Refractive Astigmatism Outcomes of Femtosecond Laser-Assisted Arcuate Keratotomies Combined with Femtosecond Laser-Assisted Cataract Surgery: Two-Year Results.

PURPOSE: To evaluate the effectiveness and stability of refractive astigmatism reduction after penetrating femtosecond laser-assisted arcuate keratotomy performed at the time of femtosecond laser-assisted cataract surgery. METHODS: Non-randomized retrospective data analysis of all patients that underwent femtosecond laser-assisted cataract surgery with femtosecond laser-assisted arcuate keratotomy over a 4-year period with a non-toric monofocal intraocular lens (2017-2021) at a tertiary care academic center. Postoperative visual acuity, manifest refraction, and predicted residual refractive error were also recorded at 1 month, 3-6 months, 12-18 months, and 2 years postoperatively. Preoperative keratometric astigmatism was compared to postoperative refractive astigmatism using vector calculations and the ASCRS double-angle plot tool. RESULTS: This study comprised 266 eyes (179 patients) that met inclusion criteria. The mean preoperative keratometric astigmatism magnitude was 0.99 ± 0.53 D. At 1 month, 3-6 months, 12-18 months, and 2 years postoperatively, the mean refractive cylinder was 0.49 ± 0.45 D, 0.49 ± 0.45 D, 0.55 ± 0.54 D, and 0.52 ± 0.46 D, respectively. Horizontal against-the-rule astigmatism showed a higher tendency toward undercorrection than vertical with-the-rule astigmatism, which had a slightly higher tendency toward overcorrection. With-the-rule astigmatism had smaller difference vectors between target-induced astigmatism and surgically induced astigmatism. CONCLUSIONS: Femtosecond laser-assisted arcuate keratotomy performed at the time of femtosecond laser-assisted cataract surgery was an effective option for correcting low-to-moderate corneal astigmatism for up to 2 years.

Evaluating keratometry and corneal astigmatism data from biometers and anterior segment tomographers and mapping to reconstructed corneal astigmatism.

BACKGROUND: To compare results from different corneal astigmatism measurement instruments; to reconstruct corneal astigmatism from the postimplantation spectacle refraction and toric intraocular lens (IOL) power; and to derive models for mapping measured corneal astigmatism to reconstructed corneal astigmatism. METHODS: Retrospective single centre study involving 150 eyes treated with a toric IOL (Alcon SN6AT, DFT or TFNT). Measurements included IOLMaster 700 keratometry (IOLMK) and total keratometry (IOLMTK), Pentacam keratometry (PK) and total corneal refractive power in 3 and 4 mm zones (PTCRP3 and PTCRP4), and Aladdin keratometry (AK). Regression-based models mapping the measured C0 and C45 components (Alpin's method) to reconstructed corneal astigmatism were derived. RESULTS: Mean C0 components were 0.50/0.59/0.51 dioptres (D) for IOLMK/PK/AK; 0.2/0.26/0.31 D for IOLMTK/PTCRP3/PTCRP4; and 0.26 D for reconstructed corneal astigmatism. All corresponding C45 components ranged around 0. The prediction models had main diagonal elements lower than 1 with some crosstalk between C0 and C45 (nonzero off-diagonal elements). Root-mean-squared residuals were 0.44/0.45/0.48/0.51/0.50/0.47 D for IOLMK/IOLMTK/PK/PTCRP3/PTCRP4/AK. CONCLUSIONS: Results from the different modalities are not consistent. On average IOLMTK/PTCRP3/PTCRP4 match reconstructed corneal astigmatism, whereas IOLMK/PK/AK show systematic C0 offsets of around 0.25 D. IOLMTK/PTCRP3/PTCRP4. Prediction models can reduce but not fully eliminate residual astigmatism after toric IOL implantation.

Vector analysis of corneal astigmatism in cataractous eyes based on IOLMaster 700 biometry.

