Background/Objectives: Corneal power has the largest impact on the variability of intraocular lens (IOL) power predictions, and corneal data from different biometers cannot be used interchangeably. We quantified the systematic differences between the Zeiss IOLMaster 700 (IOLM) and the Heidelberg Engineering Anterion and derived strategies for using both devices interchangeably in IOL power calculation. Methods: In this retrospective single-centre study, 837 eyes of 837 cataract patients were measured preoperatively with both biometers. Harmonic mean corneal front and back surface radii were derived from the flat and steep meridians, and corneal power referenced to the front apex plane was expressed as spherocylindrical power vectors (spherical equivalent, SEQ; astigmatic components C0 and C45). Three mapping strategies were compared using Bland–Altman and double-angle plots: linear regression of corneal radii without (MR) and with (MRI) intercept and multivariate linear regression of the power vector components (MMV). Results: Corneal front surface radii agreed well between devices (MR slope 1.000), whereas the IOLM reported systematically flatter posterior radii (MR slope 0.943), giving a systematically higher total corneal power (43.105 D versus 42.760 D). MRI mapping largely removed the systematic offset in the corneal radii but did not fully correct the astigmatic centroids, whereas MMV mapping aligned both the SEQ and the astigmatic centroids at the origin and yielded smaller confidence ellipses. Conclusions: Measurements from the two devices are not directly interchangeable, primarily because of systematic discrepancies in the reported posterior corneal curvature. Where identical IOL calculation concepts and formula constants are used across devices, conversion of corneal data is mandatory, and multivariate power vector mapping provides superior harmonisation compared with radius-based approaches.

Background/Objectives: Intraocular lens (IOL) constants are conventionally optimized globally across an entire calibration dataset, assuming that systematic prediction error is independent of axial length (AL). This assumption is known to fail in short and long eyes. We evaluated whether AL-segmented constant optimization reduces refractive prediction error, whether the benefit depends on formula family, and whether changepoints discovered in one population transfer to a disjoint one. Methods: In a pooled 6451-eye training dataset (6 IOL models), the corrected Akaike Information Criterion selected the optimal number (0–4) and positions of AL changepoints for six formulas (classic three-constant Haigis, new-Haigis H1/H2, SRK/T, Hoffer Q, Holladay 1), enforcing ≥40 eyes and ≥2.0 mm per segment. Locked changepoints were applied to two disjoint single-lens test subgroups (Vivinex, n = 887; SA60AT, n = 821; three-center retrospective cohort) and independently re-discovered within each. Root-mean-square prediction error (RMSE) reduction was assessed by bootstrap confidence interval, Diebold–Mariano test, and Wilcoxon signed-rank test. Results: Segmentation reduced training RMSE for all six formulas, particularly for Hoffer Q (−3.9%) and Holladay 1 (−2.8%; confidence intervals excluding zero, Diebold–Mariano p < 0.0001). With locked changepoints, both formulas again showed the largest test-dataset improvements (3.0–6.3%; confidence intervals excluding zero in all four lens–workflow combinations), followed by SRK/T (0.9–1.3%, up to 2.5% with independently discovered changepoints). Haigis-family formulas showed smaller reductions (0.2–1.6%) with confidence intervals including zero in several combinations. Conclusions: AL-segmented optimization benefits Hoffer Q and Holladay 1 most robustly—formulas lacking a direct anterior chamber depth predictor—with a smaller benefit for SRK/T and an inconsistent benefit for Haigis-family formulas. Changepoints from a pooled training population transfer usefully, though not optimally, to individual lens models.

