 1.40, -1.36 ± 1.44] Subjective refraction M (D) -0.11 ± 0.37 J 0 (DC) -0.19 ± 0.27 J 45 (DC) -0.04 ± 0.19 BCVA (LogMAR) 0.00 ± 0.05 Synthetic versus clinical variables The mean difference and 95% confidence interval (95%CI) between VA pred and BCVA were − 0.05 95% CI(-0.07,-0.03) LogMAR. The Bland-Altman analysis showed a low and upper limit of agreement of -0.25, 0.16 LogMAR respectively (Fig. 2 ). The objective prescriptions calculation varies with every single scenario and their mean differences with the subjective prescription are represented in Table 2 . The scenario where decentration and tilt were represented showed the minimum differences with the subjective prescription. Further details for the comparison between this scenario prescriptions and the clinical subjective prescription are extended in Fig. 3 . Table 2 Showed the mean difference and 95% confidence interval for each objective prescription and the subjective prescription calculated for each scenario. Aligned Decentration Tilt Decentration + Tilt MinRMS M (D) 0.59 (0.52, 0.67) 0.55 (0.47, 0.62) 0.44 (0.36, 0.52) 0.40 (0.32, 0.48) J 0 (DC) -0.05 (-0.11, 0.01) -0.06 (-0.11, 0.00) -0.11 (-0.17, -0.05) -0.11 (-0.17, -0.05) J 45 DC) 0.09 (0.05, 0.13) 0.09 (0.05, 0.13) 0.06 (0.02, 0.10) 0.08 (0.03, 0.12) Paraxial M 0.29 (0.22, 0.37) 0.24 (0.17, 0.32) 0.14 (0.07, 0.22) 0.09 (0.01, 0.17) J 0 (DC) -0.06 (-0.11, -0.00) -0.06 (-0.12, -0.01) -0.11 (-0.17, -0.06) -0.12 (-0.18, -0.06) J 45 (DC) 0.09 (0.05, 0.13) 0.09 (0.05, 0.13) 0.05 (0.01, 0.10) 0.07 (0.03, 0.11) Optimized VSX M 0.52 (0.45, 0.60) 0.43 (0.36, 0.51) 0.29 (0.21, 0.38) 0.20 (0.12, 0.29) J 0 (DC) -0.07 (-0.12, -0.02) -0.07 (-0.13, -0.02) -0.09 (-0.14, -0.04) -0.10 (-0.16, -0.05) J 45 (DC) 0.08 (0.04, 0.11) 0.08 (0.04, 0.12) 0.07 (0.03, 0.11) 0.10 (0.06, 0.14) Simulated optical changes derived from IOL tilt and decentration The wavefront error changed significantly for the RMS coma (p < 0,001), where the aligned scenario showed zero coma values and it increased its value through the next scenarios. Spherical and astigmatism aberrations slightly changed with IOL tilt and decentration. Regarding the changes in simulated optical prescriptions, while J 0 and J 45 did not changed for any prescription method, the spherical-equivalent represented by the M variable showed a progressive decline when tilt and decentration were applied to the model. This change reached statistical significance only for the optimized VSX prescription (p < 0.001), yet the MinRMS and PCM edge the threshold, p = 0.07 and p = 0.05 respectively. More details could be found in Table 3 . Table 3 Mean and standard deviation of the objective prescriptions in power vector notation and the VSX metrics value associated through different simulated scenarios. Prescription Method Variable Aligned Decentration Tilt Decentration + Tilt ANOVA p-value Wavefront RMS Spherical (µm) 0.84 ± 0.52 0.80 ± 0.52 0.73 ± 0.49 0.70 ± 0.49 0.15 Astigmatism (µm) 0.79 ± 0.44 0.79 ± 0.44 0.78 ± 0.44 0.79 ± 0.44 0.99 Coma (µm) 0.00 ± 0.00 0.11 ± 0.06 0.21 ± 0.07 0.26 ± 0.09 < 0.001 MinRMS M (D) -0.70 ± 0.59 -0.65 ± 0.60 -0.55 ± 0.60 -0.50 ± 0.60 0.07 J 0 (DC) -0.14 ± 0.47 -0.14 ± 0.47 -0.09 ± 0.47 -0.08 ± 0.48 0.68 J 45 (DC) -0.14 ± 0.32 -0.14 ± 0.32 -0.10 ± 0.33 -0.12 ± 0.33 0.87 VSX 0.80 ± 0.11 0.65 ± 0.14 0.44 ± 0.15 0.35 ± 0.17 < 0.001 Paraxial M (D) -0.40 ± 0.57 -0.35 ± 0.58 -0.25 ± 0.58 -0.20 ± 0.58 0.05 J 0 (DC) -0.14 ± 0.45 -0.13 ± 0.45 -0.08 ± 0.46 -0.07 ± 0.47 0.65 J 45 (DC) -0.13 ± 0.31 -0.13 ± 0.31 -0.10 ± 0.32 -0.12 ± 0.32 0.86 VSX 0.46 ± 0.13 0.44 ± 0.12 0.39 ± 0.11 0.33 ± 0.12 < 0.001 Optimized VSX M (D) -0.63 ± 0.57 -0.54 ± 0.59 -0.40 ± 0.60 -0.31 ± 0.61 < 0.001 J 0 (DC) -0.13 ± 0.41 -0.12 ± 0.41 -0.10 ± 0.41 -0.09 ± 0.42 0.93 J 45 (DC) -0.12 ± 0.29 -0.12 ± 0.30 -0.11 ± 0.29 -0.15 ± 0.30 0.86 VSX 0.70 ± 0.17 0.60 ± 0.17 0.46 ± 0.15 0.38 ± 0.17 < 0.001 The optical quality represented by the VSX metric statistically changed across scenarios, reducing its value as long as tilt and decentration were involved. This happened for the three objective prescriptions assessed in this study and we found that IOL tilt impacts more than decentration (p < 0.001). These differences are represented numerically in Fig. 4 . Another approach is to simulate the image convolution acquired with a prescription for every scenario. In Fig. 5 , we represent the extreme cases in the sample to depict image deterioration. Clinical impact of IOL tilt and decentration on BCVA The partial Spearman correlation between IOL tilt and BCVA, controlling IOL decentration, was not statistically significant (r = 0.07, 95% CI [-0.12, 0.26], p = 0.48). Similarly, when assessing the partial correlation between IOL decentration and BCVA while controlling for IOL tilt, no significant association was found (r = 0.13, 95% CI [-0.06, 0.32], p = 0.18).When comparing the BCVA between groups with low and high IOL tilt, no significant differences were observed (p-value = 0.23). Same result was obtained when comparing BCVA between groups with high and low IOL decentration (p-value = 0.29). Discussion The optical performance of intraocular lenses (IOLs) is not only influenced by their final axial position but also by their alignment and tilt within the eye. Numerous studies have highlighted the optical quality degradation associated with IOL tilt and decentration, mostly through optical bench experiments or computational simulations. To the best of our knowledge, this is the first study that investigates the impact of IOL misalignment using eye models based on real clinical data. Another notable contribution of this study is the characterization of monofocal aspheric IOLs. Using their anterior radius, labeled power, and manufacturer-reported spherical aberration, we were able to implement these lenses into ray-tracing simulations. Despite the aforementioned challenges, we successfully modeled the optical aberrations of the eye and evaluated the impact of IOL tilt and decentration on visual quality. A major strength of this study is the integration of clinical data with theoretical analysis, helping to bridge the gap between basic research and clinical practice. The study findings are in accordance with the theoretical changes produced by IOL tilt proposed by Atchison et al 5 , as the M value for every prescription varies when IOL tilt and decentration are present because of the variation of the effective power of the IOL. We did not appreciate great changes in terms of the astigmatism components, probably because the IOL model selected for this study was aspherical. Our findings show that both IOL tilt and decentration induce statistically significant coma aberrations. For IOL decentration, we found a mean value of 0.25 ± 0.13 mm which induced coma aberration of 0.11 ± 0.06 µm. This result is in accordance with Perez-Gracia 19 which reported a coma RMS values around 0.05–0.1 µm for 0.25 mm IOL decentration. In the same line, Perez-Merino et al 12 reported an RMS coma from 0.10 µm to 0.22 µm for 0.4 mm decentration. Our result in coma aberration is within the range of normal reported values from other authors. These results are strongly influenced by the pupil diameter and the IOL model selected (aspherical or spherical). The mean coma aberration induced by IOL tilt (5.19 ± 1.28°) in this study was 0.21 ± 0.07 µm. Other studies reported similar mean values for IOL tilt, from 2–6 degrees inducing a coma-like aberration from 0.19 22 to 0.4 microns 17 , 19 . The variability depends on several factors, such as the IOL power and design or the pupil used for the analysis. VSX metrics proved highly sensitive to IOL tilt and decentration, showing a marked reduction in value as these misalignments increased. This behavior may be attributed to the prismatic effect caused by coma aberration on the point spread function. Interestingly, the low VSX values observed in the “tilt and decentration” scenario contrast with the good clinical BCVA outcomes. Despite this, the correlation between the degree of tilt and decentration and the resulting BCVA was weak when an aspherical IOL was implanted, suggesting limited clinical impact. This raises the question of whether such induced aberrations could have a more pronounced effect in the context of multifocal IOLs, which are known to be more susceptible to higher-order aberrations and demand higher optical quality for optimal function. This study has several limitations. The most critical is the difficulty in accurately characterizing the cornea using commercial instruments, which significantly affects the overall precision of the optical model, given the dominant role of the cornea in ocular optics. Another limitation is the unavailability of exact IOL parameters from manufacturers, as such information remains proprietary. Finally, our model assumes a monochromatic light source centered at 550 nm, whereas real vision involves a broad spectrum of wavelengths and complex neural processing, which are not fully accounted for in this study. Future research should focus on improving the precision of corneal surface modeling, possibly by integrating data from advanced imaging modalities such as Scheimpflug tomography. Additionally, efforts to access and incorporate manufacturer-specific IOL design parameters would enhance the accuracy of simulations. Expanding the model to include polychromatic light and retinal image processing would provide a more comprehensive understanding of the visual impact of IOL misalignment. Although IOL tilt and decentration induced statistically significant coma aberration in the optical eye model, the analysis of clinical variables did not reveal a consistent relationship with visual outcomes. This suggests that the magnitude of coma induced by the observed levels of misalignment may not be sufficient to significantly impair the best-corrected visual acuity in eyes implanted with the studied aspheric IOL. Interestingly, The VSX was highly sensitive to IOL tilt and decentration, raising questions about how accurately this metric reflects clinical visual performance. Further studies are needed to determine whether the aberrations induced by IOL tilt and decentration have a more relevant impact on visual performance when multifocal IOLs are implanted. Declarations Funding declaration The authors received no financial support for the research, authorship, or publication of this article. Financial disclosure The authors have no conflicts of interest to disclose . Acknowledgements (optional) We would like to thank Dr. Larry Thibos for his valuable input and for kindly addressing our questions. We also acknowledge his significant contributions to the field of visual optics, which have been instrumental in shaping the present work. Author contributions Data availability statement (mandatory) The data that support the findings of this study are available from the corresponding author upon reasonable request. Additional Information (including a Competing Interests Statement) The authors have no financial or proprietary interest in the materials presented herein. References Hoffer KJ. Astigmatism from lens tilt. J Am Intraocul Implant Soc . 1985;11(1). Sanders DR, Kraff MC. Improvement of intraocular lens power calculation using empirical data. American Intra-Ocular Implant Society Journal . Published online 1980. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens implant power calculation formula. J Cataract Refract Surg . 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Velarde-Rodriguez","email":"data:image/png;base64,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","orcid":"","institution":"Hospital Universitario Fundación Jiménez Díaz","correspondingAuthor":true,"prefix":"","firstName":"Gonzalo","middleName":"","lastName":"Velarde-Rodriguez","suffix":""},{"id":527942385,"identity":"891f81c8-c751-4760-abb3-d5a7c0e85e1d","order_by":1,"name":"Nicolas Alejandre-Alba","email":"","orcid":"","institution":"Hospital Universitario Fundación Jiménez Díaz","correspondingAuthor":false,"prefix":"","firstName":"Nicolas","middleName":"","lastName":"Alejandre-Alba","suffix":""},{"id":527942386,"identity":"6458f3d6-6182-4b58-afde-188ea9dde25b","order_by":2,"name":"Azahara Sanchez-Lozano","email":"","orcid":"","institution":"Hospital Universitario Fundación Jiménez Díaz","correspondingAuthor":false,"prefix":"","firstName":"Azahara","middleName":"","lastName":"Sanchez-Lozano","suffix":""},{"id":527942387,"identity":"3b9cf009-d283-4f4a-84b3-3c5c99676ba5","order_by":3,"name":"Luis Garcia-Onrubia","email":"","orcid":"","institution":"Hospital Universitario Fundación Jiménez Díaz","correspondingAuthor":false,"prefix":"","firstName":"Luis","middleName":"","lastName":"Garcia-Onrubia","suffix":""},{"id":527942388,"identity":"88d558d1-d79e-45a7-af07-9323128c5641","order_by":4,"name":"Ignacio Jimenez-Alfaro","email":"","orcid":"","institution":"Hospital Universitario Fundación Jiménez Díaz","correspondingAuthor":false,"prefix":"","firstName":"Ignacio","middleName":"","lastName":"Jimenez-Alfaro","suffix":""},{"id":527942389,"identity":"8b52b65d-105e-4adb-a65b-1a8a884bf44b","order_by":5,"name":"Miguel Faria-Ribeiro","email":"","orcid":"","institution":"University of Minho","correspondingAuthor":false,"prefix":"","firstName":"Miguel","middleName":"","lastName":"Faria-Ribeiro","suffix":""}],"badges":[],"createdAt":"2025-08-13 10:38:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7364042/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7364042/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-33155-8","type":"published","date":"2025-12-19T15:58:30+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":93529933,"identity":"15bc16e1-7aae-42c6-befc-43a6311c36d5","added_by":"auto","created_at":"2025-10-14 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20:59:31","extension":"png","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":149993,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/7849333a68eda5525b9ade1d.png"},{"id":93530697,"identity":"b8bf7e1f-b67c-4642-a276-465d14a5c924","added_by":"auto","created_at":"2025-10-14 20:59:31","extension":"xml","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":96359,"visible":true,"origin":"","legend":"","description":"","filename":"2562f637f123422d928bc98a4e97d7af1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/c10a89a3534cdfa15b640a1a.xml"},{"id":93529946,"identity":"f7ac8ab3-5fac-4cbc-be24-fb4f8581f491","added_by":"auto","created_at":"2025-10-14 20:51:31","extension":"html","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":108342,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/4c233317c6ec55c19bdaa73c.html"},{"id":93529931,"identity":"e63dceec-7c24-4fec-b1ef-df7f79e0b099","added_by":"auto","created_at":"2025-10-14 20:51:30","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":106147,"visible":true,"origin":"","legend":"\u003cp\u003eExample for the first analyzed eye included in this study, revealing the general settings to build the synthetic eye model.