PURPOSE: The purpose of this study was to investigate the effect of the corneal back surface by comparing the keratometric astigmatism (K, derived from the corneal front surface) of a modern optical biometer against astigmatism of Total Keratometry (TK, derived from both corneal surfaces) in a large population with cataractous eyes. The results were then used to define linear prediction models to map K to TK. METHODS: From a large dataset containing bilateral biometric measurements (IOLMaster 700) in 9736 patients prior to cataract surgery, the total corneal astigmatism was decomposed into vectors for K, corneal back surface (BS), and TK. A multivariate prediction model (MV), simplified model with separation of vector components (SM) and a constant model (CM) were defined to map K to TK vector components. RESULTS: The K centroid (X/Y) showed some astigmatism with-the-rule (0.1981/-0.0211 dioptre (dpt)) whereas the TK centroid was located around zero (-0.0071/-0.0381 dpt against-the-rule) and the BS centroid showed systematic astigmatism against-the-rule (-0.2367/-0.0145 dpt). The respective TK-K centroid was located at -0.2052/-0.0302 dpt. The MV model showed the same performance (i.e. mean absolute residuum) as the SM did (0.1098 and 0.1099 dpt respectively) while the CM performed only slightly worse (0.1121 dpt mean absolute residuum). CONCLUSION: In cases where tomographic data are unavailable statistical models could be used to consider the overall contribution of the back surface to the total corneal astigmatism. Since the performance of the CM is sufficiently close to that of MV and SM we recommend using the CM which can be directly considered e.g. as surgically induced astigmatism.

Performance of a simplified strategy for formula constant optimisation in intraocular lens power calculation.

PURPOSE: To investigate the performance of a simple prediction scheme for the formula constants optimised for a mean refractive prediction error. METHODS: Analysis based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). IOLMaster 700 biometric data, power of the implanted lens and postoperative spherical equivalent refraction were used to calculate the optimised constants (.)opt for SRKT, HofferQ, Holladay and Haigis formula with an iterative nonlinear optimisation. For detuning start values by ±1.5 from (.)opt, the predicted formula constants (.)pred were calculated and compared with (.)opt. Formula performance metrics mean (MPE), median (MEDPE), mean absolute (MAPE), median absolute (MEDAPE), root mean squared (RMSPE) and standard deviation (SDPE) of the formula prediction error were analysed for (.)opt and (.)pred. RESULTS: (.)pred - (.)opt showed a 2nd order parabolic behaviour with maximal deviations up to 0.09 at the tails of detuning and a minimal deviation up to -0.01 for all formulae. The performance curves of different metrics of PE as functions of detuning variations show that the formula constants for zeroing MPE and MEDPE yield almost identical formula constants, optimisation for MAPE, MEDAPE and RMSPE yielded formula constants very close to (.)opt, and optimisation for SDPE could result in formula constants up to 0.5 off (.)opt which is unacceptable for clinical use. CONCLUSION: This simple prediction scheme for formula constant optimisation for zero mean refraction error performs excellently in our monocentric dataset, even for larger deviations of the start value from (.)opt. Further studies with multicentric data and larger sample sizes are required to investigate the performance in a clinical setting further.

Surrogate optimisation strategies for intraocular lens formula constant optimisation.

PURPOSE: To investigate surrogate optimisation (SO) as a modern, purely data-driven, nonlinear adaptive iterative strategy for lens formula constant optimisation in intraocular lens power calculation. METHODS: A SO algorithm was implemented for optimising the root mean squared formula prediction error (rmsPE, defined as predicted refraction minus achieved refraction) for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formulae in a dataset of N = 888 cataractous eyes with implantation of the Hoya Vivinex hydrophobic acrylic aspheric lens. A Gaussian Process estimator was used as the model, and the SO was initialised with equidistant datapoints within box constraints, and the number of iterations restricted to either 200 (SRKT, Hoffer Q, Holladay) or 700 (Haigis, Castrop). The performance of the algorithm was compared to the classical gradient-based Levenberg-Marquardt algorithm. RESULTS: The SO algorithm showed stable convergence after fewer than 50/150 iterations (SRKT, HofferQ, Holladay, Haigis, Castrop). The rmsPE was reduced systematically to 0.4407/0.4288/0.4265/0.3711/0.3449 dioptres. The final constants were A = 119.2709, pACD = 5.7359, SF = 1.9688, -a0 = 0.5914/a1 = 0.3570/a2 = 0.1970, C = 0.3171/H = 0.2053/R = 0.0947 for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formula and matched the respective constants optimised in previous studies. CONCLUSION: The SO proves to be a powerful adaptive nonlinear iteration algorithm for formula constant optimisation, even in formulae with one or more constants. It acts independently of a gradient and is in general able to search within a (box) constrained parameter space for the best solution, even where there are multiple local minima of the target function.