PURPOSE:To develop, implement and demonstrate a data driven strategy to identify 'suspects' and 'outliers' in datasets of biometric measurements taken before cataract surgery. METHODS:A shallow autoencoder with one hidden layer and 3 neurons was trained on a large multicentre dataset (N = 152,397, 9 clinical centres) from the IOLMaster 700 including axial length (AL), central corneal thickness (CCT), anterior chamber depth (ACD), lens thickness (LT) and corneal front surface radius (R). Measurements were identified as 'suspects' or 'outliers' depending on the mean squared prediction error. Training was performed on 7 of the 9 datasets, and the remaining 2 datasets were used to evaluate the performance of the autoencoder. RESULTS:Crossvalidation proved that the autoencoder with 3 neurons showed no noticeable overfitting. Measurements were marked as 'suspects' or 'outliers' based on the 95% and 99% quantiles as derived from the mean squared error with the training data. After piecewise linear correction of the autoencoder prediction error to correct for trend errors probably due to internal calibrations of the biometer, the autoencoder successfully identified potentially faulty measurements for the 2 test datasets. CONCLUSIONS:Autoencoders are quite popular for different application fields in engineering, and could also help in ophthalmology to identify potentially faulty biometric measurements which could lead to refractive surprises if used for intraocular lens power calculation. Further studies are required to validate this concept with other parameters or datasets from other biometers.

To develop a concept for predicting the power of an intraocular lens (IOL) and the spectacle refraction after cataract surgery based on aphakic refraction (REFa) using vergence transforms with a two-surface cornea model. This simulation study is based on a large dataset originally used in IOLCon ( www.IOLCon.org ) for optimising lens constants. Proxy values for REFa calculated from the available information in this dataset were used to develop a strategy for predicting the effective lens position (ELP). A variety of models, including linear, quadratic, sigmoidal and two stepwise linear models, were evaluated. Using this ELP, vergence transform techniques were applied to derive the IOL power for a given target refraction or the spectacle refraction for a given IOL power. This concept was applied to subsets of the IOLCon dataset with the Hoya Vivinex and the Bausch Lomb enVista lenses to show the efficiency of the calculation. After evaluating the ELP prediction models on the 22,577 IOLCon data, it was decided to use the sigmoidal model for calculating the ELP corrected by a linear term for the A constant. Compared with the fully disclosed Castrop formula, the predicted ELP showed a root-mean-squared deviation of 0.221/0.221 mm with the Vivinex/enVista lens and the predicted IOL power showed a root-mean-squared deviation of 0.369/0.375 D. Where biometric data for a classical IOL power calculation are unavailable, this vergence-based calculation concept may help to identify the appropriate IOL power and to predict the spectacle refraction after cataract surgery. A clinical study with ‘real’ REFa measurements is required to validate these results.

Background/Objectives: The purpose of this study was to investigate the variation in subjective manifest refraction measures in a patient cohort screened for myopic refractive surgery. Methods: In this retrospective non-randomised cross-sectional single-centre study, we evaluated a dataset containing sequences of three refraction measurements performed by four experienced optometrists in 175 eyes screened for refractive corneal or lens surgery for myopia or myopic astigmatism. Refraction was converted from sphere (SPH), cylinder (CYL) and axis to power vector components (spherical equivalent SEQ and cylinder projections C0 and C45). The mean power vectors of the three repeat measurements (MEAN) and the deviations (DEV) of the repeat measurements from the MEAN were evaluated. Results: MEAN values for SPH/CYL/SEQ/C0/C45 were −5.93/0.99/−5.44/−0.47/0.02 D and the corresponding standard deviations were 0.20/0.16/0.17/0.17/0.16 D. DEV of both SEQ and CYL correlated significantly with patient age (Spearman R = 0.16 and 0.20). DEV of CYL correlated with mean (myopic) SEQ (R = −0.22) and CYL (R = 0.27) whereas DEV of SEQ showed no significant correlation with mean SEQ or CYL. Conclusions: The variation in subjective manifest refraction with repeat measurements is in a range of ±0.16 to ±0.20 D for SPH, CYL and the power vector components SEQ, C0 and C45. If reliable subjective refraction measurements are mandatory, e.g., for planning refractive surgery procedures or for formula constant optimisation, repeat refractometry measures could help to ensure representative data and to estimate the intraindividual variations.

