A New Method to Minimize the Standard Deviation and Root Mean Square of the Prediction Error of Single-Optimized IOL Power Formulas.

Purpose: The purpose of this study was to develop a simplified method to approximate constants minimizing the standard deviation (SD) and the root mean square (RMS) of the prediction error in single-optimized intraocular lens (IOL) power calculation formulas. Methods: The study introduces analytical formulas to determine the optimal constant value for minimizing SD and RMS in single-optimized IOL power calculation formulas. These formulas were tested against various datasets containing biometric measurements from cataractous populations and included 10,330 eyes and 4 different IOL models. The study evaluated the effectiveness of the proposed method by comparing the outcomes with those obtained using traditional reference methods. Results: In optimizing IOL constants, minor differences between reference and estimated A-constants were found, with the maximum deviation at -0.086 (SD, SRK/T, and Vivinex) and -0.003 (RMS, PEARL DGS, and Vivinex). The largest discrepancy for third-generation formulas was -0.027 mm (SD, Haigis, and Vivinex) and 0.002 mm (RMS, Hoffer Q, and PCB00/SN60WF). Maximum RMS differences were -0.021 and +0.021, both involving Hoffer Q. Post-minimization, the largest mean prediction error was 0.726 diopters (D; SD) and 0.043 D (RMS), with the highest SD and RMS after adjustments at 0.529 D and 0.875 D, respectively, indicating effective minimization strategies. Conclusions: The study simplifies the process of minimizing SD and RMS in single-optimized IOL power predictions, offering a valuable tool for clinicians. However, it also underscores the complexity of achieving balanced optimization and suggests the need for further research in this area. Translational Relevance: The study presents a novel, clinically practical approach for optimizing IOL power calculations.

High hyperopic LASIK with reduction of corneal prolateness to control induced spherical aberration.

PURPOSE: To evaluate visual outcomes of high hyperopic LASIK, using corneal aspherization to control the induced spherical aberration. SETTING: Fondation Ophtalmologique Adolphe de Rothschild. DESIGN: Prospective interventional case series. METHODS: Prospective interventional study of consecutive high hyperopes (≥+3D of Spherical Equivalent SE) undergoing LASIK with the WaveLight FS200 femtosecond and EX500 excimer laser platform. An aspheric ablation profile (planned change in corneal asphericity ΔQ = +0.2) was delivered using the Custom-Q nomogram (Alcon Laboratories, Inc., Fort Worth, TX) on an optical zone of ≥ 6.5mm centered near the corneal vertex. Uncorrected and best-corrected distance visual acuity (UDVA-BDVA), as well as changes in SE, corneal asphericity (ΔQ) and Higher order aberrations (HOAs), were analyzed preoperatively and on day1, 1, 3, 6, and 12 months. RESULTS: 117 eyes of 63 patients, (mean age of 30.1 ± 5.6 years), were included. Preoperatively and at 12 months postoperatively, the mean SE was 5.1 ± 1.1 D and 0.00 ± 0.7 D, respectively. 88% of eyes achieved 0 Log Mar or better UDVA at 12 months. One month after surgery, there was a statistically significant induction of positive spherical aberration decreasing progressively and significantly until the last visit (Preop SA4 = 0.09 ± 0.11 µm, Day 1 SA4 = 0.30 ± 0.32 µm, 12 Months SA4 = 0.08 ± 0.21 µm, p=0.056). Two eyes needed enhancement at 12 months. CONCLUSION: LASIK for high levels of hyperopia showed good outcomes mainly due to aspheric-customized ablation profile with a change of ΔQ = +0.2 in corneal asphericity.

Leaving trusted paths: Estimating corneal keratometric index in cataract surgery eyes with zero-power implants.

PURPOSE: This study aimed to estimate the corneal keratometric index in the eyes of cataract surgery patients who received zero-power intraocular lenses (IOLs). METHODOLOGY: This retrospective study analyzed postoperative equivalent spherical refraction and axial length, mean anterior curvature radius and aqueous humor refractive index to calculate the theoretical corneal keratometric index value (nk). Data was collected from 2 centers located in France and Germany. RESULTS: Thirty-six eyes were analyzed. The results revealed a mean corneal keratometric index of 1.329 ± 0.005 for traditional axial length (AL) and 1.331 ± 0.005 for Cooke modified axial length (CMAL). Results ranged from minimum values of 1.318/1.320 to maximum values of 1.340/1.340. CONCLUSION: The corneal keratometric index is a crucial parameter for ophthalmic procedures and calculations, particularly for IOL power calculation. Notably, the estimated corneal keratometric index value of 1.329/1.331 in this study is lower than the commonly used 1.3375 index. These findings align with recent research demonstrating that the theoretical corneal keratometric index should be approximately 1.329 using traditional AL and 1.331 using CMAL, based on the ratio between the mean anterior and posterior corneal curvature radii (1.22).