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).

Repeatability of biometric measures from the IOLMaster 700 in a cataractous population.

PURPOSE: The purpose of this study was to investigate the repeatability of biometric measures and also to assess the interactions between the uncertainties in these measures for use in an error propagation model, using data from a large patient cohort. METHODS: In this cross-sectional non-randomised study we evaluated a dataset containing 3379 IOLMaster 700 biometric measurements taken prior to cataract surgery. Only complete scans with at least 3 successful measurements for each eye performed on the same day were considered. The mean (Mean) and standard deviations (SD) for each sequence of measurements were derived and analysed. Correlations between the uncertainties were assessed using Spearman rank correlations. RESULTS: In the dataset with 677 eyes matching the inclusion criteria, the within subject standard deviation and repeatability for all parameters match previously published data. The SD of the axial length (AL) increased with the Mean AL, but there was no noticeable dependency of the SD of any of the other parameters on their corresponding Mean value. The SDs of the parameters are not independent of one another, and in particular we observe correlations between those for AL, anterior chamber depth, aqueous depth, lens thickness and corneal thickness. CONCLUSIONS: The SD change over Mean for AL measurement and the correlations between the uncertainties of several biometric parameters mean that a simple Gaussian error propagation model cannot be used to derive the effect of biometric uncertainties on the predicted intraocular lens power and refraction after cataract surgery.

The Influence of Lens Position, Vault Prediction, and Posterior Cornea on Phakic Posterior Chamber Intraocular Lens Power.

BACKGROUND: Achieving precise refractive outcomes in phakic posterior chamber intraocular lens (pIOL) implantation is crucial for patient satisfaction. This study investigates factors affecting pIOL power calculations, focusing on myopic eyes, and evaluates the potential benefits of advanced predictive models. DESIGN: Retrospective, single-center, algorithm improvement study. METHODS: Various variations with different effective lens position (ELP) algorithms were analyzed. The algorithms included a fixed constant model, and a multiple linear regression model and were tested with and without incorporation of the posterior corneal curvature (Rcp). Furthermore, the impact of inserting the postoperative vault, the space between the pIOL and the crystalline lens, into the ELP algorithm was examined, and a simple vault prediction model was assessed. RESULTS: Integrating Rcp and the measured vault into pIOL calculations did not significantly improve accuracy. Transitioning from constant model approaches to ELP concepts based on linear regression models significantly improved pIOL power calculations. Linear regression models outperformed constant models, enhancing refractive outcomes for both ICL and IPCL pIOL platforms. CONCLUSIONS: This study underscores the utility of implementing ELP concepts based on linear regression models into pIOL power calculation. Linear regression based ELP models offered substantial advantages for achieving desired refractive outcomes, especially in lower to medium power pIOL models. For pIOL power calculations in both pIOL platforms we tested with preoperative measurements from a Scheimpflug device, we found improved results with the LION 1ICL formula and LION 1IPCL formula. Further research is needed to explore the applicability of these findings to a broader range of pIOL designs and measurement devices.

Comparison of Pre- and Post-DMEK Keratometry and Total Keratometry Values for IOL Power Calculations in Eyes Undergoing Triple DMEK.