PURPOSE:To investigate the similarity and symmetry of biometric measures between eyes in a large dataset of measurements of both eyes taken with the LenStar optical biometer. METHODS:Cross-sectional non-randomised study evaluating a dataset containing 13,420 bilateral LenStar 900 biometric measurements on patients without history of eye surgery or ocular pathology taken before cataract surgery, consisting of scalar parameters axial length AL, corneal thickness CCT, anterior chamber depth ACD, lens thickness LT and corneal diameter WTW. The keratometric power vector components equivalent power KEQ were assessed for similarity, and the projections of corneal astigmatism vector KC0 and KC45 were analysed for direct and mirror symmetry with respect to the vertical (sagittal) plane. RESULTS:Mean / standard deviation (squared correlation coefficient) difference between right and left eye measures was 0.02 ± 0.31(0.95) / 0.00 ± 0.01(0.93) / 0.00 ± 0.14(0.88) / -0.01 ± 0.22(0.78) / -0.02 ± 0.17(0.87) mm for AL / CCT / ACD / LT / WTW and -0.06 ± 0.48(0.92) dioptres for KEQ. Keratometric astigmatism showed a high degree of mirror symmetry (KC45 of left eyes inverted in sign) which outperforms direct symmetry. The median deviation of the keratometric axes of both eyes considering mirror symmetry was 15 degrees compared to 29 degrees for direct symmetry. CONCLUSIONS:In most cases, biometric measures match between eyes of a subject, but there are rare situations with large deviations between eyes. Keratometric astigmatism exhibits mirror symmetry. In most cases the biometric measures from the contralateral eye could be used where biometry is unavailable or to double-check before cataract surgery.

Purpose: The aim of this study was to develop a concept for adjustment planning of intraocular lens orientation axes after cataract surgery with implantation of toric intraocular lenses (tIOLs) and to predict the spectacle refraction after tIOL re-alignment. Methods: This calculation concept based on paraxial spherocylindrical vergence transformations uses the actual spherocylindrical refraction at the spectacle plane, corneal power, and the labelled power and measured axis of the implanted tIOL to minimise the refractive cylinder by simulating the rotation of the tIOL in the eye. The axial lens position is derived from simple prediction models using anterior chamber depth and lens thickness or axial length from preoperative biometry or the equivalent tIOL power. The new target axis is predicted together with the spherocylindrical refraction after re-alignment of the tIOL. Results: To show the applicability of this calculation model, we provide four clinical working examples: example 1 deals with keratometric power values; example 2 deals with keratometric curvature values, including surgically induced astigmatism and a statistical posterior astigmatism correction for the cornea (both examples with a thin cornea model); example 3 deals with corneal curvature data for the front and back surface; and example 4 deals with keratometric power data and corneal back surface power data, including surgically induced astigmatism (both examples with a thick cornea model). Conclusions: The effect of tIOL axis adjustment after cataract surgery can be predicted based on actual refraction, corneal power, tIOL power and the measured axis, and a simulation of the tIOL axis rotation enables the best orientation with the lowest refractive cylinder at the spectacle plane to be found.

Background/Objectives: To derive and validate a simplified modification of the Haigis intraocular lens (IOL) power calculation formula by reducing the three-constant effective lens position (ELP) model to a single constant while introducing an optimized keratometer index and axial length correction. Methods: In this retrospective study, a large multicentric dataset (Dataset 1; 22,466 eyes, 113 IOL models) was used to optimize the Haigis constant triplet and keratometer index using nonlinear programming with Cooke's axial length correction. A second independent dataset (Dataset 2; 3181 eyes, six IOL models) was used for cross-validation. Three approaches were compared: classical Haigis, modified triplet, and two single-constant models acting on IOL power (H1) or ELP (H2). Results: The optimized keratometer index (1.3296 ± 0.0003) was significantly lower than the classical value, indicating systematic overestimation of corneal power. Modified triplet and single-constant approaches achieved comparable or slightly lower prediction errors than the classical formula. The H1 approach showed marginally superior performance. Bootstrapping confirmed parameter stability. Conclusions: A single-constant modification of the Haigis formula incorporating an optimized keratometer index and axial length correction maintains prediction accuracy while simplifying clinical implementation.