Differences Between Keratometry and Total Keratometry Measurements in a Large Dataset Obtained With a Modern Swept Source Optical Coherence Tomography Biometer.

PURPOSE: This study aimed to explore the concept of total keratometry (TK) by analyzing extensive international datasets representing diverse ethnic backgrounds. The primary objective was to quantify the disparities between traditional keratometry (K) and TK values in normal eyes and assess their impact on intraocular lens (IOL) power calculations using various formulas. DESIGN: Retrospective multicenter intra-instrument reliability analysis. METHODS: The study involved the analysis of biometry data collected from ten international centers across Europe, the United States, and Asia. Corneal power was expressed as equivalent power and astigmatic vector components for both K and TK values. The study assessed the influence of these differences on IOL power calculations using different formulas. The results were analyzed and plotted using Bland-Altman and double angle plots. RESULTS: The study encompassed a total of 116,982 measurements from 57,862 right eyes and 59,120 left eyes. The analysis revealed a high level of agreement between K and TK values, with 93.98% of eyes exhibiting an absolute difference of 0.25 D or less. Astigmatism vector differences exceeding 0.25 D and 0.50 D were observed in 39.43% and 1.08% of eyes, respectively. CONCLUSIONS: This large-scale study underscores the similarity between mean K and TK values in healthy eyes, with rare clinical implications for IOL power calculation. Noteworthy differences were observed in astigmatism values between K and TK. Future investigations should delve into the practicality of TK values for astigmatism correction and their implications for surgical outcomes.

Monte-Carlo simulation of a thick lens IOL power calculation.

BACKGROUND: The purpose of this Monte-Carlo study is to investigate the effect of using a thick lens model instead of a thin lens model for the intraocular lens (IOL) on the resulting refraction at the spectacle plane and on the ocular magnification based on a large clinical data set. METHODS: A pseudophakic model eye with a thin spectacle correction, a thick cornea (curvatures for both surfaces and central thickness) and a thick IOL (equivalent power PL derived from a thin lens IOL, Coddington factor CL (uniformly distributed from -1.0 to 1.0), either preset central thickness LT = 0.9 mm (A) or optic edge thickness ET = 0.2 mm, (B)) was set up. Calculations were performed on a clinical data set containing 21 108 biometric measurements of a cataractous population based on linear Gaussian optics to derive spectacle refraction and ocular magnification using the thin and thick lens IOL models. RESULTS: A prediction model (restricted to linear terms without interactions) was derived based on the relevant parameters identified with a stepwise linear regression approach to provide a simple method for estimating the change in spectacle refraction and ocular magnification where a thick lens IOL is used instead of a thin lens IOL. The change in spectacle refraction using a thick lens IOL with (A) or (B) instead of a thin lens IOL with identical power was within limits of around ±1.5 dpt when the thick lens IOL was placed with its haptic plane at the plane of the thin lens IOL. In contrast, the change in ocular magnification from considering the IOL as a thick lens instead of a thin lens was small and not clinically significant. CONCLUSION: This Monte-Carlo simulation shows the impact of using a thick lens model IOL with preset LT or ET on the resulting spherical equivalent refraction and ocular magnification. If IOL manufacturers would provide all relevant data on IOL design data and refractive index for all power steps, this would make it possible to perform direct calculations of refraction and ocular magnification.

Angle Kappa Influence on Multifocal IOL Outcomes.

