[Basic aspects of IOL calculation]. / Grundlegende Aspekte zur IOL-Berechnung.

IOL calculation can now be considered a solved problem. However, the problem of sharing the knowledge of the underlying physical and mathematical basics is still unsolved. Also, the necessary hard- and software tools for an IOL calculation approximating the accuracy of prescribed glasses are not yet generally available. The aim of this survey is a clarification of the basics and of some historical pitfalls that still lead to persisting misunderstandings.

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. The target variable was the defocus equivalent (DEQ) derived using the Castrop (DEQC) and the Haigis (DEQH) formulae. RESULTS: Mean/median / 90% quantile DEQC was 0.22/0.21/0.36 D and DEQH was 0.20/0.19/0.32 D. Ignoring the variation in lens power labelling and toric axis alignment the respective DEQC was 0.20/0.19/0.32 D and DEQH was 0.18/0.17/0.29 D. DEQC and DEQH increased with shorter eyes, steeper corneas, equivalent lens power and highly with toric lens power. CONCLUSIONS: According to our simulation results, uncertainties in biometric measures, lens power labelling tolerances, and axis alignment errors are responsible for a significant part of the refraction prediction error after cataract surgery with toric lens implantation. Additional labelling of the exact equivalent and toric power on the lens package could be a step to improve postoperative results.

Effect of defocus incorporated multiple segments (DIMS) spectacle lenses on myopia progression in children: a retrospective analysis in a German real-life clinical setting.

OBJECTIVES: This retrospective analysis evaluates the treatment success of "Defocus Incorporated Multiple Segments" (DIMS) spectacle lenses in a real-life clinical setting in Germany. MATERIALS AND METHODS: Axial length (AL) and objective refraction of 166 eyes treated with DIMS at baseline and 12-month follow-up were analyzed. Annual AL growth rate within the range of physiological growth rate was considered a successful treatment. Myopia progression of ≥ -0.5 D/yr accounted as treatment success. Differences in percentages of treatment success of subgroups depending on baseline AL and age against treatment success of the total population were investigated. RESULTS: Considering all eyes, treatment success regarding AL growth and myopia progression was achieved in 46% and 65%, respectively. Male eyes with moderate AL showed treatment success in a higher proportion (73%, p < 0.01; 89%, p < 0.01); eyes with high AL showed treatment success in a lower proportion (25%, p < 0.01; 51%, n.s.). Female eyes showed the same trend but without statistical significance (moderate AL: 49%; 68%; high AL: 40%; 62%). Younger children showed treatment success in a lower proportion (male: 11%, p < 0.01; 38%, p < 0.05; female: 25%, p < 0.01; 42%, p < 0.01). Older children showed treatment success in a higher proportion (male: 60%, p < 0.05; 78% p < 0.05; female: 53%, n.s.; 77% p < 0.05). CONCLUSIONS: Eyes with moderate baseline AL and of older children showed treatment success after 12 months of DIMS treatment. Eyes with a high baseline AL and of younger children showed treatment success in a smaller proportion, therefore combination treatment should be considered. In future studies, males and females should be assessed separately.

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. Start values were detuned by ±1.5 from the MPE optimized constants and formula constants generated using the simple prediction scheme were compared to the corresponding directly optimized constants. RESULTS: For all 5 formulae under test and with both datasets, constants optimized using the simple scheme showed excellent agreement with those from the iterative method with either MPE or RMSPE used as the optimization metric and good agreement with SDPE as the metric. Constants optimized for zero MPE or minimal RMSPE agreed within 0.05, whereas constants for minimal SDPE could be systematically off by up to 0.6 from the MPE values, making SDPE unsuitable as an optimization metric. CONCLUSIONS: This simple formula constant optimization scheme performs excellently for 4 disclosed formulae and one nondisclosed formula in our 2 monocentric datasets with zero MPE or minimal RMSPE as metrics. Multicentric studies with other study populations and biometers are required to further investigate the clinical applicability.

Outcomes of manual arcuate keratotomy with compression sutures for high regular postkeratoplasty astigmatism.

