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.

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).

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.

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.

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.

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.

Update on Biometry and Lens Calculation - A Review of the Basic Principles and New Developments. / Update Biometrie und Linsenberechnung ­ ein Review zu Grundlagen und neuen Entwicklungen.

These days, accurate calculation of artificial lenses is an important aspect of patient management. In addition to the classic theoretical optical formulae there are a number of new approaches, most of which are available as online calculators. This review aims to explain the background of artificial lens calculation and provide an update on study results based on the latest calculation approaches. Today, optical biometry provides the computational basis for theoretical optical formulae, ray tracing, and also empirical approaches using artificial intelligence. Manufacturer information on IOL design and IOL power recorded as part of quality control could improve calculations, especially for higher IOL powers. With modern measurement data, there is further potential for improvement in the determination of the axial length to the retinal pigment epithelium and by adopting a sum-of-segment approach. With the available data, the cornea can be assumed to be a thick lens. The Kane formula, the EVO 2.0 formula, the Castrop formula, the PEARL-DGS, formula and the OKULIX calculation software provide consistently good results for artificial lens calculations. Excellent refractive results can be achieved using these tools, with approximately 80% having an absolute prediction error within 0.50 dpt, at least in highly selected study populations. The Barrett Universal II formula also produces excellent results in the normal and long axial length range. For eyes with short axial lengths, the use of Barrett Universal II should be reconsidered; in this case, one of the methods mentioned above is preferable. Second Eye Refinement can also be considered in this patient population, in conjunction with established classic third generation formulae.

Biometry and Intraocular Lens Power Calculation in Eyes with Prior Laser Vision Correction (LVC) - A Review.

BACKGROUND: An intraocular lens (IOL) calculation in eyes that have undergone laser vision correction (LVC) poses a significant clinical issue in regards to both patient expectation and accuracy. This review aims to describe the pitfalls of IOL power calculation after LVC and give an overview of the current methods of IOL power calculation after LVC. REVIEW: Problems after LVC derive from the measurement of anterior corneal radii, central corneal thickness, asphericity, and the predicted effective lens position. A central issue is that most conventional 3rd generation formulas estimate lens position amongst other parameters on keratometry, which is altered in post-LVC eyes. CONCLUSION: An IOL power calculation results in eyes with prior LVC that are notably impaired in eyes without prior surgery. Effective corneal power including anterior corneal curvature, posterior corneal curvature, CCT (central corneal thickness), and asphericity is essential. Total keratometry in combination with the Barrett True-K, EVO (emmetropia verifiying optical formula), or Haigis formula is relatively uncomplicated and seems to provide good results, as does the Barrett True-K formula with anterior K values. The ASCRS ( American Society of Cataract and Refractive Surgery) calculator combines results of various formulae and averages results, which allows a direct comparison between the different methods. Tomography-based raytracing and the Kane and the Castrop formulae need to be evaluated by future studies.

Toric phakic IOLs in keratoconus-evaluation of preoperative parameters on the outcome of phakic anterior chamber lens implantation in patients with keratoconus.

PURPOSE: To evaluate the influence of the type of the keratectasia and preoperative keratometry readings on the efficacy of implantation of iris-fixated phakic anterior chamber intraocular lenses (pIOL) in patients with keratoconus. METHODS: In this retrospective study, iris-fixated pIOLs (Artisan/Artiflex (Ophtec®), Verisyse/Veriflex (AMO®)) were implanted in 38 eyes of 22 patients with stable keratoconus. Thirty-six eyes underwent corneal crosslinking (CXL) prior to the lens implantation. The refractive outcome was evaluated 6 weeks postoperatively and the influence of preoperative refraction and topo- and tomographical factors were analyzed. RESULTS: The mean postoperative uncorrected distance visual acuity (UDVApost) was 0.25 ± 0.15 logMAR and was not statistically different from the mean preoperative corrected distance visual acuity (CDVApre), which was 0.24 ± 0.13 logMAR. Twenty-seven eyes (71%) reached UDVApost/CDVApre ≥ 1 (efficacy index), whereas patients with PMD-like ectasia (n = 14) showed significantly (p = 0.003) higher efficacy index (100%) than patients diagnosed with keratoconus (n = 24) (54%). Higher eccentricity of the maximum posterior elevation showed a significant beneficial influence on the efficacy index (p = 0.021). Furthermore, a higher Amsler-Krumeich stage and preoperative MAE were correlated with a worse UDVApost. The mean absolute spherical equivalent was significantly decreased from 5.71 ± 4.96 D to 1.25 ± 1.20 D (p < 0.001). No significant difference was found in endothelial cell count. CONCLUSION: The results indicate that the implantation of phakic iris-fixated anterior chamber IOLs is a reasonable refractive option for patients with keratoconus. Keratoconus patients with a pellucidal marginal degeneration (PMD)-like appearance ectasia seem to benefit most from such procedures.