PURPOSE:To investigate the repeatability of biometric measures and assess interactions between their uncertainties for use in an error propagation model, using patient data. METHODS:Cross-sectional non-randomised study evaluating a dataset containing 969 LenStar 900 biometric measurements taken before cataract surgery. Only complete scans with at least 3 successful measurements for each eye performed on the same day were considered. For each sequence, the aggregated mean (AMEAN) and population standard deviations (ASD) were derived. The within-subject standard deviation Sw was extracted for: corneal thickness, CCT, anterior chamber depth ACD, lens thickness LT, axial length AL, corneal diameter WTW, and the keratometric power vector components equivalent power KEQ, and the projections of corneal astigmatism KC0 and KC45. Correlations between the uncertainties were assessed using Spearman rank correlations. RESULTS:For the 266 eyes matching the inclusion criteria, Sw was 3.6/ 24.7/35.5/ 17.7/ 107.5 µm for CCT/ ACD/ LT/ AL WTW and 0.18/ 0.12/ 0.10 dioptres for KEQ/ KC0/ KC45. The keratometric axis ASD is inversely proportional to the keratometric astigmatism AMEAN. LT and ACD uncertainties are strongly negatively correlated, with KEQ and KC0 uncertainties moderately correlated. CONCLUSIONS:The uncertainty and correlation data presented here could be used to define a Monte-Carlo based error propagation model mapping the biometric measures and uncertainties to variations in predicted refraction after cataract surgery. We recommend using power vector components for error propagation models since the large decay over keratometric astigmatism makes keratometric axis uncertainty unreliable.

Options for correcting astigmatism include spectacles or contact lenses, corneal refractive laser surgery or relaxing incisions, toric lenses in the capsular bag, or implantation of supplementary toric lenses in the phakic or pseudophakic eye. This correspondence addresses some of the potential pitfalls which could cause calculation errors when working with astigmatic surfaces and spherocylindrical vergences and gives some advice on avoiding these. To provide some insight, each potential pitfall is illustrated with a clinical example.

Purpose To investigate different measures for corneal astigmatism in the context of reconstructed corneal astigmatism (recCP) as required to correct the pseudophakic eye, and to derive prediction models to map measured corneal astigmatism to recCP. Methods Retrospective single centre study of 509 eyes of 509 cataract patients with monofocal (MX60P) IOL. Corneal power measured with the IOLMaster 700 keratometry (IOLMK), and Galilei G4 keratometry (GK), total corneal power (TCP2), and Alpin’s integrated front (CorT) and total corneal power (CorTTP). Feedforward shallow neural network (NET) and linear regression (REG) prediction models were derived to map the measured C0 and C45 power vector components to the respective recCP components. Results Both the NET and REG models showed superior performance compared to a constant model correcting the centroid error. The mean squared prediction errors for the NET/REG models were: 0.21/0.33 dpt for IOLMK, 0.23/0.36 dpt for GK, 0.24/0.35 for TCP2, 0.23/0.39 dpt for CorT and 0.22/0.36 dpt for CorTTP respectively (training data) and 0.27/0.37 dpt for IOLMK, 0.26/0.37 dpt for GK, 0.38/0.42 dpt for TCP2, 0.35/0.36 dpt for CorT, and 0.44/0.45 dpt for CorTTP respectively on the test data. Crossvalidation with model optimisation on the training (and validation) data and performance check on the test data showed a slight overfitting especially with the NET models. Conclusions Measurement modalities for corneal astigmatism do not yield consistent results. On training data the NET models performed systematically better, but on the test data REG showed similar performance to NET with the advantage of easier implementation.