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/f2404b5d3a81d97df601fc88.png"},{"id":93529932,"identity":"85a12c67-a2ce-4e58-ad35-ab31ca7abd94","added_by":"auto","created_at":"2025-10-14 20:51:31","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":64201,"visible":true,"origin":"","legend":"\u003cp\u003eBland-Altman plot that shows the agreement between the predicted visual acuity using the intersection value of the threshold function and the average modulate transfer function.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/14cb7561d04a8e2beed42d86.png"},{"id":93529944,"identity":"c6114e81-3e23-40a3-aa47-7bcfbe9d2b1a","added_by":"auto","created_at":"2025-10-14 20:51:31","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":156183,"visible":true,"origin":"","legend":"\u003cp\u003eObjective and subjective prescriptions comparative. Above the agreement using a Bland-Altman plot. Below is the histogram that represents the number of eyes (Y-axis) and the difference in diopters (X-axis) for the power vectors (M,J\u003csub\u003e0\u003c/sub\u003e and J\u003csub\u003e45\u003c/sub\u003e).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/b82d394c0c53b5c2caac9221.png"},{"id":93529942,"identity":"5f96e75d-39ad-49e2-9657-4239707678ff","added_by":"auto","created_at":"2025-10-14 20:51:31","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":30566,"visible":true,"origin":"","legend":"\u003cp\u003eVisual Strehl ratio (VSX) comparison across four intraocular lens (IOL) positioning scenarios: perfectly aligned, decentered, tilted, and combined decentration and tilt. All pairwise comparisons showed statistically significant differences (*** p \u0026lt; 0.001) using Wilcoxon rank sum test.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/b74ba32110ec44b3b38301f5.png"},{"id":93530867,"identity":"9e029d05-3c35-4949-b8f8-46c3e6c66a80","added_by":"auto","created_at":"2025-10-14 21:07:31","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":74828,"visible":true,"origin":"","legend":"\u003cp\u003eRepresentation of convolution image in three different cases. The first row shows an eye with IOL tilt and decentration within normal limits. The second row corresponds to the case with maximum IOL tilt, and the third row represents a case with significant IOL decentration.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/dd2bf363bda76a1833667917.png"},{"id":98815356,"identity":"023cfa50-648a-414d-a0ca-fa79539204e4","added_by":"auto","created_at":"2025-12-22 16:14:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1334695,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7364042/v1/363e5e6b-d18f-484a-8e4c-6d7fe5247c4f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Clinical and simulated impact of intraocular lens tilt and decentration: from real-world data to optical simulation","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe influence of intraocular lens (IOL) tilt on postoperative refraction was clinically described during the development of the first IOL power calculation formulas \u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Later, this issue and the consequences of IOL misalignment were elegantly explained using paraxial optics \u003csup\u003e\u003cspan additionalcitationids=\"CR5\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. As newer formulas and toric IOLs were developed and residual refraction improved, this topic gained even more importance \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. The sensitivity of multifocal and extended depth of focus (EDOF) IOLs to misalignment prompted researchers to investigate the topic using optical bench setups \u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e and ocular wavefront measurements \u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. More recently, ray-tracing software has been used to simulate synthetic ocular models to evaluate IOL tilt and decentration \u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eScheimpflug imaging and anterior segment optical coherence tomography (AS-OCT) have enabled clinical evaluation of IOL tilt and decentration. Studies report mean tilt values between 2\u0026deg; and 5\u0026deg;, depending on factors such as axial length, IOL haptics, capsular tension ring use, and preoperative crystalline lens tilt \u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. These factors also influence the sagittal and meridional displacement of the IOL, with typical decentration values around 0.2\u0026ndash;0.3 mm \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Both tilt and decentration can impair visual quality by inducing high-order aberrations (HOAs), and in more extreme cases, may reduce visual acuity (VA). Some studies suggest that decentration has a more significant impact on vision than tilt, although both are influenced by IOL design \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. The visual impact of decentering a spherical IOL is less pronounced than with aspheric designs; however, tilt appears to affect both types similarly \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e,\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. IOL tilt is more strongly correlated with coma-like aberrations, while both tilt and decentration contribute to induced astigmatism \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e,\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eAs premium IOLs evolve rapidly, more sophisticated designs demand a deeper understanding of ocular optics. While optical bench simulations have provided valuable insights into IOL misalignment, and clinical studies have documented its effects on visual acuity, few studies have combined both perspectives to assess the impact on ocular aberrations comprehensively. The purpose of this study is to replicate ocular parameters using optical simulation software to evaluate changes in synthetic ocular aberrations due to IOL tilt and decentration, and to correlate these findings with clinical outcomes.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eSettings\u003c/h2\u003e\u003cp\u003eThis cross-sectional study was conducted at Fundaci\u0026oacute;n Jim\u0026eacute;nez D\u0026iacute;az University Hospital between November 2023 and June 2024. The local institutional review board (Comit\u0026eacute; de Etica de la Investigaci\u0026oacute;n Fundaci\u0026oacute;n Jim\u0026eacute;nez Diaz. Code: PIC204-24) approved the study protocol, which complies with the tenets of the Declaration of Helsinki. Informed consent was obtained from all subjects following an explanation of the nature and possible consequences of the study.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003ePatient eligibility\u003c/h3\u003e\n\u003cp\u003ePatients who underwent uneventful cataract surgery of both eyes and implanted with Clareon\u0026reg; CNAT0 with a minimum follow-up of 3 months were included. The exclusion criteria comprehend amblyopia, retinal or corneal or any other ocular disease that could affect the patient\u0026rsquo;s vision performance. Also, any patient with history of ocular surgery such as refractive surgery or interventions that could affect the capsule-bag integrity like Nd-YAG capsulotomy was excluded.\u003c/p\u003e\n\u003ch3\u003eMeasurement protocol\u003c/h3\u003e\n\u003cp\u003eSubjective refraction to obtain the best corrected visual acuity (BCVA) was performed by the same experienced optometrist (ASL) using EDTRS chart. One drop of tropicamide (1%) was instilled for the next measurements.