PURPOSE: To evaluate prediction accuracy of pre- and post-DMEK keratometry (K) and total keratometry (TK) values for IOL power calculations in Fuchs endothelial corneal dystrophy (FECD) eyes undergoing DMEK with cataract surgery (triple DMEK). METHODS: Retrospective cross-sectional multicenter study of 55 FECD eyes (44 patients) that underwent triple DMEK between 2019 and 2022 between two centers in USA and Europe. Swept-source optical coherence tomography biometry (IOLMaster 700) was used for pre- and post-DMEK measurements. K and TK values were used for power calculations with ten formulae (Barrett Universal II (BUII), Castrop, Cooke K6, EVO 2.0, Haigis, Hoffer Q, Hoffer QST, Holladay I, Kane, and SRK/T). Mean error, mean absolute error (MAE), standard deviation, and percentage of eyes within ±0.50/±1.00 diopters (D) were calculated. Studied formulae were additionally adjusted using a method published previously (IOLup1D Method), which increases the IOL power by 1D. While both eyes from the same patient were considered for descriptive statistics, we restricted to one eye per individual (44 eyes for statistical comparisons. RESULTS: MAEs for all formulae were lower for post-DMEK K and TK than pre-DMEK K and TK by an average of 0.24 and 0.47 D, respectively. The lowest MAE was 0.49 D for Kane using post-DMEK TK, and the highest MAE was 1.05 D for BUII using pre-DMEK TK. Most IOLup1D formulae had lower MAEs than pre-DMEK K and TK formulae. CONCLUSIONS: The IOLup1D Method should be used instead of pre-DMEK K and TK values for triple DMEK in FECD eyes. Using post-DMEK TK values for cataract surgery after DMEK provides better refractive accuracy than any of the three studied methods used for triple DMEK procedures.

Technical variability of cornea parameters derived from anterior segment OCT fitted with Fringe Zernike polynomials.

BACKGROUND: This study uses bootstrapping to evaluate the technical variability (in terms of model parameter variation) of Zernike corneal surface fit parameters based on Casia2 biometric data. METHODS: Using a dataset containing N = 6953 Casia2 biometric measurements from a cataractous population, a Fringe Zernike polynomial surface of radial degree 10 (36 components) was fitted to the height data. The fit error (height - reconstruction) was bootstrapped 100 times after normalisation. After reversal of normalisation, the bootstrapped fit errors were added to the reconstructed height, and characteristic surface parameters (flat/steep axis, radii, and asphericities in both axes) extracted. The median parameters refer to a robust surface representation for later estimates of elevation, whereas the SD of the 100 bootstraps refers to the variability of the surface fit. RESULTS: Bootstrapping gave median radius and asphericity values of 7.74/7.68 mm and -0.20/-0.24 for the corneal front surface in the flat/steep meridian and 6.52/6.37 mm and -0.22/-0.31 for the corneal back surface. The respective SD values for the 100 bootstraps were 0.0032/0.0028 mm and 0.0093/0.0082 for the front and 0.0126/0.0115 mm and 0.0366/0.0312 for the back surface. The uncertainties for the back surface are systematically larger as compared to the uncertainties of the front surface. CONCLUSION: As measured with the Casia2 tomographer, the fit parameters for the corneal back surface exhibit a larger degree of variability compared with those for the front surface. Further studies are needed to show whether these uncertainties are representative for the situation where actual repeat measurements are possible.

Prediction of IOL decentration, tilt and axial position using anterior segment OCT data.

BACKGROUND: Intraocular lenses (IOLs) require proper positioning in the eye to provide good imaging performance. This is especially important for premium IOLs. The purpose of this study was to develop prediction models for estimating IOL decentration, tilt and the axial IOL equator position (IOLEQ) based on preoperative biometric and tomographic measures. METHODS: Based on a dataset (N = 250) containing preoperative IOLMaster 700 and pre-/postoperative Casia2 measurements from a cataractous population, we implemented shallow feedforward neural networks and multilinear regression models to predict the IOL decentration, tilt and IOLEQ from the preoperative biometric and tomography measures. After identifying the relevant predictors using a stepwise linear regression approach and training of the models (150 training and 50 validation data points), the performance was evaluated using an N = 50 subset of test data. RESULTS: In general, all models performed well. Prediction of IOL decentration shows the lowest performance, whereas prediction of IOL tilt and especially IOLEQ showed superior performance. According to the 95% confidence intervals, decentration/tilt/IOLEQ could be predicted within 0.3 mm/1.5°/0.3 mm. The neural network performed slightly better compared to the regression, but without significance for decentration and tilt. CONCLUSION: Neural network or linear regression-based prediction models for IOL decentration, tilt and axial lens position could be used for modern IOL power calculation schemes dealing with 'real' IOL positions and for indications for premium lenses, for which misplacement is known to induce photic effects and image distortion.