PURPOSE: To report functional and refractive outcomes of manual arcuate keratotomy (AK) with compression sutures for high regular postkeratoplasty astigmatism.Setting: not specified (review). DESIGN: Retrospective analysis. METHODS: This study included 90 eyes with high regular postkeratoplasty astigmatism (>4 diopters, D) who received AK with compression sutures between 2010 and 2022. Functional and refractive outcomes were assessed by evaluating topographic indices and by performing vector astigmatism and Fourier analysis. RESULTS: At last follow-up (mean=13.7±16.6 months), BCDVA improved from 0.59±0.28 logMAR to 0.34±0.25 logMAR. Cylinder magnitude decreased from 9.91±2.88 D to 5.42±3.35 D. Surface Asymmetry Index, Irregular Astigmatism Index, Corneal Eccentricity Index were equal to preoperative values, whereas Surface Regularity Index approached normal values at last follow-up. Fourier analysis indicated a decrease in the regular astigmatic component, whereas non-regular components (asymmetry and higher-order irregularity) remained stable. In vector astigmatism analysis, Target Induced Astigmatism magnitude was 9.92±2.86 D and Surgically Induced Astigmatism magnitude was 10.16±4.86 D (Correction Index of 0.91±0.48) with a Difference Vector of 5.42±3.35 D at last follow-up. Correction of astigmatism magnitude was adequate in 40% of the eyes, under-corrected in 30% and over-corrected in 30%. Angle of Error was <|22.5°| in 88% resulting in a low risk of off-axis treatment. CONCLUSION: AK with compression sutures is a simple, relatively effective and safe surgical procedure for astigmatism reduction after keratoplasty. In case of regular astigmatism, the procedure does not increase corneal irregularities. The remaining refractive error might be further corrected by spectacles, contact lenses or toric IOL implantation (in-the-bag / add-on), thus reducing the need for repeat keratoplasty.

Image Contrast and Spectral Transmission of Presbyopia-Correcting Intraocular Lenses: Evaluating the Impact of Nd:YAG Laser Associated Defects.

PURPOSE: Neodymium yttrium aluminum garnet (Nd:YAG) laser capsulotomy is considered gold standard in the treatment of posterior capsule opacification (PCO). In this laboratory study, we measured spectral transmission to evaluate the image contrast and analyze the impact of Nd:YAG associated defects in presbyopia-correcting intraocular lenses (IOLs). METHODS: Two hydrophobic, acrylic IOLs as classic multifocal lenses with diffractive ring segments and different amount of near addition (A, B), one hydrophilic, trifocal IOL (C), one sector-shaped, plate haptic IOL (D) and one hydrophobic, enhanced depth of focus (EDOF) IOL (E) were studied. Measurements included surface topography characterization, United States Air Force resolution test chart (USAF) analysis, spectral transmittance measurements and through focus contrast measurement. Measurements were done with unaltered samples, damages (n = 7) were intentionally created in the central 3.5 mm zone using a photodisruption laser (2.0 mJ) and measurements were repeated. RESULTS: Significant differences were shown between unmodified samples and samples with YAG pits. The YAG-pits decreased the image contrast and spectral transmission and changed results of USAF test images. The imaging contrast decreased to 66%, 64%, 60%, 52% and 59% with the YAG shots in samples (A-E). The light transmission decreased to 88%, 87%, 92%, 79% and 91% (A-E) on average between 400 nm to 800 nm. In all IOLs a reduction of the relative intensity of transmitted light was observed. CONCLUSION: The image performance of all tested presbyopia-correcting IOLs is significantly influenced and disturbed by YAG-pits. The intensity of transmitted light is reduced in the wavelength between 450-800 nm. USAF test targets show worse results compared to unmodified samples and contrast is significantly deteriorated. No ranking/rating among tested IOLs should be made as many other factors play a role in real world scenario. High care should be taken when performing Nd:YAG capsulotomy on premium IOLs to avoid any damages.

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

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

Prediction of Visual Acuity in Pseudophakic Cataract Population Based on Residual Refraction.

PURPOSE: The purpose of the study was to design a simple, handy prediction for the effect of spherical and cylindrical refractive error on the visual acuity degradation at different distances and validate this model on a clinical dataset. METHODS: This study examined 70 eyes from 35 patients' post-cataract surgery with aberration-free intraocular lenses. Biometric and corneal data were analysed, and subjective refraction and visual acuity were evaluated by two experienced optometrists. The study computed the spherical equivalent (SEQ), and defocus equivalent via vector addition (DEQ vec), as the sum of absolute values (DEQ abs). Predictive models were developed using univariate regression, with confidence intervals (BCa 95%) calculated through non-parametric bootstrapping (10,000 cycles). RESULTS: Various calculated equivalents included -0.44 D for spherical equivalent (SEQ), 0.70 D for defocus equivalent based on vector calculation (DEQ vec), and 0.89 D for defocus equivalent based on absolute values (DEQ abs). Uncorrected and corrected visual acuity averaged 0.07 logMAR and -0.04 logMAR, respectively. The absolute defocus equivalent (DEQ abs) exhibited the smallest confidence interval (BCa 95%) at 0.07. CONCLUSION: The defocus equivalent based on the addition of absolute values (DEQ abs) emerged as the most practical predictor for the described applications. Notably, it offers the advantage of easy calculability through a simple equation: VA loss = DEQ abs ⋅ 0.23. In 95% of cases, this predicted loss would have an accuracy of ±0.03 lines.

