Evaluation of keratometric and total corneal astigmatism measurements from optical biometers and anterior segment tomographers and mapping to reconstructed corneal astigmatism vector components.

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).

Prediction of refraction error after toric lens implantation with biometric input data uncertainties and power labelling tolerances.

Background: The purpose of this study was to simulate the impact of biometric measure uncertainties, lens equivalent and toric power labelling tolerances and axis alignment errors on the refractive outcome after cataract surgery with toric lens implantation.

Methods: In this retrospective non-randomised cross sectional Monte-Carlo simulation study we evaluated a dataset containing 7458 LenStar 900 preoperative biometric measurements. The biometric uncertainties from literature, lens power labelling according to ISO 11979, and axis alignment tolerances of a modern toric lens (Hoya Vivinex) were taken to be normally distributed and used in a Monte-Carlo simulation with 100 000 samples per eye.

Performance Evaluation of a Simple Strategy to Optimize Formula Constants for Zero Mean or Minimal Standard Deviation or Root-Mean-Squared Prediction Error in Intraocular Lens Power Calculation.

Purpose: To investigate the performance of a simple prediction scheme for the formula constants optimized for a mean (MPE), standard deviation (SDPE) or root-mean-squared refractive prediction error (RMSPE).

Design: Retrospective cross-sectional study.

Methods: Using IOLMaster 700 biometric data from 888 eyes treated with the Hoya Vivinex lens and 821 eyes treated with the Alcon SA60AT lens, plus the power of the implanted lens and postoperative spherical equivalent refraction, optimized constants for SRKT, Hoffer Q, Holladay 1, Haigis, and K6 formulae were calculated using an iterative nonlinear optimization for zero MPE and minimal SDPE and RMSPE.

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.

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).

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

Purpose: To investigate the performance of a simple prediction scheme for the formula constants optimised for a mean refractive prediction error.

Methods: Analysis based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). IOLMaster 700 biometric data, power of the implanted lens and postoperative spherical equivalent refraction were used to calculate the optimised constants (.

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

Purpose: The purpose of this study was to investigate the effect of the corneal back surface by comparing the keratometric astigmatism (K, derived from the corneal front surface) of a modern optical biometer against astigmatism of Total Keratometry (TK, derived from both corneal surfaces) in a large population with cataractous eyes. The results were then used to define linear prediction models to map K to TK.

Methods: From a large dataset containing bilateral biometric measurements (IOLMaster 700) in 9736 patients prior to cataract surgery, the total corneal astigmatism was decomposed into vectors for K, corneal back surface (BS), and TK.

Surrogate optimisation strategies for intraocular lens formula constant optimisation.

Purpose: To investigate surrogate optimisation (SO) as a modern, purely data-driven, nonlinear adaptive iterative strategy for lens formula constant optimisation in intraocular lens power calculation.

Methods: A SO algorithm was implemented for optimising the root mean squared formula prediction error (rmsPE, defined as predicted refraction minus achieved refraction) for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formulae in a dataset of N = 888 cataractous eyes with implantation of the Hoya Vivinex hydrophobic acrylic aspheric lens. A Gaussian Process estimator was used as the model, and the SO was initialised with equidistant datapoints within box constraints, and the number of iterations restricted to either 200 (SRKT, Hoffer Q, Holladay) or 700 (Haigis, Castrop).

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

Purpose: The purpose of this study was to investigate the repeatability of biometric measures and also to assess the interactions between the uncertainties in these measures for use in an error propagation model, using data from a large patient cohort.

Methods: In this cross-sectional non-randomised study we evaluated a dataset containing 3379 IOLMaster 700 biometric measurements taken prior to cataract surgery. Only complete scans with at least 3 successful measurements for each eye performed on the same day were considered.

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.

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.

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.

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.

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.

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

Background: Intraocular lenses are typically calculated based on a pseudophakic eye model, and for toric lenses (tIOL) a good estimate of corneal astigmatism after cataract surgery is required in addition to the equivalent corneal power. The purpose of this study was to investigate the differences between the preoperative IOLMaster (IOLM) and the preoperative and postoperative Casia2 (CASIA) tomographic measurements of corneal power in a cataractous population with tIOL implantation, and to predict total power (TP) from the IOLM and CASIA keratometric measurements.