To study the performance of different corneal surface models to be used for ray tracing. Models based on geometric surfaces and polynomial fits were compared and the differences discussed. For this simulation study, five characteristic generic surface configurations were generated: (A) perfect biconic, (B) decentred biconic with white noise, (C) biconic with paracentral hollow simulating the situation after myopic LASIK, (D) biconic with random dot irregularities and (E) rotationally symmetric conic with mid-peripheral bump simulating the situation of corneal ectasia. A floating best fit sphere (BFS), conic (BFC), biconic (BFBC), fringe Zernike on top of a BFS (BFSZ), fringe Zernike (BFZ) and Gaussian process surface model (BFGP) were fitted and the root-mean-squared fit error was analysed. Surfaces A and B were well described by BFBC, BFSZ, BFZ and BFGP, but not by BFS and BFC. Surface C was not well represented by BFS, BFC and BFBC, but reasonably with BFSZ and BFZ and quite well with BFGP. Surfaces D and E were poorly represented, especially with BFS, BFC and BFBC, but also with BFSZ and BFZ and quite well with BFGP. There was no systematic difference between the two Zernike representations BFSZ and BFZ, even for surface B. Representing corneal point cloud data with a closed surface model plays a key role in ray tracing. Simple surface models such as BFS, BFC or BFBC are easy to handle but do not fully represent clinical situations with local irregularities after corneal refractive surgery or with ectasia.

PURPOSE:To design a vergence-based lens power formula based on the classical Haigis formula for better outcomes while retaining the original formula architecture. METHODS:Four new formula variants (A-D) incorporating a sum of segments correction for axial length, harmonic mean of corneal radii instead of arithmetic mean (all variants), and differing combinations of lower keratometer index (C, D) and an additional term (a3) representing the lens thickness in the effective lens position (B, D) were assessed in an analysis based on four datasets of IOLMaster 700 biometric data for eyes treated with the Hoya Vivinex lens (dataset 1), Alcon SA60AT lens (2), Johnson & Johnson ZCB00 lens (3), and the Bausch & Lomb MX60 lens (4). All parameters (formula constants and keratometer index) were calculated by nonlinear iterative optimisation techniques for minimising the root mean squared prediction error (RMSPE). Performance was assessed in terms of the final RMSPE. RESULTS:All four variants showed reductions in RMSPE ranging from 2.8% to 12.6% over the original Haigis formula. For each of the four datasets, variants B and D (with the additional a3 constant) performed better in this respect than variants A and C. In all four cases, variants C and D (with the adjusted keratometer index) performed slightly better than A and B, respectively. CONCLUSION:Although not amenable to statistical analysis, the % improvements in RMSPE would appear to be clinically relevant. However, the benefit has to be proven in a prospective multicentric study with a large sample size.

BACKGROUND:To develop and validate various models to predict total keratometry (TK) power vector components TKC0 and TKC45 from classical keratometry (K) KC0 and KC45 based on a large dataset of pre cataract surgery IOLMaster 700 measurements. METHODS:Retrospective cross-sectional multicentric study evaluating a dataset containing 13 6378 IOLMaster 700 measurements including K and TK. Left eyes were mirrored about the facial axis. Based on 80% training data, we developed a global and segmented constant model (CM and CMS), a global and segmented (according to the angle A1 of the flat keratometric meridian) linear model (LM and LMS), a harmonic model (HM) and compared these to a classical constant (CMR) and linear models (LMR) segmented into with-the-rule, against-the-rule and oblique astigmatism. The performance was cross-validated using the root-mean-squared model fit error (RMSE). RESULTS:In the 20% test data, RMSE was 0.173 D before correction and was reduced by 40%-42% to 0.100 and 0.104 D with the correction models. The segmented models performed slightly better than the global models, and the linear models performed slightly better than the constant models. With the individually adjusted changepoints, the CMS and LMS performed slightly better than the reference models CMR and LMR. There was no systematic difference between the RMSE with training and test data, indicating no overfit of the models. CONCLUSION:As the performance is quite similar for all tested correction models, we recommend using a simple global constant model to predict TK vector components. This could easily be implemented in any consumer software.