Impact of uncertainties in biometric parameters on intraocular lens power formula predicted refraction using a Monte-Carlo simulation.

PURPOSE: The purpose of this study was to investigate the uncertainty in the formula predicted refractive outcome REFU after cataract surgery resulting from measurement uncertainties in modern optical biometers using literature data for within-subject standard deviation Sw. METHODS: This Monte-Carlo simulation study used a large dataset containing 16 667 preoperative IOLMaster 700 biometric measurements. Based on literature Sw values, REFU was derived for both the Haigis and Castrop formulae using error propagation strategies. Using the Hoya Vivinex lens (IOL) as an example, REFU was calculated both with (WLT) and without (WoLT) consideration of IOL power labelling tolerances. RESULTS: WoLT the median REFU was 0.10/0.12 dpt for the Haigis/Castrop formula, and WLT it was 0.13/0.15 dpt. WoLT REFU increased systematically for short eyes (or high power IOLs), and WLT this effect was even more pronounced because of increased labelling tolerances. WoLT the uncertainty in the measurement of the corneal front surface radius showed the largest contribution to REFU, especially in long eyes (and low power IOLs). WLT the IOL power uncertainty dominated in short eyes (or high power IOLs) and the uncertainty of the corneal front surface in long eyes (or low power IOLs). CONCLUSIONS: Compared with published data on the formula prediction error of refractive outcome after cataract surgery, the uncertainty of biometric measures seems to contribute with ⅓ to ½ to the entire standard deviation. REFU systematically increases with IOL power and decreases with axial length.

Evaluation of statistical correction strategies for corneal back surface astigmatism with toric lenses: a vector analysis.

PURPOSE: To compare actual and formula-predicted postoperative refractive astigmatism using measured posterior corneal power measurements and 4 different empiric posterior corneal astigmatism correction models. SETTING: Tertiary care center. DESIGN: Single-center retrospective consecutive case series. METHODS: Using a dataset of 211 eyes before and after tIOL implantation (Hoya Vivinex), IOLMaster 700 (IOLM) or Casia2 (CASIA) keratometric and front/back surface corneal power measurements were converted to power vector components C0 (0/90 degrees) and C45 (45/135 degrees). Differences between postoperative and Castrop formula predicted refraction at the corneal plane using the labeled parameters of the tIOL and the keratometric or front/back surface corneal powers were recorded as the effect of corneal back surface astigmatism (BSA). RESULTS: Generally, the centroid of the difference shifted toward negative C0 values indicating that BSA adds some against the rule corneal astigmatism (ATR). From IOLM/CASIA keratometry, the average difference in C0 was 0.39/0.32 diopter (D). After correction with the Abulafia-Koch, Goggin, La Hood, and Castrop nomograms, it was -0.18/-0.24 D, 0.27/0.18 D, 0.13/0.08 D, and 0.17/0.10 D. Using corneal front/back surface data from IOLM/CASIA, the difference was 0.18/0.12 D. CONCLUSIONS: The Abulafia-Koch method overcorrected the ATR, while the Goggin, La Hood, and Castrop models slightly undercorrected ATR, and using measurements from the CASIA tomographer seemed to produce slightly less prediction error than IOLM.

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.

Unilateral intraindividual comparison and bilateral performance of a monofocal spherical and diffractive extended depth of field intraocular lens mix-and-match approach.