Methods: The analysis was based on a dataset of 88 eyes of 88 patients from 1 clinical centre before and after tIOL implantation.

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.

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.

Prediction of spectacle refraction uncertainties with discrete IOL power steps and manufacturing tolerances according to ISO using a Monte Carlo model.

Purpose: The purpose of this study was to develop a concept for predicting the effects of both discrete intraocular lens (IOL) power steps (PS) and power labelling tolerances (LT) on the uncertainty of the refractive outcome (REFU).

Design: Retrospective non-randomised cross-sectional Monte Carlo simulation study.

Methods: We evaluated a dataset containing 16 669 IOLMaster 700 preoperative biometric measurements.

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 S.

Methods: This Monte-Carlo simulation study used a large dataset containing 16 667 preoperative IOLMaster 700 biometric measurements. Based on literature S values, REFU was derived for both the Haigis and Castrop formulae using error propagation strategies.

Bootstrapping of Corneal Optical Coherence Tomography Data to Investigate Conic Fit Robustness.

Background: Fitting of parametric model surfaces to corneal tomographic measurement data is required in order to extract characteristic surface parameters. The purpose of this study was to develop a method for evaluating the uncertainties in characteristic surface parameters using bootstrap techniques.

Methods: We included 1684 measurements from a cataractous population performed with the tomographer Casia2.

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

Background: The purpose of this Monte-Carlo study is to investigate the effect of using a thick lens model instead of a thin lens model for the intraocular lens (IOL) on the resulting refraction at the spectacle plane and on the ocular magnification based on a large clinical data set.

Methods: A pseudophakic model eye with a thin spectacle correction, a thick cornea (curvatures for both surfaces and central thickness) and a thick IOL (equivalent power PL derived from a thin lens IOL, Coddington factor CL (uniformly distributed from -1.0 to 1.

Particle swarm optimisation strategies for IOL formula constant optimisation.

Purpose: To investigate particle swarm optimisation (PSO) as a modern purely data driven non-linear iterative strategy for lens formula constant optimisation in intraocular lens power calculation.

Methods: A PSO algorithm was implemented for optimising the root mean squared formula prediction error (rmsPE, defined as achieved refraction minus predicted refraction) for the Castrop formula in a dataset of N = 888 cataractous eyes with implantation of the Hoya Vivinex hydrophobic acrylic aspheric lens. The hyperparameters were set to inertia: 0.

Formula constant optimisation techniques including variation of keratometer or corneal refractive index and consideration for classical and modern IOL formulae.

Background: To investigate whether variation of the keratometer/corneal refractive index nK/nC improves the performance (prediction error PE) of classical and a modern intraocular lens (IOL) power calculation formula and further, to establish whether any trend error of PE for corneal radius R could be eliminated using formula constant and nK/nC optimisation.

Methods: Based on 2 large datasets (1: N = 888 Hoya Vivinex aberration-correcting and 2: N = 822 Alcon SA60AT spherical lens) a classical formula constant optimisation has been performed for the Hoffer Q, Holladay 1, Haigis and Castrop formulae, to minimise the root mean squared (rms) PE (situation A). In two further optimisations, the formula constants and the formula specific nK/nC value were optimised to minimise the rms PE (situation B) or rms PE and trend error of PE for R (situation C).

Preconditioning of clinical data for intraocular lens formula constant optimisation using Random Forest Quantile Regression Trees.

Purpose: To implement a fully data driven strategy for identifying outliers in clinical datasets used for formula constant optimisation, in order to achieve proper formula predicted refraction after cataract surgery, and to assess the capabilities of this outlier detection method.

Methods: 2 clinical datasets (DS1/DS2: N = 888/403) of eyes treated with a monofocal aspherical intraocular lens (Hoya XY1/Johnson&Johnson Vision Z9003) containing preoperative biometric data, power of the lens implant and postoperative spherical equivalent (SEQ) were transferred to us for formula constant optimisation. Original datasets were used to generate baseline formula constants.