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.

Refractive Astigmatism Outcomes of Femtosecond Laser-Assisted Arcuate Keratotomies Combined with Femtosecond Laser-Assisted Cataract Surgery: Two-Year Results.

PURPOSE: To evaluate the effectiveness and stability of refractive astigmatism reduction after penetrating femtosecond laser-assisted arcuate keratotomy performed at the time of femtosecond laser-assisted cataract surgery. METHODS: Non-randomized retrospective data analysis of all patients that underwent femtosecond laser-assisted cataract surgery with femtosecond laser-assisted arcuate keratotomy over a 4-year period with a non-toric monofocal intraocular lens (2017-2021) at a tertiary care academic center. Postoperative visual acuity, manifest refraction, and predicted residual refractive error were also recorded at 1 month, 3-6 months, 12-18 months, and 2 years postoperatively. Preoperative keratometric astigmatism was compared to postoperative refractive astigmatism using vector calculations and the ASCRS double-angle plot tool. RESULTS: This study comprised 266 eyes (179 patients) that met inclusion criteria. The mean preoperative keratometric astigmatism magnitude was 0.99 ± 0.53 D. At 1 month, 3-6 months, 12-18 months, and 2 years postoperatively, the mean refractive cylinder was 0.49 ± 0.45 D, 0.49 ± 0.45 D, 0.55 ± 0.54 D, and 0.52 ± 0.46 D, respectively. Horizontal against-the-rule astigmatism showed a higher tendency toward undercorrection than vertical with-the-rule astigmatism, which had a slightly higher tendency toward overcorrection. With-the-rule astigmatism had smaller difference vectors between target-induced astigmatism and surgically induced astigmatism. CONCLUSIONS: Femtosecond laser-assisted arcuate keratotomy performed at the time of femtosecond laser-assisted cataract surgery was an effective option for correcting low-to-moderate corneal astigmatism for up to 2 years.

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 (.)opt for SRKT, HofferQ, Holladay and Haigis formula with an iterative nonlinear optimisation. For detuning start values by ±1.5 from (.)opt, the predicted formula constants (.)pred were calculated and compared with (.)opt. Formula performance metrics mean (MPE), median (MEDPE), mean absolute (MAPE), median absolute (MEDAPE), root mean squared (RMSPE) and standard deviation (SDPE) of the formula prediction error were analysed for (.)opt and (.)pred. RESULTS: (.)pred - (.)opt showed a 2nd order parabolic behaviour with maximal deviations up to 0.09 at the tails of detuning and a minimal deviation up to -0.01 for all formulae. The performance curves of different metrics of PE as functions of detuning variations show that the formula constants for zeroing MPE and MEDPE yield almost identical formula constants, optimisation for MAPE, MEDAPE and RMSPE yielded formula constants very close to (.)opt, and optimisation for SDPE could result in formula constants up to 0.5 off (.)opt which is unacceptable for clinical use. CONCLUSION: This simple prediction scheme for formula constant optimisation for zero mean refraction error performs excellently in our monocentric dataset, even for larger deviations of the start value from (.)opt. Further studies with multicentric data and larger sample sizes are required to investigate the performance in a clinical setting further.

Long-term astigmatism after intraocular pressure sensor implantation and nonpenetrating glaucoma surgery: EYEMATE-SC trial.