\u003c/p\u003e\u003cp\u003ePostoperative biometry using IOL-Master 700 (Carl Zeiss Meditec, AG, Jenna, Germany, version 1.90.33.04) was used to acquire axial length. Patients anterior segment was measured with AS-OCT CASIA II (TOMEY corp, Nagoya, Japan, version 50.6B.07) using the cataract protocol examination. Only measurements labeled as OK by the instrument were included in this study. IOL edge detection was performed by a researcher (GVR) using the semi-trace method included in the AS-OCT software.\u003c/p\u003e\n\u003ch3\u003eIOL parametrization\u003c/h3\u003e\n\u003cp\u003eThe anterior radii of curvature and central thickness of each implanted IOL were measured using the AS-OCT software. Although the software also reports the posterior radius of curvature, accurate identification of the posterior IOL surface was often impaired by the proximity of the posterior capsule, leading to acquisition errors.\u003c/p\u003e\u003cp\u003eTo address this limitation, it was assumed that the labeled paraxial power of IOL matched its nominal value. Based on this assumption and using the refractive index provided by the manufacturer (Nd\u0026thinsp;=\u0026thinsp;1.55, at 35 \u0026ordm;C), the posterior radius of curvature was calculated such that the combination of anterior radius, central thickness, and material index would result in the labeled paraxial power.\u003c/p\u003e\u003cp\u003eEach IOL\u0026rsquo;s anterior surface was then modeled as a fourth-order even asphere, excluding the 2nd-order term. The conic constant (\u0026#119896;) and fourth-order aspheric coefficient (\u0026#119886;₄) were optimized in Zemax OpticStudio to ensure that the IOL corrected \u0026minus;\u0026thinsp;0.20 \u0026micro;m of fourth-order corneal spherical aberration (Zernike term) in a physiological model eye, assuming a 6.0 mm entrance pupil.\u003c/p\u003e\n\u003ch3\u003eSynthetic eye model and simulating different scenarios\u003c/h3\u003e\n\u003cp\u003eAnsys Zemax OpticStudio (v 22.1) was used to build the eye model. Coordinates breaks were used to include pupil decentration, IOL tilt and decentration and corneal angle shift of the principal axes (Z-axis tilt). The anterior and posterior corneal surface were included as a biconic surface with data from IOL Master 700 principal meridians (setting conic constant to zero). The iris was represented by a stop surface of pupil\u0026rsquo;s patient diameter and situated 0.75 millimeters before the IOL anterior surface. IOL anterior surface was described as a fourth order even asphere and a posterior standard surface, adhering to the data collected by de AS-OCT and the IOL power labelled by manufacturer. The system setting was adjusted for a wavelength of 550 nm with no field modification. The selected pupil for the analysis was 4 mm. The corneal index used in this model 1.3752 and 1.336 for the aqueous and vitreous humors. More information is available in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFour scenarios were simulated using this eye model. The first situation was with the IOL totally aligned. In the second one, the measured IOL decentration (AS-OCT) was introduced, then the IOL tilt was set and finally the IOL decentration was set to zero. Therefore, four scenarios were evaluated as \u0026ldquo;Aligned\u0026rdquo;, \u0026ldquo;Decentration\u0026rdquo;, \u0026ldquo;Decentration\u0026thinsp;+\u0026thinsp;tilt\u0026rdquo; and \u0026ldquo;Tilted\u0026rdquo; respectively. The wavefront phase and its associated Zernike coefficients values (up to sixth order) were collected for each situation.\u003c/p\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003eObjective synthetic refraction\u003c/h2\u003e\u003cp\u003eA total of three refractions for each of the described scenarios were obtained for each patient derived from the synthetic ocular wavefront. Two objective refractions were directly obtained from the Zernike coefficient values: minimum root min square (MinRMS) and paraxial curvature matching (PCM)\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Another refraction was calculated by maximizing the retinal image quality weighted by a neural function\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. The selected metric was the visual strehl in the special domain (VSX). This was performed using an iterative process of testing lenses with the aberration map and maximizing the metric value. The following equation describes how we calculate this metric:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:VSX=\\:\\frac{\\iint\\:PSF\\:\\left(x,y\\right)*iCSF\\:\\left(x,y\\right)\\:dxdy}{\\iint\\:{PSF}_{DL}\\:\\left(x,y\\right)*iCSF\\:\\left(x,y\\right)dxdy}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere PSF is the point spread function and the iCSF is the inverse fourier transform of the contrast sensitivity function (CSF)\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eThe optimizing process was carried out testing a combination of sphero-cylindrical lenses with a range from \u0026minus;\u0026thinsp;3 to 3 D in steps of 0.25 D. The step for the refractive axis was 5\u0026ordm;, from 0 to 175 degrees. These values were converted into power vectors (M,J0 and J45) and finally into their equivalent Zernike coefficients Z (2,0), Z (2,-2) and Z (2,2). These variables were converted into wavefront error in microns and added to the original ocular wavefront calculating the new value of the VSX. We selected the sphero-cylindrical prescription that maximize the VSX value.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eEvaluating the synthetic eye model:\u003c/h3\u003e\n\u003cp\u003eTo assess the consistency of the eye model, the predicted visual (VA\u003csub\u003epred\u003c/sub\u003e) acuity was estimated by identifying the intersection between the radial modulation transfer function (MTFr) and the contrast sensitivity threshold\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, for this purpose we choose the Mannos and Sakrison threshold curve\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Additionally, the objective prescriptions were derived from the scenario IOL decentration and tilt, which replicates the actual clinical setting in the synthetic eye model. This comparison was evaluated twofold, with the subtraction (subjective prescription \u0026ndash; objective prescription) and by the Bland-Altman agreement analysis method.\u003c/p\u003e\n\u003ch3\u003eImpact IOL tilt and decentration in visual performance\u003c/h3\u003e\n\u003cp\u003eWe evaluated this subject with two different approaches; On one hand variables derived from the synthetic eye and on the other hand clinical variables measurements.\u003c/p\u003e\u003cp\u003eThe synthetic eye model allows the statistical comparison of the image quality metrics such as VSX or the optical aberrations (RMS astigmatism and RMS Coma) for the different simulated scenarios (Aligned\u0026rsquo;, \u0026rsquo;Decentration\u0026rsquo;, Tilt\u0026rsquo; and Decentration and tilt\u0026rsquo;). These variables changes were assessed using the Anova statistical tests, a p-value\u0026thinsp;\u0026lt;\u0026thinsp;0.05 was considered statistically significant. The image quality metrics obtained for each scenario were compared using the Wilcoxon signed-ranked test and box and whiskers plots analysis.