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.

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.

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.

Comparison of 2 modern swept-source optical biometers-IOLMaster 700 and Anterion.

PURPOSE: To compare biometric measures from 2 modern swept-source OCT biometers (IOLMaster700 (Z, Carl-Zeiss-Meditec) and Anterion (H, Heidelberg Engineering)) and evaluate the effect of measurement differences on the resulting lens power (IOLP). METHODS: Biometric measurements were made on a large study population with both instruments. We compared axial length (AL), central corneal thickness (CCT), anterior chamber depth (ACD), lens thickness (LT) and corneal front and back surface curvature measurements. Corneal curvature was converted to power vectors and total power derived using the Gullstrand formula. A paraxial lens power calculation formula and a prediction for the IOL axial position according to the Castrop formula were used to estimate differences in IOLP targeting for emmetropia. RESULTS: There were no systematic differences between measurements of AL (- 0.0146 ± 0.0286 mm) and LT (0.0383 ± 0.0595 mm), whereas CCT yielded lower (7.8 ± 6.6 µm) and ACD higher (0.1200 ± 0.0531 mm) values with H. With H, CCT was lower for thicker corneas. The mean corneal front surface radius did not differ (- 0.4 ± 41.6 µm), but the corneal back surface yielded a steeper radius (- 397.0 ± 74.6 µm) with H, giving lower mean total power (- 0.3469 ± 0.2689 dpt). The astigmatic vector components in 0°/90° and 45°/135° were the same between both instruments for the front/back surface or total power. CONCLUSION: The biometric measures used in standard formulae (AL, corneal front surface curvature/power) are consistent between instruments. However, modern formulae involving ACD, CCT or corneal back surface curvature may yield differences in IOLP, and therefore, formula constant optimisation customised to the biometer type is required.

EDOF intraocular lens design: shift in image plane vs object vergence.

BACKGROUND: To compare 2 different design scenarios of EDOF-IOLs inserted in the Liou-Brennan schematic model eye using raytracing simulation as a function of pupil size. METHODS: Two EDOF IOL designs were created and optimized for the Liou-Brennan schematic model eye using Zemax ray tracing software. Each lens was optimized to achieve a maximum Strehl ratio for intermediate and far vision. In the first scenario, the object was located at infinity (O1), and the image plane was positioned at far focus (I1) and intermediate focus (I2) to emulate far and intermediate distance vision, respectively. In the second scenario, the image plane was fixed at I1 according to the first scenario. The object plane was set to infinity (O1) for far-distance vision and then shifted closer to the eye (O2) to reproduce the corresponding intermediate vision. The performance of both IOLs was simulated for the following 3 test conditions as a function of pupil size: a) O1 to I1, b) O1 to I2, and c) O2 to I1. To evaluate the imaging performance, we used the Strehl ratio, the root-mean-square (rms) of the spot radius, and the spherical aberration of the wavefront for various pupil sizes. RESULTS: Evaluating the imaging performance of the IOLs shows that the imaging performance of the IOLs is essentially identical for object/image at O1/I1. Designed IOLs perform dissimilarly to each other in near-vision scenarios, and the simulations confirm that there is a slight difference in their optical performance. CONCLUSION: Our simulation study recommends considering the difference between object shift and image plane shift in design and test conditions to achieve more accurate pseudoaccommodation after cataract surgery.

Decreased FABP5 and DSG1 protein expression following PAX6 knockdown of differentiated human limbal epithelial cells.