PURPOSE: To investigate long-term astigmatism after combined nonpenetrating glaucoma surgery (NPGS) and implantation of the first miniaturized suprachoroidal intraocular pressure (IOP) sensor EYEMATE-SC. SETTING: The study was conducted in 5 medical centers in 2 different countries. DESIGN: Retrospective multicenter clinical study. METHODS: Astigmatism of patients instrumented with the EYEMATE-SC IOP sensor was assessed over a follow-up period of 3 years. Refraction and corrected distance visual acuity (CDVA) were obtained preoperatively, after 6 months, 1, 2, and 3 years. A canaloplasty-operated patient cohort served as control. Astigmatism was evaluated using 3-dimensional power vector analysis involving the spherical equivalent M, and the Jackson crossed cylinder projections J 0 and J 45 . Exclusion criteria included neovascular and angle-closure glaucoma, myopia, axial length outside 22 to 26 mm, other ocular diseases, prior glaucoma surgery, other ocular surgery within 6 months (cataract surgery within 3 months) before NPGS, serious generalized conditions, and other active medical head/neck implants. RESULTS: Multivariate analysis indicated no changes in astigmatism along the observation period in both the EYEMATE-SC (n = 24) and the canaloplasty (n = 24) group ( P > .05 or nonsignificant after Bonferroni correction). Astigmatism was unchanged between the EYEMATE-SC and the canaloplasty group at all timepoints ( P > .05). CDVA did not change along the observation period of 3 years in each of both groups ( P > .05). CONCLUSIONS: Despite its suprachoroidal localization, this study indicated that the miniaturized EYEMATE-SC IOP sensor did not negatively affect long-term astigmatism after combined implantation with NPGS.

Rose Bengal Photodynamic Therapy (RB-PDT) Modulates the Inflammatory Response in LPS-Stimulated Human Corneal Fibroblasts By Influencing NF-κB and p38 MAPK Signaling Pathways.

PURPOSE: To investigate the effect of rose bengal photodynamic therapy on lipopolysaccharide-induced inflammation in human corneal fibroblasts. Furthermore, to analyze potential involvement of the mitogen-activated protein kinase and nuclear factor kappa B signaling pathways in this process. METHODS: Human corneal fibroblast cultures underwent 0-2.0 µg/mL lipopolysaccharide treatment, and 24 h later rose bengal photodynamic therapy (0.001% RB, 565 nm wavelength illumination, 0.17 J/cm2 fluence). Interleukin-6, interleukin-8, intercellular adhesion molecule-1, interferon regulatory factor-3, interferon α2, and interferon ß1 gene expressions were determined by quantitative PCR. Interleukin-6, interleukin-8, and C-C motif chemokine ligand-4 concentrations in the cell culture supernatant were measured by enzyme-linked immunosorbent assays and intercellular adhesion molecule-1 protein level in human corneal fibroblasts by western blot. In addition, the nuclear factor kappa B and mitogen-activated protein kinase signaling pathways were investigated by quantitative PCR and phosphorylation of nuclear factor kappa B p65 and p38 mitogen-activated protein kinase by western blot. RESULTS: Rose bengal photodynamic therapy in 2.0 µg/mL lipopolysaccharide-stimulated human corneal fibroblasts triggered interleukin-6 and interleukin-8 mRNA (p < .0001) and interleukin-6 protein increase (p < .0001), and downregulated intercellular adhesion molecule-1 expression (p < .001). C-C motif chemokine ligand-4, interferon regulatory factor-3, interferon α2, and interferon ß1 expressions remained unchanged (p ≥ .2). Rose bengal photodynamic therapy increased IκB kinase subunit beta, nuclear factor kappa B p65, extracellular signal-regulated kinases-2, c-Jun amino terminal kinase, and p38 transcription (p ≤ .01), and triggered nuclear factor kappa B p65 and p38 mitogen-activated protein kinase phosphorylation (p ≤ .04) in lipopolysaccharide treated human corneal fibroblasts. CONCLUSION: Rose bengal photodynamic therapy of lipopolysaccharide-stimulated human corneal fibroblasts can modify the inflammatory response by inducing interleukin-6 and interleukin-8 expression, and decreasing intercellular adhesion molecule-1 production. C-C motif chemokine ligand-4, interferon regulatory factor-3, and interferon α and ß expressions are not affected by rose bengal photodynamic therapy in these cells. The underlying mechanisms may be associated with nuclear factor kappa B and p38 mitogen-activated protein kinase pathway activation.

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. A multivariate prediction model (MV), simplified model with separation of vector components (SM) and a constant model (CM) were defined to map K to TK vector components. RESULTS: The K centroid (X/Y) showed some astigmatism with-the-rule (0.1981/-0.0211 dioptre (dpt)) whereas the TK centroid was located around zero (-0.0071/-0.0381 dpt against-the-rule) and the BS centroid showed systematic astigmatism against-the-rule (-0.2367/-0.0145 dpt). The respective TK-K centroid was located at -0.2052/-0.0302 dpt. The MV model showed the same performance (i.e. mean absolute residuum) as the SM did (0.1098 and 0.1099 dpt respectively) while the CM performed only slightly worse (0.1121 dpt mean absolute residuum). CONCLUSION: In cases where tomographic data are unavailable statistical models could be used to consider the overall contribution of the back surface to the total corneal astigmatism. Since the performance of the CM is sufficiently close to that of MV and SM we recommend using the CM which can be directly considered e.g. as surgically induced astigmatism.

