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

BACKGROUND: The purpose of this Monte-Carlo study is to investigate the effect of using a thick lens model instead of a thin lens model for the intraocular lens (IOL) on the resulting refraction at the spectacle plane and on the ocular magnification based on a large clinical data set. METHODS: A pseudophakic model eye with a thin spectacle correction, a thick cornea (curvatures for both surfaces and central thickness) and a thick IOL (equivalent power PL derived from a thin lens IOL, Coddington factor CL (uniformly distributed from -1.0 to 1.0), either preset central thickness LT = 0.9 mm (A) or optic edge thickness ET = 0.2 mm, (B)) was set up. Calculations were performed on a clinical data set containing 21 108 biometric measurements of a cataractous population based on linear Gaussian optics to derive spectacle refraction and ocular magnification using the thin and thick lens IOL models. RESULTS: A prediction model (restricted to linear terms without interactions) was derived based on the relevant parameters identified with a stepwise linear regression approach to provide a simple method for estimating the change in spectacle refraction and ocular magnification where a thick lens IOL is used instead of a thin lens IOL. The change in spectacle refraction using a thick lens IOL with (A) or (B) instead of a thin lens IOL with identical power was within limits of around ±1.5 dpt when the thick lens IOL was placed with its haptic plane at the plane of the thin lens IOL. In contrast, the change in ocular magnification from considering the IOL as a thick lens instead of a thin lens was small and not clinically significant. CONCLUSION: This Monte-Carlo simulation shows the impact of using a thick lens model IOL with preset LT or ET on the resulting spherical equivalent refraction and ocular magnification. If IOL manufacturers would provide all relevant data on IOL design data and refractive index for all power steps, this would make it possible to perform direct calculations of refraction and ocular magnification.

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.

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

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

Prediction of 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. The PS and the delivery range of two modern IOLs (Bausch and Lomb enVista and Alcon SA60AT) were considered for this Monte Carlo simulation. The uncertainties from PS or LT were assumed to be normally distributed according to ±½ the IOL PS or the ISO 11979 LT. REFU was recorded and analysed for all simulations. RESULTS: With both lenses the REFU from discrete PS ranged from 0.11 to 0.12 dpt. Due to the larger PS for low/high power lenses with the enVista/SA60AT, REFU is more dominant in initially myopic/hyperopic eyes. REFU from LT ranged from 0.18 to 0.19 dpt for both lenses. Since LT increases stepwise with IOL power, REFU is more prevalent in initially hyperopic eyes requiring high IOL power values, and for lenses with a wide delivery range towards higher powers. CONCLUSIONS: Since surgeons and patients are typically aware of the effect of discrete PS on REFU, these might be tolerated in cataract surgery. However, REFU resulting from LT is inevitable while the true measured IOL power is not reported on the package, leading to background noise in postoperative achieved refraction.

Assessment of Rose Bengal Photodynamic Therapy on Viability and Proliferation of Human Keratolimbal Epithelial and Stromal Cells In Vitro.

PURPOSE: To investigate the effect of Rose Bengal photodynamic therapy (RB-PDT) on viability and proliferation of human limbal epithelial stem cells (T-LSCs), human corneal epithelial cells (HCE-T), human limbal fibroblasts (LFCs), and human normal and keratoconus fibroblasts (HCFs and KC-HCFs) in vitro. METHODS: T-LSCs and HCE-T cell lines were used in this research. LFCs were isolated from healthy donor corneal limbi (n = 5), HCFs from healthy human donor corneas (n = 5), and KC-HCFs from penetrating keratoplasties of keratoconus patients (n = 5). After cell culture, RB-PDT was performed using 0.001% RB concentration and 565 nm wavelength illumination with 0.14 to 0.7 J/cm2 fluence. The XTT and the BrdU assays were used to assess cell viability and proliferation 24 h after RB-PDT. RESULTS: RB or illumination alone did not change cell viability or proliferation in any of the cell types (p ≥ 0.1). However, following RB-PDT, viability decreased significantly from 0.17 J/cm2 fluence in HCFs (p < 0.001) and KC-HCFs (p < 0.0001), and from 0.35 J/cm2 fluence in T-LSCs (p < 0.001), HCE-T (p < 0.05), and LFCs ((p < 0.0001). Cell proliferation decreased significantly from 0.14 J/cm2 fluence in T-LSCs (p < 0.0001), HCE-T (p < 0.05), and KC-HCFs (p < 0.001) and from 0.17 J/cm2 fluence in HCFs (p < 0.05). Regarding LFCs proliferation, no values could be determined by the BrdU assay. CONCLUSIONS: Though RB-PDT seems to be a safe and effective treatment method in vivo, its dose-dependent phototoxicity on corneal epithelial and stromal cells has to be respected. The data and experimental parameters applied in this study may provide a reliable reference for future investigations.

Translation model for CW chord to angle Alpha derived from a Monte-Carlo simulation based on raytracing.