Purpose:To evaluate the rotational stability of four different monofocal toric intraocular lenses (IOLs) from surgery to 4-6 months postoperative. Methods:This was a subset of data from a prospective multi-center randomized clinical study. High resolution retro-illuminated images of eyes implanted with four different toric IOLs were obtained immediately after surgery, and at 1 day, 1 week, 1 month and 4-6 months after surgery. Fixed scleral features were identified in the surgical image. An independent reading center evaluated the orientation of the IOL from all images, based on the angle between the toric axis marks and these fixed scleral landmarks. Rotational stability was determined by calculating differences in orientation between visits. Results:Digital images from 299 eyes implanted with one of the four IOLs were available for analysis. Orientation data were successfully determined in about 90% of images. Biometry and IOL orientation were not significantly associated with IOL rotation. The Vivinex lens showed the lowest absolute rotation, with a mean value less than 1.5 degrees at all time intervals measured, with a maximum standard deviation of 1.4 degrees. The AcrySof lens was next lowest, with an absolute rotation below two degrees for all intervals. Mean absolute rotation for the Tecnis lens was significantly higher than for the other IOLs (>2 degrees for all intervals). For the AcrySof and Vivinex lenses, there were no reported rotations >10 degrees for any interval; 97% or more of results were <5 degrees, compared to 93% for the AT Torbi lens and 90% for the Tecnis lens. Only 6 lenses (4 Tecnis: 8.3%, 2 AT Torbi: 4.3%) had a rotation > 10 degrees at any time point. Conclusion:Rotational stability appeared excellent for the Vivinex and AcrySof toric IOLs, with slightly more variable performance evident with the AT Torbi and Tecnis IOLs.

Purpose To study the effects of corneal imaging and focusing using a raytracing simulation with 2 and 3 surface corneal models based on customized surface representations of corneal tomography data . Methods Raytracing simulation using surface data for the epithelium (S1), stroma (S2) and endothelium (S3) extracted from MS-39 anterior segment tomographer CSV export files. Customized surface representations were derived using Gaussian Process Predictors, and rays traced through the cornea and a 3.5 mm aperture stop located 3.66 mm behind the corneal apex. 4 clinical examples were evaluated: A) after hyperopic LASIK, B) after myopic LASIK, C) keratoconus, and D) after PRK with postoperatively developed Salzmann nodules. Results The raytracing based bundle focus and wavefront focus distances of the 2 surface (S1 and S3) and 3 surface cornea models (S1, S2 and S3) were comparable, whereas the paraxial focus derived from a 1 surface cornea (S1), 2 (S1 and S3) or 3 surface cornea (S1, S2 and S3) using floating best fit sphere representations for S1, S1 and S3 showed systematically lower / higher focal distance with B) / C) indicating an overestimation / underestimation of corneal power with paraxial calculations. Conclusions The clinical examples in this study exhibited only minor differences between the mono- and dual layer cornea models. We recommend verification in a larger clinical study. Three surface corneal raytracing models could be of clinical relevance in intraocular lens calculations and LASIK ablation nomograms, offering potential improvements over paraxial calculations especially in cases with surface irregularities.

Purpose To develop, implement and demonstrate a calculation strategy to derive the best shape spherical or aspherical intraocular lens (IOL) considering corneal spherical aberration (SA). Methods The simulation concept is based on 2D raytracing and involves an ideal plano or spherical wavefront with an optical path length correction which simulates corneal SA. The IOL defined with its equivalent power PIOL, Coddington shape factor (CSF) and edge thickness (ET) could be located with its secondary principal plane (PP2) or its haptic plane (HP) at the predicted axial lens position (ELP).The lens geometry is optimised for the root-mean-squared wavefront error (RMSWF) and the best wavefront and rayscatter focus are derived. Results The custom simulation software package is written in Matlab (version 2024a). The applicability of the simulation software is shown with some examples to show the performance of the results. The simulation results are structured to give some insight into best shape spherical and aspheric lenses, the impact of CSF, corneal spherical aberration to be corrected, and the concept of using the ELP to predict either the PP2 or the HP of the lens. Conclusions The simulation tool seems to be very robust in optimising best shape spherical and aspherical lenses based on available data for corneal power and spherical aberration. In all examples the spherical aberrations were completely eliminated or reduced to a negligible amount using individually shaped biconvex aspheric IOLs. An implementation in an industrial manufacturing process of customised aspheric lenses and a clinical study are needed to validate the concept in a clinical setting.