BACKGROUND: To evaluate the intraindividual visual performance of a spherical and extended depth of field (EDOF) IOL used in a mix-and-match approach. METHODS: Single centre (tertiary care centre), retrospective consecutive case series. Included patients had uneventful cataract surgery with implantation of a spherical monofocal IOL (CT Spheris 204) in the dominant eye and a diffractive EDOF IOL (AT LARA 829) in the non-dominant eye. Monocular and binocular defocus curves and visual acuity at various distances were assessed. In addition, binocular reading speed, contrast sensitivity, and patient satisfaction using QOV, Catquest 9SF, and glare/halo questionnaires are reported. RESULTS: A total of 29 patients (58 eyes) were included. We observed significant intra-individual differences for monocular DCIVA, DCNVA, UIVA, and UNVA. There were no differences in monocular BCDVA or UDVA. The monocular defocus curves for the two IOLs significantly differed at defocus steps between -1.0 and -3.5 D. 93.10% of patients reported they would opt for the same combination of IOLs. CONCLUSION: Excellent uncorrected and corrected distance visual acuity was demonstrated in both groups. The mix-and-match approach described in this study yielded good intermediate vision and improved near vision with high-patient satisfaction.

Evaluation of corneal power from an AS-OCT thick lens model and ray tracing: reliability of the keratometer index.

PURPOSE: To investigate and compare different strategies of corneal power calculations using keratometry, paraxial thick lens calculations and ray tracing. SETTING: Tertiary care center. DESIGN: Retrospective single-center consecutive case series. METHODS: Using a dataset with 9780 eyes of 9780 patients from a cataractous population the corneal front (Ra/Qa) and back (Rp/Qp) surface radius/asphericity, central corneal thickness (CCT), and entrance pupil size (PUP) were recorded using the Casia 2 tomographer. Beside keratometry with the Zeiss (PK Z ) and Javal (PK J ) keratometer index, a thick lens paraxial formula (PG) and ray tracing (PR) was implemented to extract corneal power for pupil sizes from 2 mm to 5 mm in steps of 1 mm and PUP. RESULTS: With PUP PK Z /PK J overestimates the paraxial corneal power PG in around 97%/99% of cases and PR in around 80% to 85%/99%. PR is around 1/6 or 5/6 diopters (D) lower compared with PK Z or PK J . For a 2 mm pupil PR is around 0.20/0.91 D lower compared with PK Z /PK J and for a 5 mm pupil PR is comparable with PK Z (around 0.03 D lower) but around 0.70 to 0.75 D lower than PK J . CONCLUSIONS: "True" values of corneal power are mostly required in lens power calculations before cataract surgery, and overestimation of corneal power could induce trend errors in refractive outcome with axial length and lens power if compensated with the effective lens position.

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.

Limitations of constant optimization with disclosed intraocular lens power formulae.

PURPOSE: To investigate the effect of formula constants on predicted refraction and limitations of constant optimization for classical and modern intraocular lens (IOL) power calculation formulae. SETTING: Tertiary care center. DESIGN: Retrospective single-center consecutive case series. METHODS: This analysis is based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). Spherical equivalent refraction predSEQ was predicted using IOLMaster 700 data, IOL power, and formula constants from IOLCon ( https://iolcon.org ). The formula prediction error (PE) was derived as predSEQ minus achieved spherical equivalent refraction for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulae. The gradient of predSEQ (gradSEQ) as a measure for the effect of the constants on refraction was calculated and used for constant optimization. RESULTS: Using initial formula constants, the mean PE was -0.1782 ± 0.4450, -0.1814 ± 0.4159, -0.1702 ± 0.4207, -0.1211 ± 0.3740, and -0.1912 ± 0.3449 diopters (D) for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulas, respectively. gradSEQ for all formula constants (except gradSEQ for the Castrop R) decay with axial length because of interaction with the effective lens position (ELP). Constant optimization for a zero mean PE (SD: 0.4410, 0.4307, 0.4272, 0.3742, 0.3436 D) results in a change in the PE trend over axial length in all formulae where the constant acts directly on the ELP. CONCLUSIONS: With IOL power calculation formulae where the constant(s) act directly on the ELP, a change in constant(s) always changes the trend of the PE according to gradSEQ. Formulae where at least 1 constant does not act on the ELP have more flexibility to zero the mean or median PE without coupling with a PE trend error over axial length.