PURPOSE: To characterize angle kappa and study the relationship between preoperative angle kappa and postoperative refractive accuracy, visual outcomes, and patient satisfaction in a large population of eyes with multifocal intraocular lens (MIOL) implantation. METHODS: A comprehensive electronic medical record chart review of 26,470 consecutive eyes that underwent immediate sequential bilateral cataract or refractive lens exchange with MIOLs was conducted. The primary outcome measures were postoperative monocular uncorrected distance visual acuity (UDVA), manifest refraction sphere and cylinder, spherical equivalent (SEQ), defocus equivalent (DEQ), subjective quality of vision at near, intermediate, and distance, and the likelihood of recommending the procedure. Relationships between preoperative angle kappa and postoperative outcomes were assessed with Pearson correlations. RESULTS: Angle kappa followed a right-skewed normal distribution (R2 = 0.99) with a mean ± standard deviation of 0.64 ± 0.27 mm. No clinically meaningful relationship was found between preoperative angle kappa and postoperative sphere, cylinder, SEQ, and DEQ, all with R2 ⩽ 0.0005. Similarly, there was no clinically meaningful relationship between preoperative angle kappa and postoperative UDVA (R2 = 0.001), postoperative satisfaction for near, intermediate, and distance vision (all R2 ⩽ 0.0023), or for recommending the MIOL surgery to friends and relatives (R2 = 0.0000). CONCLUSIONS: Preoperative angle kappa does not have a predictive clinical impact on postoperative MIOL visual outcomes, refractive accuracy, or subjective patient satisfaction. Angle kappa as a single variable cannot be used to determine MIOL candidacy. [J Refract Surg. 2023;39(12):840-849.].

Impact of Single Constant Optimization on the Precision of IOL Power Calculation.

Purpose: The primary objective of this research is to examine how precision in intraocular lens calculation formulas can be impacted by zeroing the mean error through adjustments in the effective lens position value. Additionally, the study aims to evaluate how this modification influences outcomes differently based on the source of the prediction error. Methods: In order to analyze the impact of individual variables on the standard deviation, the study maintained all variables constant except for one at a time. Subsequently, variations were introduced to specific parameters, such as corneal curvature radius, keratometric refractive index, axial length, and predicted implant position. Results: According to our findings, when zeroing the mean error is applied to correct for inaccuracies in corneal power estimation, it results in a significant and exponential rise in standard deviation, thus adversely affecting the formula's precision. However, when zeroing is employed to compensate for prediction errors stemming from axial length measurements or predicted implant position, the effect on precision is minimal or potentially beneficial. Conclusions: The study highlights the potential risks associated with the indiscriminate but necessary zeroing of prediction errors in implant power calculation formulas. The impact on formula precision greatly depends on the source of the error, underscoring the importance of error source when analyzing variations in the standard deviation of the prediction error after zeroing. Translational Relevance: Our study contributes to the ongoing effort to enhance the accuracy and reliability of these formulas, thereby improving the surgical outcomes for cataract patients.

The Development of a Thick-Lens Post-Myopic Laser Vision Correction Intraocular Lens Calculation Formula.

PURPOSE: To describe the development of the post-myopic laser vision correction (LVC) version of the PEARL-DGS intraocular lens (IOL) calculation formula and to evaluate its outcomes on an independent test set. DESIGN: Retrospective, single-center case series. METHODS: A modified lens position prediction algorithm was designed along with methods to predict the posterior corneal curvature radius and correct the corneal power measurement error. A different set of previously operated eyes that underwent LVC was used to evaluate the prediction precision of the post-LVC formula. RESULTS: Post-LVC PEARL-DGS formula significantly reduced mean absolute error of prediction in comparison to Haigis-L, Shammas, and American Society of Cataract and Refractive Surgery (ASCRS) average formulas (P < .001). It exhibited similar postoperative refractive precision as the Barrett True-K No History formula (P = .61). CONCLUSION: The post-LVC formula development process described in this article performed as well as the state-of-the-art post-LVC formula on the present test set. Further studies are required to assess its efficacy in other independent sets.

Discrimination between keratoconus, forme fruste keratoconus, and normal eyes using a novel OCT-based tomographer.