\u003c/p\u003e\u003cp\u003eConcerning the clinical measurements, we studied the IOL positioning (tilt and decentration) and BCVA. First, we performed a partial correlation analysis to determine the relationship between IOL tilt, decentration and BCVA. But also, we explore the BCVA differences between patients with high IOL tilt (more than third quartile) or decentration to those that presented low values (less than first quartile) of these variables. For that purpose, we used Mann-Whitney U test with the mentioned statistical threshold.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eA total of 105 right eyes from 105 participants (53% females and 47% males) were included in this study. The mean patients age was 73.35\u0026thinsp;\u0026plusmn;\u0026thinsp;8.39 years old and follow-up period was 9.41\u0026thinsp;\u0026plusmn;\u0026thinsp;4.54 months after cataract surgery. A statistical summary of the main clinical variables is presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The main modulus of the vectors tilt and decentration were 5.19\u0026thinsp;\u0026plusmn;\u0026thinsp;1.28\u0026deg; and 0.25\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13 mm, respectively. The study of the IOL tilt revealed a tendency, the nasal-superior IOL edge was shifted towards the cornea compared to the temporal edge. The maximum value for tilt was 9.3\u0026ordm; (eye 12) and decentration was 0.83 mm (eye 36).\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\u003eSummarize the results for the demographic and clinical variables.\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=\"left\" 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\u003eCategory\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eParameter\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eValues\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003e\u003cb\u003eDemographic\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eNumber of patients (M-F)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e105 (49\u0026ndash;56)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eNumber of eyes (R-L)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e105 (105-0)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"8\" rowspan=\"9\"\u003e\u003cp\u003e\u003cb\u003eBiometrical data\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eAnterior corneal radius (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e7.72\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003ePosterior corneal radius (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6.52\u0026thinsp;\u0026plusmn;\u0026thinsp;0.21\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eCorneal central thickness (\u0026micro;m)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e543.03\u0026thinsp;\u0026plusmn;\u0026thinsp;31.35\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eAnterior chamber depth (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4.64\u0026thinsp;\u0026plusmn;\u0026thinsp;0.25\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003ePupil decentration [X,Y] (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e[-0.26\u0026thinsp;\u0026plusmn;\u0026thinsp;0.21, -0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.22]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eAxial length (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e23.57\u0026thinsp;\u0026plusmn;\u0026thinsp;1.09\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eIOL power (D)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e21.22\u0026thinsp;\u0026plusmn;\u0026thinsp;3.25\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eIOL decentration [X,Y] (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e[-0.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.19, 0.03\u0026thinsp;\u0026plusmn;\u0026thinsp;0.18]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eIOL tilt [X,Y] (mm)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e[-4.77\u0026thinsp;\u0026plusmn;\u0026thinsp;1.40, -1.36\u0026thinsp;\u0026plusmn;\u0026thinsp;1.44]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003e\u003cb\u003eSubjective refraction\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM (D)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.37\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.19\u0026thinsp;\u0026plusmn;\u0026thinsp;0.27\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e-0.04\u0026thinsp;\u0026plusmn;\u0026thinsp;0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eBCVA (LogMAR)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.00\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eSynthetic versus clinical variables\u003c/h2\u003e\u003cp\u003eThe mean difference and 95% confidence interval (95%CI) between VA\u003csub\u003epred\u003c/sub\u003e and BCVA were \u0026minus;\u0026thinsp;0.05 95% CI(-0.07,-0.03) LogMAR. The Bland-Altman analysis showed a low and upper limit of agreement of -0.25, 0.16 LogMAR respectively (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The objective prescriptions calculation varies with every single scenario and their mean differences with the subjective prescription are represented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The scenario where decentration and tilt were represented showed the minimum differences with the subjective prescription. Further details for the comparison between this scenario prescriptions and the clinical subjective prescription are extended in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\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\u003eShowed the mean difference and 95% confidence interval for each objective prescription and the subjective prescription calculated for each scenario.\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=\"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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAligned\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDecentration\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eTilt\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eDecentration\u0026thinsp;+\u0026thinsp;Tilt\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e\u003cb\u003eMinRMS\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM (D)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.59 (0.52, 0.67)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.55 (0.47, 0.62)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.44 (0.36, 0.52)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.40 (0.32, 0.48)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.05 (-0.11, 0.01)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.06 (-0.11, 0.