Examination of Subbasal Nerve Plexus and Central Corneal Stromal Microstructure in Subjects With Congenital Aniridia, Using in Vivo Confocal Laser Scanning Microscopy.

PURPOSE: During life up to 70% of aniridia subjects develop aniridia-associated keratopathy (AAK). AAK is characterized by limbal stem cell insufficiency, impaired corneal epithelial cell differentiation and abnormal cell adhesion, which leads to centripetal spreading vascularization, conjunctivalization, and thickening of the cornea. Our aim was to examine the subbasal nerve plexus and central corneal stromal microstructure in subjects with congenital aniridia, using in vivo confocal laser scanning microscopy CLSM. METHODS: 31 eyes of 18 patients (55.6% males, mean age: 25.22 ± 16.35 years) with congenital aniridia and 46 eyes of 29 healthy subjects (41.4% males, mean age 30 ± 14.82 years) were examined using the Rostock Cornea Module of Heidelberg Retina Tomograph-III. At the subbasal nerve plexus, corneal nerve fiber density (CNFD), corneal nerve fiber length (CNFL), corneal total branch density (CTBD), and corneal nerve fiber width (CNFW) were analyzed using ACCMetrics software. Keratocyte density in the anterior, middle and posterior stroma was assessed manually. RESULTS: The CNFD (2.02 ± 4.08 vs 13.99 ± 6.34/mm2), CNFL (5.78 ± 2.68 vs 10.56 ± 2.82 mm/mm2) and CTBD (15.08 ± 15.62 vs 27.44 ± 15.05/mm2) were significantly lower in congenital aniridia subjects than in controls (p < 0.001 for all). CNFW was significantly higher in aniridia subjects than in controls (0.03 ± 0.004 vs 0.02 ± 0.003 mm/mm2) (p = 0.003). Keratocyte density was significantly lower in all stromal layers of aniridia subjects than in controls (p < 0.001 for all). Stromal alterations included confluent keratocytes, keratocytes with long extensions and hyperreflective dots between keratocytes in aniridia. CONCLUSIONS: Decrease in CNFD, CNFL, and CTBD, as well as increase in CNFW well refer to the congenital aniridia-associated neuropathy. The decreased keratocyte density and the stromal alterations may be related to an increased cell death in congenital aniridia, nevertheless, stromal changes in different stages of AAK have to be further analyzed in detail.

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). The performance of the algorithm was compared to the classical gradient-based Levenberg-Marquardt algorithm. RESULTS: The SO algorithm showed stable convergence after fewer than 50/150 iterations (SRKT, HofferQ, Holladay, Haigis, Castrop). The rmsPE was reduced systematically to 0.4407/0.4288/0.4265/0.3711/0.3449 dioptres. The final constants were A = 119.2709, pACD = 5.7359, SF = 1.9688, -a0 = 0.5914/a1 = 0.3570/a2 = 0.1970, C = 0.3171/H = 0.2053/R = 0.0947 for the SRKT, Hoffer Q, Holladay, Haigis and Castrop formula and matched the respective constants optimised in previous studies. CONCLUSION: The SO proves to be a powerful adaptive nonlinear iteration algorithm for formula constant optimisation, even in formulae with one or more constants. It acts independently of a gradient and is in general able to search within a (box) constrained parameter space for the best solution, even where there are multiple local minima of the target function.

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).

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. The mean (Mean) and standard deviations (SD) for each sequence of measurements were derived and analysed. Correlations between the uncertainties were assessed using Spearman rank correlations. RESULTS: In the dataset with 677 eyes matching the inclusion criteria, the within subject standard deviation and repeatability for all parameters match previously published data. The SD of the axial length (AL) increased with the Mean AL, but there was no noticeable dependency of the SD of any of the other parameters on their corresponding Mean value. The SDs of the parameters are not independent of one another, and in particular we observe correlations between those for AL, anterior chamber depth, aqueous depth, lens thickness and corneal thickness. CONCLUSIONS: The SD change over Mean for AL measurement and the correlations between the uncertainties of several biometric parameters mean that a simple Gaussian error propagation model cannot be used to derive the effect of biometric uncertainties on the predicted intraocular lens power and refraction after cataract surgery.