PURPOSE: To combine objective machine-derived corneal parameters obtained with new swept-source optical coherence tomography (SS-OCT) tomographer (Anterion) to differentiate between normal (N), keratoconus (KC) and forme fruste KC (FFKC). SETTING: Laser Center, Hôpital Fondation Adolphe de Rothschild, Paris, France. DESIGN: Retrospective study. METHODS: 281 eyes of 281 patients were included and divided into 3 groups: N (n = 156), FFKC (n = 43), and KC (n = 82). Eyes were included in each group based on objective evaluation using Nidek Corneal Navigator, and subjective evaluation by authors. The SS-OCT system provided anterior and posterior corneal surface and pachymetry derived variables. The training set was composed of 143 eyes (95 N, 43 FFKC). Discriminant analysis was used to determine the group of an observation based on a set of variables. The obtained formula was tested in the validation set composed of 61 N and 82 KC. RESULTS: Among curvature parameters, the FFKC had significantly higher irregularity index at 3 mm and 5 mm, higher inferior-superior index, higher SteepK-OppositeK index and inferiorly decentered posterior steepest keratometry. Among thickness parameters: central pachymetry, thinnest pachymetry, percentage of thickness increase from center to periphery, and inferior decentration of the thinnest point were statistically different between groups. Combination of multiple variables into a discriminant function (F1) included 5 parameters and reached an area under the receiver operating characteristic curve (AUROC) of 0.95 (sensitivity = 75%, specificity = 98.5%) for detection of FFKC. F1 differentiates N from KC with AUROC = 0.99 (sensitivity = 99%, specificity = 99%). CONCLUSIONS: Combining anterior and posterior curvatures variables along with pachymetric data obtained from SS-OCT allowed automated detection of early KC and KC with very good accuracy (87% and 99.5% respectively).

Theoretical Impact of Intraocular Lens Design Variations on the Accuracy of IOL Power Calculations.

To ascertain the theoretical impact of optical design variations of the intraocular lens (IOL) on the accuracy of IOL power formulas based on a single lens constant using a thick lens eye model. This impact was also simulated before and after optimization. We modeled 70 thick-lens pseudophakic eyes implanted with IOLs of symmetrical optical design and power comprised between 0.50 D and 35 D in 0.5-step increments. Modifications of the shape factor resulting in variations in the anterior and posterior radii of an IOL were made, keeping the central thickness and paraxial powers static. Geometry data from three IOL models were also used. Corresponding postoperative spherical equivalent (SE) were computed for different IOL powers and assimilated to a prediction error of the formula due to the sole change in optical design alone. Formula accuracy was studied before and after zeroization on a uniform and non-uniform realistic IOL power distribution. The impact of the incremental change in optic design variability depended on the IOL power. Design modifications theoretically induce an increase in the standard deviation (SD), Mean Absolute Error (MAE), and Root Mean Square (RMS) of the error. The values of these parameters reduce dramatically after zeroization. While the variations in optical design can affect refractive outcomes, especially in short eyes, the zeroization of the mean error theoretically reduces the impact of the IOL's design and power on the accuracy of IOL power calculation.

A Simplified Method to Minimize Systematic Bias of Single-Optimized Intraocular Lens Power Calculation Formulas.

PURPOSE: To provide a simplified method to optimize lens constants to zero the mean prediction error (ME) of an intraocular lens (IOL) calculation formula, without the need to program the formula itself, by exploring the influence of IOL and corneal power on the refractive impact of variations in effective lens position. DESIGN: Theoretical development of an optimized formula and retrospective clinical evaluation on documented datasets. METHODS: Retrospective data from 8878 patients with cataracts with pre- and postoperative measurements available using 4 IOL models and 6 IOL power calculation formulas were examined. A schematic eye model was used to study the impact of small variations in effective lens position (ELP) on the postoperative spherical equivalent (SE) refraction. The impact of keratometry (K) and IOL power (P) on SE was investigated. A theoretical thick lens model was used to devise a formula to zero the average prediction error of an IOL power calculation formula. This was achieved by incrementing the predicted ELP, which could then be translated into an increment in the IOL constant. This method was tested on documented real-life postoperative datasets, using different IOL models and single-constant optimized IOL calculation formulas. RESULTS: For small variations in ELP, there was an exponential relationship between IOL power and the resultant postoperative refractive variation. The ELP adjustment necessary to zero the ME equated to a ratio between the ME and the mean of the following expression: 0.0006*(P2+2K*P) on the considered datasets. The accuracy of the values obtained using this formula was confirmed on documented postoperative datasets, and on published and nonpublished formulas. CONCLUSION: The proposed method allows surgeons without special expertise to optimize an IOL constant to nullify the ME on a documented dataset without coding the different formulas. The influence of individual eyes is proportional to the squared power of the implanted IOL.

Theoretical Relationship Between the Anterior-Posterior Corneal Curvature Ratio, Keratometric Index, and Estimated Total Corneal Power.