PAX6 haploinsufficiency related aniridia is characterized by disorder of limbal epithelial cells (LECs) and aniridia related keratopathy. In the limbal epithelial cells of aniridia patients, deregulated retinoic acid (RA) signaling components were identified. We aimed to visualize differentiation marker and RA signaling component expression in LECs, combining a differentiation triggering growth condition with a small interfering RNA (siRNA) based aniridia cell model (PAX6 knock down). Primary LECs were isolated from corneoscleral rims of healthy donors and cultured in serum free low Ca2+ medium (KSFM) and in KSFM supplemented with 0.9 mmol/L Ca2+. In addition, LECs were treated with siRNA against PAX6. DSG1, PAX6, KRT12, KRT 3, ADH7, RDH10, ALDH1A1, ALDH3A1, STRA6, CYP1B1, RBP1, CRABP2, FABP5, PPARG, VEGFA and ELOVL7 expression was determined using qPCR and western blot. DSG1, FABP5, ADH7, ALDH1A1, RBP1, CRABP2 and PAX6 mRNA and FABP5 protein expression increased (p ≤ 0.03), PPARG, CYP1B1 mRNA expression decreased (p ≤ 0.0003) and DSG1 protein expression was only visible after Ca2+ supplementation. After PAX6 knock down and Ca2+ supplementation, ADH7 and ALDH1A1 mRNA and DSG1 and FABP5 protein expression decreased (p ≤ 0.04), compared to Ca2+ supplementation alone. Using our cell model, with Ca2+ supplementation and PAX6 knockdown with siRNA treatment against PAX6, we provide evidence that haploinsufficiency of the master regulatory gene PAX6 contributes to differentiation defect in the corneal epithelium through alterations of RA signalling. Upon PAX6 knockdown, DSG1 differentiation marker and FABP5 RA signaling component mRNA expression decreases. A similar effect becomes apparent at protein level though differentiation triggering Ca2+ supplementation in the siRNA-based aniridia cell model. Expression data from this cell model and from our siRNA aniridia cell model strongly indicate that FABP5 expression is PAX6 dependent. These new findings may lead to a better understanding of differentiation processes in LECs and are able to explain the insufficient cell function in AAK.

Meridional ocular magnification after cataract surgery with toric and non-toric intraocular lenses.

BACKGROUND: Overall ocular magnification (OOM) and meridional ocular magnification (MOM) with consequent image distortions have been widely ignored in modern cataract surgery. The purpose of this study was to investigate OOM and MOM in a general situation with an astigmatic refracting surface. METHODS: From a large dataset containing biometric measurements (IOLMaster 700) of both eyes of 9734 patients prior to cataract surgery, the equivalent (PIOLeq) and cylindric power (PIOLcyl) were derived for the HofferQ, Haigis, and Castrop formulae for emmetropia. Based on the pseudophakic eye model, OOM and MOM were extracted using 4 × 4 matrix algebra for the corrected eye (with PIOLeq/PIOLcyl (scenario 1) or with PIOLeq and spectacle correction of the residual refractive cylinder (scenario 2) or with PIOLeq remaining the residual uncorrected refractive cylinder (blurry image) (scenario 3)). In each case, the relative image distortion of MOM/OOM was calculated in %. RESULTS: On average, PIOLeq/PIOLcyl was 20.73 ± 4.50 dpt/1.39 ± 1.09 dpt for HofferQ, 20.75 ± 4.23 dpt/1.29 ± 1.01 dpt for Haigis, and 20.63 ± 4.31 dpt/1.26 ± 0.98 dpt for Castrop formulae. Cylindric refraction for scenario 2 was 0.91 ± 0.70 dpt, 0.89 ± 0.69 dpt, and 0.89 ± 0.69 dpt, respectively. OOM/MOM (× 1000) was 16.56 ± 1.20/0.08 ± 0.07, 16.56 ± 1.20/0.18 ± 0.14, and 16.56 ± 1.20/0.08 ± 0.07 mm/mrad with HofferQ; 16.64 ± 1.16/0.07 ± 0.06, 16.64 ± 1.16/0.18 ± 0.14, and 16.64 ± 1.16/0.07 ± 0.06 mm/mrad with Haigis; and 16.72 ± 1.18/0.07 ± 0.05, 16.72 ± 1.18/0.18 ± 0.14, and 16.72 ± 1.18/0.07 ± 0.05 mm/mrad with Castrop formulae. Mean/95% quantile relative image distortion was 0.49/1.23%, 0.41/1.05%, and 0.40/0.98% for scenarios 1 and 3 and 1.09/2.71%, 1.07/2.66%, and 1.06/2.64% for scenario 2 with HofferQ, Haigis, and Castrop formulae. CONCLUSION: Matrix representation of the pseudophakic eye allows for a simple and straightforward prediction of OOM and MOM of the pseudophakic eye after cataract surgery. OOM and MOM could be used for estimating monocular image distortions, or differences in overall or meridional magnifications between eyes.