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.11 (-0.17, -0.05)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.11 (-0.17, -0.05)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003eDC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.09 (0.05, 0.13)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.09 (0.05, 0.13)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.06 (0.02, 0.10)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.08 (0.03, 0.12)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e\u003cb\u003eParaxial\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.29 (0.22, 0.37)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.24 (0.17, 0.32)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.14 (0.07, 0.22)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.09 (0.01, 0.17)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.06 (-0.11, -0.00)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.06 (-0.12, -0.01)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.11 (-0.17, -0.06)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.12 (-0.18, -0.06)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.09 (0.05, 0.13)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.09 (0.05, 0.13)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.05 (0.01, 0.10)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.07 (0.03, 0.11)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e\u003cb\u003eOptimized VSX\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.52 (0.45, 0.60)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.43 (0.36, 0.51)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.29 (0.21, 0.38)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.20 (0.12, 0.29)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e-0.07 (-0.12, -0.02)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e-0.07 (-0.13, -0.02)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e-0.09 (-0.14, -0.04)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e-0.10 (-0.16, -0.05)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.08 (0.04, 0.11)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.08 (0.04, 0.12)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.07 (0.03, 0.11)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.10 (0.06, 0.14)\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\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eSimulated optical changes derived from IOL tilt and decentration\u003c/h2\u003e\u003cp\u003eThe wavefront error changed significantly for the RMS coma (p\u0026thinsp;\u0026lt;\u0026thinsp;0,001), where the aligned scenario showed zero coma values and it increased its value through the next scenarios. Spherical and astigmatism aberrations slightly changed with IOL tilt and decentration.\u003c/p\u003e\u003cp\u003eRegarding the changes in simulated optical prescriptions, while J\u003csub\u003e0\u003c/sub\u003e and J\u003csub\u003e45\u003c/sub\u003e did not changed for any prescription method, the spherical-equivalent represented by the M variable showed a progressive decline when tilt and decentration were applied to the model. This change reached statistical significance only for the optimized VSX prescription (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), yet the MinRMS and PCM edge the threshold, p\u0026thinsp;=\u0026thinsp;0.07 and p\u0026thinsp;=\u0026thinsp;0.05 respectively. More details could be found in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\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\u003eMean and standard deviation of the objective prescriptions in power vector notation and the VSX metrics value associated through different simulated scenarios.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\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=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePrescription Method\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eVariable\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eAligned\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDecentration\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eTilt\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eDecentration\u0026thinsp;+\u0026thinsp;Tilt\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eANOVA p-value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003e\u003cb\u003eWavefront RMS\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eSpherical (\u0026micro;m)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e0.84\u0026thinsp;\u0026plusmn;\u0026thinsp;0.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e0.80\u0026thinsp;\u0026plusmn;\u0026thinsp;0.52\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e0.73\u0026thinsp;\u0026plusmn;\u0026thinsp;0.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e0.70\u0026thinsp;\u0026plusmn;\u0026thinsp;0.49\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eAstigmatism (\u0026micro;m)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e0.79\u0026thinsp;\u0026plusmn;\u0026thinsp;0.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e0.79\u0026thinsp;\u0026plusmn;\u0026thinsp;0.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e0.78\u0026thinsp;\u0026plusmn;\u0026thinsp;0.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e0.79\u0026thinsp;\u0026plusmn;\u0026thinsp;0.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.99\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eComa (\u0026micro;m)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e0.00\u0026thinsp;\u0026plusmn;\u0026thinsp;0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e0.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e0.21\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e0.26\u0026thinsp;\u0026plusmn;\u0026thinsp;0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003e\u003cb\u003eMinRMS\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM (D)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.70\u0026thinsp;\u0026plusmn;\u0026thinsp;0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.65\u0026thinsp;\u0026plusmn;\u0026thinsp;0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.50\u0026thinsp;\u0026plusmn;\u0026thinsp;0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.07\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.09\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.08\u0026thinsp;\u0026plusmn;\u0026thinsp;0.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.68\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.33\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.87\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eVSX\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e0.80\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e0.65\u0026thinsp;\u0026plusmn;\u0026thinsp;0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e0.44\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e0.35\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003e\u003cb\u003eParaxial\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM (D)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.40\u0026thinsp;\u0026plusmn;\u0026thinsp;0.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.35\u0026thinsp;\u0026plusmn;\u0026thinsp;0.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.25\u0026thinsp;\u0026plusmn;\u0026thinsp;0.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.20\u0026thinsp;\u0026plusmn;\u0026thinsp;0.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.14\u0026thinsp;\u0026plusmn;\u0026thinsp;0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.08\u0026thinsp;\u0026plusmn;\u0026thinsp;0.46\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.07\u0026thinsp;\u0026plusmn;\u0026thinsp;0.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eVSX\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e0.46\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e0.44\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e0.39\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e0.33\u0026thinsp;\u0026plusmn;\u0026thinsp;0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e\u003cp\u003e\u003cb\u003eOptimized VSX\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eM (D)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.63\u0026thinsp;\u0026plusmn;\u0026thinsp;0.57\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.54\u0026thinsp;\u0026plusmn;\u0026thinsp;0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.40\u0026thinsp;\u0026plusmn;\u0026thinsp;0.