PURPOSE: To predict the relationships between the keratometric index value that would match the total Gaussian corneal power and its related variables: anterior and posterior radii of curvature of the cornea, anterior-posterior corneal radius ratio (APR), and central corneal thickness. METHODS: The relationship between the APR and the keratometric index was approximated by calculating the analytical expression for the theoretical value of the keratometric index, which would make the keratometric power of the cornea equal to the total paraxial Gaussian power of the cornea. RESULTS: The study of the impact of variations in the radius of anterior and posterior curvature and central corneal thickness showed that the difference between exact and approximated best-matching theoretical keratometric index was less than 0.001 for all of the performed simulations. This translated to a variation in the total corneal power estimation of less than ±0.128 diopters. After refractive surgery, the estimated optimal keratometric index value is a function of the preoperative anterior keratometry, the preoperative APR, and the delivered correction. The larger the magnitude of myopic corrections, the greater the increase in postoperative APR value. CONCLUSIONS: It is possible to estimate the most compatible value of the keratometric index that allows simulated keratometric power to equal the total Gaussian corneal power. The obtained equations enable the evaluation of the impact of corneal variables such as the APR on the ideal keratometric index value. The use of 1.3375 for the keratometric index results in an overestimation of the total corneal power in most clinical situations. [J Refract Surg. 2023;39(4):266-272.].

Descemet Membrane Endothelial Keratoplasty-Induced Refractive Shift and Descemet Membrane Endothelial Keratoplasty-Induced Intraocular Lens Calculation Error.

PURPOSE: The aim of this study was to determine the mechanisms leading to the refractive shift and intraocular lens calculation error induced by Descemet membrane endothelial keratoplasty (DMEK), using ocular biometry and corneal elevation tomography data. METHODS: This is a retrospective, monocentric cohort study. Eyes which underwent uncomplicated DMEK surgery with available pre-DMEK and post-DMEK Scheimpflug rotating camera data (Pentacam, Oculus, Wetzlar, Germany) were considered for inclusion with an age-matched control group of healthy corneas. Cataract surgery data were collected for triple-DMEK cases. DMEK-induced refractive shift (DIRS) and intraocular lens calculation error (DICE) were calculated. Pearson r correlation coefficient was calculated between each corneal parameter variation and both DIRS and DICE. RESULTS: DIRS was calculable for 49 eyes from 43 patients. It was 30.61% neutral, 53.06% hyperopic (36.73% > 1D), and 16.32% myopic (6.12% > 1 D). DICE was calculable for 30 eyes of 26 patients: It was 46.67% neutral, 40.00% hyperopic (10.00% > 1D), and 13.33% myopic (3.33% > 1D). DIRS and DICE were mainly associated with variations in PRC/ARC ratio, anterior average radii of curvature (ARC), posterior average radii of curvature (PRC), and posterior Q. CONCLUSIONS: Our results suggest that ARC variations, PRC/ARC ratio variations, PRC variations, and posterior Q variations are the most influential parameters for both DIRS and DICE. We suggest that a distinction between those different phenomenons, both currently described as "hyperopic shift" in the literature, should be made by researchers and clinicians.

Considerations of a thick lens formula for intraocular lens power calculation.

BACKGROUND: In recent years, some lens manufacturers have committed to providing lens shape data for some of their lens models. The purpose of this study is to present a strategy for prediction of intraocular lens power and residual refraction based on a pseudophakic model eye containing 5 refractive surfaces and to show its applicability using worked examples. METHODS: A pseudophakic model eye with a thin spectacle correction, a thick cornea (radius of curvatures for both surfaces and central thickness) and a thick IOL (either radius of curvatures RLa and RLp for front and back surface or equivalent power PL and Coddington factor CL; and either central thickness LT or edge thickness and optic diameter) was set up. Calculations were performed based on linear Gaussian optics (vergence formulae). Formulae were provided to derive the lens power/shape and the residual equivalent spectacle refraction SEQ. From the lens shape the location of the haptic plane HP, the image sided principal plane of the lens HL, and the ocular magnification OM were extracted. RESULTS: The calculation of a thick intraocular lens and the prediction of residual refraction is presented with reference to 3 working examples: A) lens varied in PL and shifted with its haptic plane keeping the CL constant, B) lens varied in CL and shifted with its haptic plane keeping PL constant, and C) CL and PL of the lens varied keeping its haptic plane position in the eye constant. For each combination of parameters (PL, CL, or haptic plane shift) the parameters influencing SEQ, OM and HL-HP were analysed. CONCLUSION: Some modern optical biometers currently on the market provide the radii of curvature of both corneal surface and all relevant distances in the eye. With additional data on the lens shape, it would be possible to improve lens power calculations by switching from thin to thick lens models for the cornea and for the lens. This would overcome one of the major drawbacks of current lens power calculation methods.