Prediction of corneal back surface power - Deep learning algorithm versus multivariate regression.

BACKGROUND: The corneal back surface is known to add some against the rule astigmatism, with implications in cataract surgery with toric lens implantation. This study aimed to set up and validate a deep learning algorithm to predict corneal back surface power from the corneal front surface power and biometric measures. METHODS: This study was based on a large dataset of IOLMaster 700 measurements from two clinical centres. N = 19,553 measurements of 19,553 eyes with valid corneal front (CFSPM) and back surface power (CBSPM) data and other biometric measures. After a vector decomposition of CFSPM and CBSPM into equivalent power and projections of astigmatism to the 0°/90° and 45°/135° axes, a multi-output feedforward neural network was derived to predict vector components of CBSPM from CFSPM and other measurements. The predictions were compared with a multivariate linear regression model based on CFSPM components only. RESULTS: After pre-conditioning, a network with two hidden layers each having 12 neurons was derived. The dataset was split into training (70%), validation (15%) and test (15%) subsets. The prediction error (predicted corneal back surface power CBSPP - CBSPM) of the network after training and crossvalidation showed no systematic offset, narrower distributions for CBSPP - CBSPM and no trend error of CBSPP - CBSPM vs. CBSPM for any of the vector components. The multivariate linear model also showed no systematic offset, but broader distributions of the prediction error components and a systematic trend of all vector components vs. CFSPM components. CONCLUSION: The neural network approach based on CFSPM vector components and other biometric measures outperforms the multivariate linear model in predicting corneal back surface power vector components. Modern biometers can supply all parameters required for this algorithm, enabling reliable predictions for corneal back surface data where direct corneal back surface data are unavailable.

Calculation of Equivalent and Toric Power in AddOn Lenses Based on a Monte Carlo Simulation.

INTRODUCTION: Additional lenses implanted in the ciliary sulcus (AddOn) are one option for permanent correction of refractive error or generate pseudoaccommodation in the pseudophakic eye. The purpose of this paper was to model the power and magnification behaviour of toric AddOn and to show the effect sizes with a Monte Carlo simulation. METHODS: Anonymized data of a cataractous population uploaded for formula constant optimization were extracted from the IOLCon platform. After filtering out data with refractive spherical equivalent (RSEQ) between -0.75 and 0.25 dpt and refractive cylinder (RCYL) lower than 0.75, for each of the N = 6,588 records, a toric AddOn was calculated which transfers the refraction error from spectacle plane to AddOn plane using a matrix-based calculation strategy based on linear Gaussian optics. The equivalent (AddOnEQ) and toric (AddOnCYL) power of the AddOn and the overall lateral magnification change and meridional magnification were derived for the situations before and after AddOn implantation, and a linear modelling was fitted for all 4 parameters. RESULTS: RSEQ is the dominant effect size in the prediction of AddOnEQ and overall change in magnification (ΔM), whereas the lens position (LP), corneal thickness (CCT), and mean corneal radius (CPa) play a minor role. In a simplified model, AddOnEQ can be estimated by 0.0179 + 1.4104 RSEQ. RCYL and corneal radius difference (CPad) are the dominant effect sizes in the prediction of AddOnCYL and the change in meridional magnification (ΔMmer), whereas LP, CCT, CPa, and RSEQ play a minor role. In a simplified model, AddOnCYL can be predicted by -0.0005 + 0.0328 CPad + 1.4087 RCYL. Myopic eyes gain in overall magnification, whereas in hyperopic eyes, we observe a loss. Meridional distortion could be in general reduced to 35% on average with a toric AddOn. CONCLUSION: Our simulation shows that with a linear model, the equivalent and toric AddOn power, as well as overall change in magnification, meridional distortion before and after AddOn implantation, and the reduction in meridional distortion, can be easily predicted from the biometric data in pseudophakic eyes with moderate refractive error.