BACKGROUND: The Chang-Waring chord is provided by many ophthalmic instruments, but proper interpretation of this chord for use in centring refractive procedures at the cornea is not fully understood. The purpose of this study is to develop a strategy for translating the Chang-Waring chord (position of pupil centre relative to the Purkinje reflex PI) into angle Alpha using raytracing techniques. METHODS: The retrospective analysis was based on a large dataset of 8959 measurements of 8959 eyes from 1 clinical centre, using the Casia2 anterior segment tomographer. An optical model based on: corneal front and back surface radius Ra and Rp, asphericities Qa and Qp, corneal thickness CCT, anterior chamber depth ACD, and pupil centre position (X-Y position: PupX and PupY), was defined for each measurement. Using raytracing rays with an incident angle IX and IY the CW chord (CWX and CWY) was calculated. Using these data, a multivariable linear model was built up in terms of a Monte-Carlo simulation for a simple translation of incident ray angle to CW chord. RESULTS: Raytracing allows for calculation of the CW chord CWX/CWY from biometric measures and the incident ray angle IX/IY. In our dataset mean values of CWX = 0.32±0.30 mm and CWY = -0.10±0.26 mm were derived for a mean incident ray angle (angle Alpha) of IX = -5.02±1.77° and IY = 0.01±1.47°. The raytracing results could be modelled with a linear multivariable model, and the effect sizes for the prediction model for CWX are identified as Ra, Qa, Rp, CCT, ACD, PupX, PupY, IX, and for CWY they are Ra, Rp, PupY, and IY. CONCLUSION: Today the CW chord can be directly measured with any biometer, topographer or tomographer. If biometric measures of Ra, Qa, Rp, CCT, ACD, PupX, PupY are available in addition to the CW chord components CWX and CWY, a prediction of angle Alpha is possible using a simple matrix operation.

Translation model for anterior segment tomographic data to corneal spherical aberration derived from a Monte-Carlo simulation based on raytracing.

BACKGROUND: Intraocular lenses with a negative aspherical design for correction of corneal spherical aberration (SA) have gained popularity in recent decades. In most cases, a 'one size fits all' concept is followed, where all eyes receive lenses with the same SA correction. The purpose of this study is to develop a strategy based on raytracing using anterior segment tomography data to extract corneal SA and to provide simple multivariable linear models for prediction of corneal SA. METHODS: The analysis was based on a large dataset of 8737 measurements of 8737 eyes from 1 clinical centre, using the Casia2 anterior segment tomographer. An optical model based on: corneal front and back surface radius Ra and Rp, asphericities Qa and Qp, corneal thickness CCT, anterior chamber depth ACD, and pupil centre position (X-Y position: PupX and PupY ), was defined for each measurement. Corneal SA was derived using a 6-mm aperture perpendicular to the incident ray and centred on the chief ray, and linear prediction models were derived for SA using biometric data. Cross-validation was used for model performance evaluation. RESULTS: Using raytracing, the wavefront error within an aperture (6-mm diameter centred on the intersection of the chief ray with the cornea) was calculated and corneal SA was extracted. After identifying the relevant effect sizes (Ra, Qa, Rp Qp, ACD, PupX and PupY ) using stepwise linear regression, linear mixed-effects models (model 1: all effect sizes, model 2: Ra, Qa, Rp and Qp, model 3: Ra and Qa) were set up on the training data in terms of a Monte-Carlo simulation. On the test data (training data), model 1 with a mean absolute/root-mean-squared prediction error of 0.0095/0.0130 (0.0095/0.0127) performed similarly to model 2 with 0.0097/0.0131 (0.0096/0.0127), and both outperformed model3 with 0.0152/0.0197 (0.0148/0.0190). CONCLUSION: Based on the Casia2 anterior segment tomographer, corneal SA could be derived using shape data (curvature and asphericities) of both corneal surfaces (model 2). This information could easily be used for selection of the appropriate negative aspherical lens design in cataract surgery.

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.

Ratio of torus and equivalent power to refractive cylinder and spherical equivalent in phakic lenses - a Monte-Carlo simulation study.