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.31\u0026thinsp;\u0026plusmn;\u0026thinsp;0.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e0\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.10\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.09\u0026thinsp;\u0026plusmn;\u0026thinsp;0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u003csub\u003e\u003cb\u003e45\u003c/b\u003e\u003c/sub\u003e \u003cb\u003e(DC)\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e-0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e-0.12\u0026thinsp;\u0026plusmn;\u0026thinsp;0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e-0.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e-0.15\u0026thinsp;\u0026plusmn;\u0026thinsp;0.30\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e0.86\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cb\u003eVSX\u003c/b\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e\u003cp\u003e0.70\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c4\"\u003e\u003cp\u003e0.60\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c5\"\u003e\u003cp\u003e0.46\u0026thinsp;\u0026plusmn;\u0026thinsp;0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c6\"\u003e\u003cp\u003e0.38\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.001\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\u003eThe optical quality represented by the VSX metric statistically changed across scenarios, reducing its value as long as tilt and decentration were involved. This happened for the three objective prescriptions assessed in this study and we found that IOL tilt impacts more than decentration (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). These differences are represented numerically in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Another approach is to simulate the image convolution acquired with a prescription for every scenario. In Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, we represent the extreme cases in the sample to depict image deterioration.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003eClinical impact of IOL tilt and decentration on BCVA\u003c/h2\u003e\u003cp\u003eThe partial Spearman correlation between IOL tilt and BCVA, controlling IOL decentration, was not statistically significant (r\u0026thinsp;=\u0026thinsp;0.07, 95% CI [-0.12, 0.26], p\u0026thinsp;=\u0026thinsp;0.48). Similarly, when assessing the partial correlation between IOL decentration and BCVA while controlling for IOL tilt, no significant association was found (r\u0026thinsp;=\u0026thinsp;0.13, 95% CI [-0.06, 0.32], p\u0026thinsp;=\u0026thinsp;0.18).When comparing the BCVA between groups with low and high IOL tilt, no significant differences were observed (p-value\u0026thinsp;=\u0026thinsp;0.23). Same result was obtained when comparing BCVA between groups with high and low IOL decentration (p-value\u0026thinsp;=\u0026thinsp;0.29).\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe optical performance of intraocular lenses (IOLs) is not only influenced by their final axial position but also by their alignment and tilt within the eye. Numerous studies have highlighted the optical quality degradation associated with IOL tilt and decentration, mostly through optical bench experiments or computational simulations. To the best of our knowledge, this is the first study that investigates the impact of IOL misalignment using eye models based on real clinical data.\u003c/p\u003e\u003cp\u003eAnother notable contribution of this study is the characterization of monofocal aspheric IOLs. Using their anterior radius, labeled power, and manufacturer-reported spherical aberration, we were able to implement these lenses into ray-tracing simulations. Despite the aforementioned challenges, we successfully modeled the optical aberrations of the eye and evaluated the impact of IOL tilt and decentration on visual quality. A major strength of this study is the integration of clinical data with theoretical analysis, helping to bridge the gap between basic research and clinical practice.\u003c/p\u003e\u003cp\u003eThe study findings are in accordance with the theoretical changes produced by IOL tilt proposed by Atchison et al\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, as the M value for every prescription varies when IOL tilt and decentration are present because of the variation of the effective power of the IOL. We did not appreciate great changes in terms of the astigmatism components, probably because the IOL model selected for this study was aspherical.\u003c/p\u003e\u003cp\u003eOur findings show that both IOL tilt and decentration induce statistically significant coma aberrations. For IOL decentration, we found a mean value of 0.25\u0026thinsp;\u0026plusmn;\u0026thinsp;0.13 mm which induced coma aberration of 0.11\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06 \u0026micro;m. This result is in accordance with Perez-Gracia\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e which reported a coma RMS values around 0.05\u0026ndash;0.1 \u0026micro;m for 0.25 mm IOL decentration. In the same line, Perez-Merino et al\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e reported an RMS coma from 0.10 \u0026micro;m to 0.22 \u0026micro;m for 0.4 mm decentration. Our result in coma aberration is within the range of normal reported values from other authors. These results are strongly influenced by the pupil diameter and the IOL model selected (aspherical or spherical). The mean coma aberration induced by IOL tilt (5.19\u0026thinsp;\u0026plusmn;\u0026thinsp;1.28\u0026deg;) in this study was 0.21\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07 \u0026micro;m. Other studies reported similar mean values for IOL tilt, from 2\u0026ndash;6 degrees inducing a coma-like aberration from 0.19 \u003csup\u003e22\u003c/sup\u003e to 0.4 microns \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. The variability depends on several factors, such as the IOL power and design or the pupil used for the analysis.\u003c/p\u003e\u003cp\u003eVSX metrics proved highly sensitive to IOL tilt and decentration, showing a marked reduction in value as these misalignments increased. This behavior may be attributed to the prismatic effect caused by coma aberration on the point spread function. Interestingly, the low VSX values observed in the \u0026ldquo;tilt and decentration\u0026rdquo; scenario contrast with the good clinical BCVA outcomes.\u003c/p\u003e\u003cp\u003eDespite this, the correlation between the degree of tilt and decentration and the resulting BCVA was weak when an aspherical IOL was implanted, suggesting limited clinical impact. This raises the question of whether such induced aberrations could have a more pronounced effect in the context of multifocal IOLs, which are known to be more susceptible to higher-order aberrations and demand higher optical quality for optimal function.\u003c/p\u003e\u003cp\u003eThis study has several limitations. The most critical is the difficulty in accurately characterizing the cornea using commercial instruments, which significantly affects the overall precision of the optical model, given the dominant role of the cornea in ocular optics. Another limitation is the unavailability of exact IOL parameters from manufacturers, as such information remains proprietary. Finally, our model assumes a monochromatic light source centered at 550 nm, whereas real vision involves a broad spectrum of wavelengths and complex neural processing, which are not fully accounted for in this study.