The Castrop formula for calculation of toric intraocular lenses.

PURPOSE: To explain the concept behind the Castrop toric lens (tIOL) power calculation formula and demonstrate its application in clinical examples. METHODS: The Castrop vergence formula is based on a pseudophakic model eye with four refractive surfaces and three formula constants. All four surfaces (spectacle correction, corneal front and back surface, and toric lens implant) are expressed as spherocylindrical vergences. With tomographic data for the corneal front and back surface, these data are considered to define the thick lens model for the cornea exactly. With front surface data only, the back surface is defined from the front surface and a fixed ratio of radii and corneal thickness as preset. Spectacle correction can be predicted with an inverse calculation. RESULTS: Three clinical examples are presented to show the applicability of this calculation concept. In the 1st example, we derived the tIOL power for a spherocylindrical target refraction and corneal tomography data of corneal front and back surface. In the 2nd example, we calculated the tIOL power with keratometric data from corneal front surface measurements, and considered a surgically induced astigmatism and a correction for the corneal back surface astigmatism. In the 3rd example, we predicted the spherocylindrical power of spectacle refraction after implantation of any toric lens with an inverse calculation. CONCLUSIONS: The Castrop formula for toric lenses is a generalization of the Castrop formula based on spherocylindrical vergences. The application in clinical studies is needed to prove the potential of this new concept.

Simulation of Corneal imaging properties for near objects.

PURPOSE: Using raytracing simulation to study the effect of corneal imaging metrics for different aperture sizes as a function of object distances with different schematic model eyes. METHODS: This raytracing simulation determined the best focus (with the least root-mean-square (rms) ray scatter) and the best wavefront focus (with least rms wavefront error) for four schematic model eyes (Liou-Brennan (LBME), Atchison (ATCHME), Gullstrand (GULLME) and Navarro (NAVME)) with 4 aperture sizes (2-5 mm) and 30 object distances in a logscale from 10 cm to 10 m plus infinity. For each configuration, 10,000 rays were traced through the cornea, and the aperture stop was located at the lens front apex plane as described in the model eyes. The wavefront was decomposed into Zernike components to extract the spherical aberration term. RESULTS: The focal distance with respect to the corneal front apex increases from around 31 mm for objects at infinity to around 40 mm for objects at 10 cm. The best (wavefront) focus was systematically closer to the cornea compared with the paraxial focus, and the overestimation of focal length with the paraxial focus was larger for large aperture sizes and small object distances. The rms ray scatter and wavefront error were both systematically larger with large aperture and small object sizes. At best focus the rms wavefront error was systematically larger, and the rms ray scatter was systematically smaller compared to the best wavefront focus. Spherical aberration varied more with GULLME than with LBME or NAVME, and increased strongly at smaller object distances. CONCLUSIONS: The imaging properties of the cornea, especially spherical aberration, increase strongly as the object distance decreases. This effect should be considered, especially when considering aberration correcting lenses for near vision such as multifocal or enhanced depth of focus lenses.

Calculation of ocular magnification in phakic and pseudophakic eyes based on anterior segment OCT data.