We investigated the repeatability of the MS-39 in determining power vector components—the spherical equivalent (SEQ) and astigmatic powers (C0 and C45) and asphericity (Q)—of corneal epithelium, stroma, and endothelium in a large patient cohort. In this retrospective cross-sectional single-centre study, we evaluated a dataset containing 600 MS-39 anterior segment tomography measurements from 200 eyes (three repeat measurements each) taken prior to cataract surgery. The exported measurements included height map data for the epithelium, stroma, and endothelium surface. Model surfaces (spherocylinder (SphCyl), cylindrical conoid (CylConoid), and biconic (Biconic), all in the 3/6 mm zone) were fitted using nonlinear iterative optimisation, minimising the height difference between the measurement and model. The mean (MEAN) and standard deviation (SD) for each sequence of measurements were derived and analysed. In the 3 mm and 6 mm zone, the MEAN SEQ was 53.47/53.56/53.57 and 53.21/53.54/53.54 D for SphCyl/CylConoid/Biconic for the epithelium, −4.47/−4.51/−4.51 and −4.45/−4.50/−4.50 D for the stroma, and −6.23/−6.26/−6.26 and −6.18/−6.29/−6.30 D for the endothelium. With the three surface models and the 3/6 mm zone, the SD for SEQ/C0/C45 was in the range of 0.04 to 0.11/0.05 to 0.13/0.04 to 0.11 D for epithelium; 0.01 to 0.02/0.01 to 0.05/0.01 to 0.06 D for stroma; and 0.01 to 0.02/0.02 to 0.07/0.03 to 0.07 D for endothelium. Fitting floating model surfaces with astigmatism to map data of the corneal epithelium, stroma, and endothelium seems to be a robust and reliable method for extracting equivalent power and astigmatism using all the datapoints within a region of interest.

PURPOSE:The purpose of this study was to develop a method for evaluating intraocular lens (IOL) formula constant uncertainties using two modern statistical techniques-jackknife and bootstrap resampling. METHODS:Using two datasets (dataset 1: 888 eyes treated with the aberration correcting Hoya Vivinex IOL, dataset 2: 821 eyes with the spherical Alcon SA60AT/SN60AT IOL), formula constant uncertainties for the SRK/T (Aconst), Hoffer-Q (pACD), Holladay 1 (SF), simplified Haigis (a0) with preset a1/a2, Haigis (triplet a0/a1/a2), Castrop (triplet C/H/R) and Olsen formula (ACD) were evaluated. All input parameters were jackknife and bootstrap (NB = 1000) resampled, and formula constants for each sample derived using nonlinear iterative optimisation techniques. RESULTS:In single constant formulae where the constant acts directly on the effective lens position (Hoffer-Q, Holladay 1, simplified Haigis, Olsen), the formula constant in each case showed a standard deviation (SD) of about 0.01 with both jackknife and bootstrap sampling. The SRK/T Aconst showed a SD of about 0.018, and the Haigis and Castrop formulae with constant triplets showed large variations in the 3 constants (a0/a1/a2 about 0.036/0.005/0.002, C/H/R about 0.001/0.011/0.012). Direct formula reversion and solving for the formula constant yielded systematically larger SD values (Aconst/pACD,SF/a0/ACD = 0.586/0.395/0.403/0.324/0.304) with highly skewed distributions. CONCLUSION:The distributions of formula constants with relevant benchmarks such as SD or confidence intervals can be derived with jackknife and bootstrap resampling techniques, offering potential advantages over direct formula reversion which yields skewed distributions, making central metrics such as the formula constant distribution mean unsuitable for constant optimisation.