BACKGROUND: Spherical and astigmatic powers for phakic intraocular lenses are frequently calculated using fixed ratios of phakic lens refractive power to refractive spherical equivalent, and of phakic lens astigmatism to refractive cylinder. In this study, a Monte-Carlo simulation based on biometric data was used to investigate how variations in biometrics affect these ratios, in order to improve the calculation of implantable lens parameters. METHODS: A data set of over sixteen thousand biometric measurements including axial length, phakic anterior chamber depth, and corneal equivalent and astigmatic power was used to construct a multidimensional probability density distribution. From this, we determined the axial position of the implanted lens and estimated the refractive spherical equivalent and refractive cylinder. A generic data model resampled the density distributions and interactions between variables, and the implantable lens power was determined using vergence propagation. RESULTS: 50 000 artificial data sets were used to calculate the phakic lens spherical equivalent and astigmatism required for emmetropization, and to determine the corresponding ratios for these two values. The spherical ratio ranged from 1.0640 to 1.3723 and the astigmatic ratio from 1.0501 to 1.4340. Both ratios are unaffected by the corneal spherical / astigmatic powers, or the refractive cylinder, but show strong correlation with the refractive spherical equivalent, mild correlation with the lens axial position, and moderate negative correlation with axial length. As a simplification, these ratios could be modelled using a bi-variable linear regression based on the first two of these factors. CONCLUSION: Fixed spherical and astigmatic ratios should not be used when selecting high refractive power phakic IOLs as their variation can result in refractive errors of up to ±0.3 D for a 8 D lens. Both ratios can be estimated with clinically acceptable precision using a linear regression based on the refractive spherical equivalent and the axial position.

Back-calculation of keratometer index based on OCT data and raytracing - a Monte Carlo simulation.

PURPOSE: This study aims to develop a raytracing-based strategy for calculating corneal power from anterior segment optical coherence tomography data and extracting the individual keratometer index, which converts the corneal front surface radius to corneal power. METHODS: A large OCT dataset (10,218 eyes of 8,430 patients) from the Casia 2 (Tomey, Japan) was post-processed in MATLAB (MathWorks, USA). Radius of curvature, asphericity of the corneal front and back surface, central corneal thickness and pupil size (aperture) were used to trace a bundle of rays through the cornea and derive the best focus plane. Corneal power was calculated with respect to the corneal front vertex plane, and the keratometer index was back-calculated using corneal power and front surface radius. Keratometer index was analysed in a multivariate linear model. RESULTS: The averaged resulting keratometer index was 1.3317 ± 0.0017 with a median of 1.3317 and range from 1.3233 to 1.3390. In a univariate model, only the front surface asphericity affected the keratometer index. The multivariate model for modelling the keratometer index using all 6 input parameters performed very well (RMS error: 5.54e-4, R2 : 0.90, significance vs. constant model: <0.0001). CONCLUSIONS: In the classical calculation, the keratometer index used for converting corneal radius to dioptric power uses several model assumptions. As these assumptions are not generally satisfied, corneal power cannot be calculated from corneal front surface radius alone. Considering all 6 input variables, the linear prediction model performs well and can be used if all input parameters are measured with a tomographer.

[Monte Carlo simulation of biometric effect sizes and their influence on the translational ratio of corneal astigmatism in the cylinders of toric intraocular lenses]. / Monte-Carlo-Simulation biometrischer Effektgrößen und deren Einfluss auf das Übersetzungsverhältnis des Hornhautastigmatismus in den Zylinder torischer Intraokularlinsen.

BACKGROUND AND OBJECTIVE: Toric intraocular lenses (IOL) provide a reliable and predictable option for permanent correction of corneal astigmatism. In order to determine the lens strength necessary for achieving the desired correction, the operator can either use the calculation mode implemented in the biometry device or the calculation service offered by the lens manufacturer; however, in many cases a classical lens calculation from biometric data is not carried out but only a simplified estimation, which translates the corneal astigmatism into the torus of the toric IOL. This translational ratio, which is mostly used as an average standard value, can however show a substantial range of variation, so that in a worst case scenario an undercorrection of the refractive cylinder of up to 12.5 % or an overcorrection of up to 17 % can result. The purpose of this study was to elaborate the biometric effect sizes which determine the relationship between the corneal astigmatism to be corrected and the torus necessary for a full correction of an IOL. METHODS: A total of 16,744 datasets were extracted from the IOLCon web platform and initially the axial position of the IOL implant was derived independent of a formula, based on the preoperative biometric values and the postoperative spherical equivalent. Subsequently, based on a ray propagation strategy for spherocylindrical vergences, the corresponding refractive value of a full correcting toric IOL was calculated. The translational relationship as a ratio between lens toricity and corneal astigmatism was analyzed for potential biometric effect sizes with a Monte Carlo simulation. RESULTS: The Monte Carlo simulation showed that the ratio of lens toricity to corneal astigmatism cannot be assumed as being constant. The analyzed data revealed an average translational ratio of 1.3938 ± 0.0595 (median 1.3921) with a range from 1.2131 to 1.5974. The axial position of the IOL was found to have the greatest influence, whereby the more posterior the lens position the higher the ratio. Due to the correlation of axial eye length and axial lens position, the eye length can be assumed to be an indirect effect size. The corneal equivalent refractive strength and the corneal astigmatism have no noteworthy effect on the translational ratio. CONCLUSION: Many calculation tools on the market simplify toric IOL power calculation by assuming a constant ratio of lens toricity to corneal astigmatism; however, the present simulation study showed that such a simplification can lead to clearly incorrect results. Accordingly, an individual calculation of IOL toricity based on biometric parameters (e.g. based on vergence propagation matrices or full aperture ray tracing) is recommended.