PURPOSE: The purpose of this study is to develop a straightforward mathematical concept for determination of object to image magnification in both phakic and pseudophakic eyes, based on biometric measures, refractometry and data from an anterior segment optical coherence tomography (OCT). METHODS: We have developed a strategy for calculating ocular magnification based on axial length measurement, phakic anterior chamber and lens thickness, keratometry and crystalline lens front and back surface curvatures for the phakic eye, and axial length measurement, anterior chamber and lens thickness, keratometry and intraocular lens power, refractive index and shape factor for the pseudophakic eye. Comparing the magnification of both eyes of one individual yields aniseikonia, while comparing the preoperative and postoperative situation of one eye provides the gain or loss in ocular magnification. The applicability of this strategy is shown using a clinical example and a small case series in 78 eyes of 39 patients before and after cataract surgery. RESULTS: For the phakic eye, the refractive index of the crystalline lens was adjusted to balance the optical system. The pseudophakic eye is fully determined and we proposed three strategies for considering a potential mismatch of the data: (A) with spherical equivalent refraction, (B) with intraocular lens power and (C) with the shape factor of the lens. Magnification in the phakic eye was -0.00319 ± 0.00014 and with (A) was -0.00327 ± 0.00013, with (B) was -0.00323 ± 0.00014 and with (C) was -0.00326 ± 0.00013. With A/B/C, the magnification of the pseudophakic eye was on average 2.52 ± 2.83%/1.31 ± 2.84%/2.14 ± 2.80% larger compared with the phakic eye. Magnification changes were within a range of ±10%. CONCLUSIONS: On average, ocular magnification does not change greatly after cataract surgery with implantation of an artificial lens, but in some cases, the change could be up to ±10%. If the changes are not consistent between the left and right eyes, then this could lead to post-cataract aniseikonia.

IOL Formula Constants: Strategies for Optimization and Defining Standards for Presenting Data.

PURPOSE: The aim of this study is to present strategies for optimization of lens power (IOLP) formula constants and to show options how to present the results adequately. METHODS: A dataset of N = 1,601 preoperative biometric values, IOLP data and postoperative refraction data was split into a training set and a test set using a random sequence. Based on the training set, we calculated the formula constants for established lens calculation formulae with different methods. Based on the test set, we derived the formula prediction error (PE) as difference of the achieved refraction from the formula predicted refraction. RESULTS: For formulae with 1 constant, it is possible to back-calculate the individual constant for each case using formula inversion. However, this is not possible for formulae with >1 constant. In these cases, more advanced concepts such as non-linear optimization strategies are necessary to derive the formula constants. During cross-validation, measures such as the mean absolute or the root mean squared PE or the ratio of cases within mean absolute PE (MAE) limits could be used as quality measures. CONCLUSIONS: Different constant optimization concepts yield different results. To test the performance of optimized formula constants, a cross-validation strategy is mandatory. We recommend performance curves, where the ratio of cases within absolute PE limits is plotted against the MAE.

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.

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.

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.

The Homburg-Adelaide toric IOL nomogram: How to predict corneal power vectors from preoperative IOLMaster 700 keratometry and total corneal power in toric IOL implantation.

PURPOSE: The purpose of this study is to compare the reconstructed corneal power (RCP) by working backwards from the post-implantation spectacle refraction and toric intraocular lens power and to develop the models for mapping preoperative keratometry and total corneal power to RCP. METHODS: Retrospective single-centre study involving 442 eyes treated with a monofocal and trifocal toric IOL (Zeiss TORBI and LISA). Keratometry and total corneal power were measured preoperatively and postoperatively using IOLMaster 700. Feedforward neural network and multilinear regression models were derived to map keratometry and total corneal power vector components (equivalent power EQ and astigmatism components C0 and C45) to the respective RCP components. RESULTS: Mean preoperative/postoperative C0 for keratometry and total corneal power was -0.14/-0.08 dioptres and -0.30/-0.24 dioptres. All mean C45 components ranged between -0.11 and -0.20 dioptres. With crossvalidation, the neural network and regression models showed comparable results on the test data with a mean squared prediction error of 0.20/0.18 and 0.22/0.22 dioptres2 and on the training data the neural network models outperformed the regression models with 0.11/0.12 and 0.22/0.22 dioptres2 for predicting RCP from preoperative keratometry/total corneal power. CONCLUSIONS: Based on our dataset, both the feedforward neural network and multilinear regression models showed good precision in predicting the power vector components of RCP from preoperative keratometry or total corneal power. With a similar performance in crossvalidation and a simple implementation in consumer software, we recommend implementation of regression models in clinical practice.