Monte-Carlo simulation for calculating phakic supplementary lenses based on a thick and thin lens model using anterior segment OCT data.

BACKGROUND: Phakic lenses (PIOLs, the most common and only disclosed type being the implantable collamer lens, ICL) are used in patients with large or excessive ametropia in cases where laser refractive surgery is contraindicated. The purpose of this study was to present a strategy based on anterior segment OCT data for calculating the refraction correction (REF) and the change in lateral magnification (ΔM) with ICL implantation. METHODS: Based on a dataset (N = 3659) containing Casia 2 measurements, we developed a vergence-based calculation scheme to derive the REF and gain or loss in ΔM on implantation of a PIOL having power PIOLP. The calculation concept is based on either a thick or thin lens model for the cornea and the PIOL. In a Monte-Carlo simulation considering, all PIOL steps listed in the US patent 5,913,898, nonlinear regression models for REF and ΔM were defined for each PIOL datapoint. RESULTS: The calculation shows that simplifying the PIOL to a thin lens could cause some inaccuracies in REF (up to ½ dpt) and ΔM for PIOLs with high positive power. The full range of listed ICL powers (- 17 to 17 dpt) could correct REF in a range from - 17 to 12 dpt with a change in ΔM from 17 to - 25%. The linear regression considering anterior segment biometric data and the PIOLP was not capable of properly characterizing REF and ΔM, whereas the nonlinear model with a quadratic term for the PIOLP showed a good performance for both REF and ΔM prediction. CONCLUSION: Where PIOL design data are available, the calculation concept should consider the PIOL as thick lens model. For daily use, a nonlinear regression model can properly predict REF and ΔM for the entire range of PIOL steps if a vergence calculation is unavailable.

Prediction of corneal power vectors after cataract surgery with toric lens implantation-A vector analysis.

BACKGROUND: Intraocular lenses are typically calculated based on a pseudophakic eye model, and for toric lenses (tIOL) a good estimate of corneal astigmatism after cataract surgery is required in addition to the equivalent corneal power. The purpose of this study was to investigate the differences between the preoperative IOLMaster (IOLM) and the preoperative and postoperative Casia2 (CASIA) tomographic measurements of corneal power in a cataractous population with tIOL implantation, and to predict total power (TP) from the IOLM and CASIA keratometric measurements. METHODS: The analysis was based on a dataset of 88 eyes of 88 patients from 1 clinical centre before and after tIOL implantation. All IOLM and CASIA keratometric and total corneal power measurements were converted to power vector components, and the differences between preoperative IOLM or CASIA and postoperative CASIA measurements were assessed. Feedforward neural network and multivariate linear regression prediction algorithms were implemented to predict the postoperative total corneal power (as a reference for tIOL calculation) from the preoperative IOLM and CASIA keratometric measurements. RESULTS: On average, the preoperative IOLM keratometric / total corneal power under- / overestimates the postoperative CASIA keratometric / real corneal power by 0.12 dpt / 0.21 dpt. The prediction of postoperative CASIA real power from preoperative IOLM or CASIA keratometry shows that postoperative total corneal power is systematically (0.18 dpt / 0.27 dpt) shifted towards astigmatism against the rule, which is not reflected by keratometry. The correlation of postoperative CASIA real power to the corresponding preoperative CASIA values is better than those as compared to the preoperative IOLM keratometry. However, there is a large variation from preoperative IOLM or CASIA keratometry to the postoperative CASIA real power of up to 1.1 dpt (95% confidence interval). CONCLUSION: One of the challenges of tIOL calculation is the prediction of postoperative total corneal power from preoperative keratometry. Keratometric power restricted to a front surface measurement does not fully reflect the situation of corneal back surface astigmatism, which typically adds some extra against the rule astigmatism.