Theoretical Relationship Among Effective Lens Position, Predicted Refraction, and Corneal and Intraocular Lens Power in a Pseudophakic Eye Model.

Purpose: To ascertain the theoretical impact of anatomical variations in the effective lens position (ELP) of the intraocular lens (IOL) in a thick lens eye model. The impact of optimization of IOL power formulas based on a single lens constant was also simulated. Methods: A schematic eye model was designed and manipulated to reflect changes in the ELP while keeping the optical design of the IOL unchanged. Corresponding relationships among variations in ELP, postoperative spherical equivalent refraction, and required IOL power adjustment to attain target refractions were computed for differing corneal powers (38 diopters [D], 43 D, and 48 D) with IOL power ranging from 1 to 35 D. Results: The change in ELP required to compensate for various systematic biases increased dramatically with low-power IOLs (less than 10 D) and was proportional to the magnitude of the change in refraction. The theoretical impact of the variation in ELP on postoperative refraction was nonlinear and highly dependent on the optical power of the IOL. The concomitant variations in IOL power and refraction at the spectacle plane, induced by varying the ELP, were linearly related. The influence of the corneal power was minimal. Conclusions: The consequences of variations in the lens constant mainly concern eyes receiving high-power IOLs. The compensation of a systematic bias by a constant increment of the ELP may induce a nonsystematic modification of the predicted IOL power, according to the biometric characteristics of the eyes studied. Translational Relevance: Optimizing IOL power formulas by altering the ELP may induce nonsystematic modification of the predicted IOL power.

Quantitative interocular comparison of total corneal surface area and corneal diameter in patients with highly asymmetric keratoconus.

Keratoconus is a progressive corneal disorder which is frequently asymmetric. The aetiology of keratoconus remains unclear, and the concept of keratoconus as an ectatic disorder has been challenged recently. We carried out a retrospective study in 160 eyes of 80 patients, to evaluate and compare interocular differences in corneal diameter and surface area in patients with unilateral or highly asymmetric keratoconus (UHAKC). Calculations were performed using raw topographic elevation data derived from topographic measurements using Orbscan II, and we extrapolated surface areas up to measured corneal diameter. We also evaluated inter-eye correlation, and correlation between corneal surface area, corneal diameter and keratoconus severity. Our results showed a statistically significant but not clinically important greater corneal diameter (12.14 mm and 12.17 mm; p = 0.04), and corneal surface area (paired t-test, p < 0.0001; p = 0.0009 respectively) in more affected eyes. Inter-eye comparison revealed corneal diameter, anterior chamber depth, and corneal surface area were strongly correlated between eyes. Corneal surface area remained strongly correlated, and Bland-Altman analysis also showed strong inter-ocular agreement. Our results show that in patients with UHAKC the interocular difference in corneal diameter and corneal surface area is clinically insignificant, and are consistent with a redistribution, rather than increase, of corneal surface area with keratoconus progression.

Using the First-Eye Back-Calculated Effective Lens Position to Improve Refractive Outcome of the Second Eye.

The present study is a retrospective, monocentric case series that aims to compare the second-eye IOL power calculation precision using the back-calculated lens position (LP) as a lens position predictor versus using a predetermined correction factor (CF) for thin- and thick-lens IOL calculation formulas. A set of 878 eyes from 439 patients implanted with Finevision IOLs (BVI PhysIOL, Liège, Belgium) with both operated eyes was used as a training set to create Haigis-LP and PEARL-LP formulas, using the back-calculated lens position of the contralateral eye as an effective lens position (ELP) predictor. Haigis-CF, Barrett-CF, and PEARL-CF formulas using an optimized correction factor based on the prediction error of the first eye were also designed. A different set of 1500 eyes from 1500 patients operated in the same center was used to compare the basal and enhanced formula performances. The IOL power calculation for the second eye was significantly enhanced by adapting the formulas using the back-calculated ELP of the first eye or by using a correction factor based on the prediction error of the first eye, the latter giving slightly higher precision. A decrease in the mean absolute error of 0.043D was observed between the basal PEARL and the PEARL-CF formula (p < 0.001). The optimal correction factor was close to 60% of the first-eye prediction error for every formula. A fixed correction factor of 60% of the postoperative refractive error of the first operated eye improves the second-eye refractive outcome better than the methods based on the first eye's effective lens position back-calculation. A significant interocular biometric dissimilarity precludes the enhancement of the second-eye IOL power calculation according to the first-eye results.