\u003c/p\u003e\u003cp\u003eFuture research should focus on improving the precision of corneal surface modeling, possibly by integrating data from advanced imaging modalities such as Scheimpflug tomography. Additionally, efforts to access and incorporate manufacturer-specific IOL design parameters would enhance the accuracy of simulations. Expanding the model to include polychromatic light and retinal image processing would provide a more comprehensive understanding of the visual impact of IOL misalignment.\u003c/p\u003e\u003cp\u003eAlthough IOL tilt and decentration induced statistically significant coma aberration in the optical eye model, the analysis of clinical variables did not reveal a consistent relationship with visual outcomes. This suggests that the magnitude of coma induced by the observed levels of misalignment may not be sufficient to significantly impair the best-corrected visual acuity in eyes implanted with the studied aspheric IOL. Interestingly, The VSX was highly sensitive to IOL tilt and decentration, raising questions about how accurately this metric reflects clinical visual performance. Further studies are needed to determine whether the aberrations induced by IOL tilt and decentration have a more relevant impact on visual performance when multifocal IOLs are implanted.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eFunding declaration\u003c/p\u003e\n\u003cp\u003eThe authors received no financial support for the research, authorship, or publication of this article.\u003c/p\u003e\n\u003cp\u003eFinancial disclosure\u003c/p\u003e\n\u003cp\u003eThe authors have no conflicts of interest to disclose\u003cstrong\u003e.\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAcknowledgements (optional)\u003c/p\u003e\n\u003cp\u003eWe would like to thank Dr. Larry Thibos for his valuable input and for kindly addressing our questions. We also acknowledge his significant contributions to the field of visual optics, which have been instrumental in shaping the present work.\u003c/p\u003e\n\u003cp\u003eAuthor contributions\u003c/p\u003e\n\u003cp\u003eData availability statement (mandatory)\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003eAdditional Information (including a Competing Interests Statement)\u003c/p\u003e\n\u003cp\u003eThe authors have no financial or proprietary interest in the materials presented herein.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eHoffer KJ. Astigmatism from lens tilt. \u003cem\u003eJ Am Intraocul Implant Soc\u003c/em\u003e. 1985;11(1).\u003c/li\u003e\n \u003cli\u003eSanders DR, Kraff MC. 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Influence of intraocular lens tilt and decentration on wavefront aberrations. \u003cem\u003eJ Cataract Refract Surg\u003c/em\u003e. 2004;30(10).\u003c/li\u003e\n \u003cli\u003eRobert Iskander D, Davis BA, Collins MJ, Franklin R. Objective refraction from monochromatic wavefront aberrations via Zernike power polynomials. \u003cem\u003eOphthalmic and Physiological Optics\u003c/em\u003e. 2007;27(3):245-255.\u003c/li\u003e\n \u003cli\u003eThibos LN, Xin H, Bradley A, Applegate RA. Accuracy and precision of objective refraction from wavefront aberrations. \u003cem\u003eJ Vis\u003c/em\u003e. 2004;4(4):329-351.\u003c/li\u003e\n \u003cli\u003eCampbell FW, Green DG. Optical and retinal factors affecting visual resolution. \u003cem\u003eJ Physiol\u003c/em\u003e. 1965;181(3).\u003c/li\u003e\n \u003cli\u003eKrueger RR, Applegate RAlan, MacRae Scott. \u003cem\u003eWavefront Customized Visual Correction : The Quest for Super Vision II\u003c/em\u003e. SLACK; 2004.\u003c/li\u003e\n \u003cli\u003eMannos JL, Sakrison DJ. The Effects of a Visual Fidelity Criterion on the Encoding of Images. \u003cem\u003eIEEE Trans Inf Theory\u003c/em\u003e. 1974;20(4).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-7364042/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7364042/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo evaluate the optical impact of IOL tilt and decentration, we built synthetic eye models from real postoperative data and compared simulated image quality metrics with clinical outcomes. We included 105 eyes implanted with a monofocal aspheric IOL and measured their positioning using a tomographic device. With the clinical data we reconstruct each eye in Zemax optical software and evaluate four scenarios: aligned, decentered, tilted, and combined decentration and tilt. For each case, we calculated wavefront aberrations, three objective refractions, and predicted visual acuity from the intersection of the MTF and a threshold function. The average IOL tilt was 5.19 ± 1.28° and decentration was 0.25 ± 0.13 mm. Coma RMS increased from 0.00 µm in the aligned model to 0.26 ± 0.09 µm in the most altered scenario (p \u0026lt; 0.001), and VSX decreased from 0.80 ± 0.11 to 0.35 ± 0.17. Despite this optical degradation, BCVA remained unaffected, with a mean of 0.00 ± 0.05 LogMAR, and no significant correlation was found with tilt or decentration. The best agreement between simulated and clinical refraction was observed when both tilt and decentration were included. These results suggest that moderate IOL misalignment degrades optical quality without compromising visual acuity in monofocal IOLs, but further studies are needed for multifocal designs.\u003c/p\u003e","manuscriptTitle":"Clinical and simulated impact of intraocular lens tilt and decentration: from real-world data to optical simulation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-14 20:51:26","doi":"10.21203/rs.3.rs-7364042/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-19T10:54:59+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-02T15:55:11+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"302311212941453389053880839358725337226","date":"2025-10-20T05:37:44+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-18T12:30:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"50844412535128739965199995361385531241","date":"2025-10-17T08:30:22+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-01T04:28:37+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-19T04:26:50+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-18T03:58:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-08-13T10:30:39+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"02fee7dc-9d26-4cb6-8d9b-f63d0c1d5b2e","owner":[],"postedDate":"October 14th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":56121741,"name":"Health sciences/Diseases"},{"id":56121742,"name":"Health sciences/Health care"},{"id":56121743,"name":"Health sciences/Medical research"}],"tags":[],"updatedAt":"2025-12-22T16:11:58+00:00","versionOfRecord":{"articleIdentity":"rs-7364042","link":"https://doi.org/10.1038/s41598-025-33155-8","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2025-12-19 15:58:30","publishedOnDateReadable":"December 19th, 2025"},"versionCreatedAt":"2025-10-14 20:51:26","video":"","vorDoi":"10.1038/s41598-025-33155-8","vorDoiUrl":"https://doi.org/10.1038/s41598-025-33155-8","workflowStages":[]},"version":"v1","identity":"rs-7364042","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7364042","identity":"rs-7364042","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}