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.

Influence of ACPA-positive rheumatoid arthritis on visual field testing in patients with arterial hypertension: A comparative cross-sectional study.

PURPOSE: To evaluate a possible influence of anti-cyclic citrullinated peptide autoantibodies (ACPA) - positive rheumatoid arthritis (RA) on visual field (VF) testing in patients with arterial hypertension (aHT). METHODS: We conducted an observational cross-sectional study comparing patients with ACPA-positive RA and aHT, patients with aHT and healthy subjects. Further inclusion criteria were visual acuity (VA) of 0.8 or better and age between 40 and 60 years. VF testing was performed with standard automated achromatic perimetry (SAP), short wavelength automated perimetry (SWAP) (Octopus 300® ) and flicker perimetry (Pulsar® ). Results were analysed for a possible correlation with blood pressure or RA-activity. RESULTS: Twenty subjects with RA and aHT, 26 patients with aHT and 22 healthy participants were examined. Significant differences were found for mean sensitivity (MS) in SWAP comparing RA-patients with healthy participants (ΔMS -3.06, p = 0.001) and with hypertensive patients (ΔMS -2.32, p = 0.007). In SAP we observed a significant difference between patients with RA and healthy subjects regarding loss variance (LV) (ΔLV = +9.77, p = 0.004). Flicker perimetry did not demonstrate significant differences between groups. A correlation of VF changes with blood pressure level or RA-activity was not observed. CONCLUSION: Patients with ACPA-positive RA and aHT showed significant impairment of VF performance in SWAP compared to patients with aHT alone and healthy subjects. SAP also revealed a significant difference of LV between RA-patients and healthy subjects. aHT does not seem to induce functional changes in VF testing alone.

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.

Artificial Intelligence, Machine Learning and Calculation of Intraocular Lens Power. / Künstliche Intelligenz, maschinelles Lernen und Intraokularlinsenberechnung.

BACKGROUND AND PURPOSE: In the last decade, artificial intelligence and machine learning algorithms have been more and more established for the screening and detection of diseases and pathologies, as well as for describing interactions between measures where classical methods are too complex or fail. The purpose of this paper is to model the measured postoperative position of an intraocular lens implant after cataract surgery, based on preoperatively assessed biometric effect sizes using techniques of machine learning. PATIENTS AND METHODS: In this study, we enrolled 249 eyes of patients who underwent elective cataract surgery at Augenklinik Castrop-Rauxel. Eyes were measured preoperatively with the IOLMaster 700 (Carl Zeiss Meditec), as well as preoperatively and postoperatively with the Casia 2 OCT (Tomey). Based on preoperative effect sizes axial length, corneal thickness, internal anterior chamber depth, thickness of the crystalline lens, mean corneal radius and corneal diameter a selection of 17 machine learning algorithms were tested for prediction performance for calculation of internal anterior chamber depth (AQD_post) and axial position of equatorial plane of the lens in the pseudophakic eye (LEQ_post). RESULTS: The 17 machine learning algorithms (out of 4 families) varied in root mean squared/mean absolute prediction error between 0.187/0.139 mm and 0.255/0.204 mm (AQD_post) and 0.183/0.135 mm and 0.253/0.206 mm (LEQ_post), using 5-fold cross validation techniques. The Gaussian Process Regression Model using an exponential kernel showed the best performance in terms of root mean squared error for prediction of AQDpost and LEQpost. If the entire dataset is used (without splitting for training and validation data), comparison of a simple multivariate linear regression model vs. the algorithm with the best performance showed a root mean squared prediction error for AQD_post/LEQ_post with 0.188/0.187 mm vs. the best performance Gaussian Process Regression Model with 0.166/0.159 mm. CONCLUSION: In this paper we wanted to show the principles of supervised machine learning applied to prediction of the measured physical postoperative axial position of the intraocular lenses. Based on our limited data pool and the algorithms used in our setting, the benefit of machine learning algorithms seems to be limited compared to a standard multivariate regression model.

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.