The PEARL-DGS Formula: The Development of an Open-source Machine Learning-based Thick IOL Calculation Formula.

PURPOSE: To describe an open-source, reproducible, step-by-step method to design sum-of-segments thick intraocular lens (IOL) calculation formulas, and to evaluate a formula built using this methodology. DESIGN: Retrospective, multicenter case series METHODS: A set of 4242 eyes implanted with Finevision IOLs (PhysIOL, Liège, Belgium) was used to devise the formula design process and build the formula. A different set of 677 eyes from the same center was kept separate to serve as a test set. The resulting formula was evaluated on the test set as well as another independent data set of 262 eyes. RESULTS: The lowest standard deviation (SD) of prediction errors on Set 1 were obtained with the PEARL-DGS formula (±0.382 D), followed by K6 and Olsen (±0.394 D), EVO 2.0 (±0.398 D), RBF 3.0, and BUII (±0.402 D). The formula yielding the lowest SD on Set 2 was the PEARL-DGS (±0.269 D), followed by Olsen (±0.272 D), K6 (±0.276 D), EVO 2.0 (±0.277 D), and BUII (±0.301 D). CONCLUSION: Our methodology achieved an accuracy comparable to other state-of-the-art IOL formulas. The open-source tools provided in this article could allow other researchers to reproduce our results using their own data sets, with other IOL models, population settings, biometric devices, and measured, rather than calculated, posterior corneal radius of curvature or sum-of-segments axial lengths.

Determining the Theoretical Effective Lens Position of Thick Intraocular Lenses for Machine Learning-Based IOL Power Calculation and Simulation.

Purpose: To describe a formula to back-calculate the theoretical position of the principal object plane of an intraocular lens (IOL), as well as the theoretical anatomic position in a thick lens eye model. A study was conducted to ascertain the impact of variations in design and IOL power, on the refractive outcomes of cataract surgery. Methods: A schematic eye model was designed and manipulated to reflect changes in the anterior and posterior radii of an IOL, while keeping the central thickness and paraxial powers static. Modifications of the shape factor (X) of the IOL affects the thick lens estimated effective lens position (ELP). Corresponding postoperative spherical equivalent (SE) were computed for different IOL powers (-5 diopters [D], 5 D, 15 D, 25 D, and 35 D) with X ranging from -1 to +1 by 0.1. Results: The impact of the thick lens estimated effective lens position shift on postoperative refraction was highly dependent on the optical power of the IOL and its thickness. Design modifications could theoretically induce postoperative refraction variations between approximately 0.50 and 3.0 D, for implant powers ranging from 15 D to 35 D. Conclusions: This work could be of interest for researchers involved in the design of IOL power calculation formulas. The importance of IOL geometry in refractive outcomes, especially for short eyes, should challenge the fact that these data are not usually published by IOL manufacturers. Translational Relevance: The back-calculation of the estimated effective lens position is central to intraocular lens calculation formulas, especially for artificial intelligence-based optical formulas, where the algorithm can be trained to predict this value.

Quantitative comparison of corneal surface areas in keratoconus and normal eyes.

Keratoconus is a highly prevalent corneal disorder characterized by progressive corneal thinning, steepening and irregular astigmatism. To date, pathophysiology of keratoconus development and progression remains debated. In this study, we retrospectively analysed topographic elevation maps from 3227 eyes of 3227 patients (969 keratoconus and 2258 normal eyes) to calculate anterior and posterior corneal surface area. We compared results from normal eyes and keratoconus eyes using the Mann-Whitney U test. The Kruskal-Wallis test was used to compare keratoconus stages according to the Amsler-Krumeich classification. Keratoconus eyes were shown to have statistically significantly larger corneal surface areas, measured at the central 4.0 mm and 8.0 mm, and total corneal diameter. However, no significant increase in corneal surface area was seen with increasing severity of keratoconus. We suggest that these results indicate redistribution, rather than increase, of the corneal surface area with keratoconus severity.