Intraocular Lens Power Calculation Formulas Research Articles

Comparison of Different Intraocular Lens Power Calculation Formulas in Eyes with Primary Angle Closure.

To compare the accuracy of six intraocular lens power calculation formulas, Barrett Universal Ⅱ (BU Ⅱ), Haigis, Hoffer QST, HolladayⅠ, Kane and SRK/T, in eyes with primary angle closure disease (PACD). Xiamen University Affiliated Xiamen Eye center, Xiamen, Fujian, China. Prospective case series. Patients diagnosed with PACD and cataract and met the indication for cataract surgery were enrolled in the study. Six intraocular lens power calculation formulas were used to calculate refractive diopter. Percentage of eyes with prediction error (PE) within ±0.50D, and the median absolute prediction error (MedAE) were compared to determine the accuracy of different formulas in PACD patients. Subgroup analysis was performed according to axial length (AL). The accuracy of Barrett Universal Ⅱ was compared between PACD patients and age-related cataract patients. 105 patients (105 eyes) with PACD and 35 patients (35 eyes) with age-related cataract were enrolled in the study. Haigis, Kane and Barrett Universal Ⅱ formula achieved a comparable outcome and outperformed over the other three formulas in PACD patients. Subgroup analysis showed that the group with long AL has lower values of MedAE. PE was significantly positively correlated with AL and negatively correlated with relative lens position (RLP) when calculated use Barrett Universal Ⅱ and Kane. Haigis, Kane and Barrett Universal Ⅱ formula achieved a comparable outcome and outperformed over the other three formulas in PACD patients.

Accuracy of 14 intraocular lens power calculation formulas in extremely long eyes.

To compare the accuracy of 14 formulas in calculating intraocular lens (IOL) power in extremely long eyes with axial length (AL) over 30.0mm. In this retrospective study, 211 eyes (211 patients) with ALs > 30.0mm were successfully treated with cataract surgery without complications. Ocular biometric parameters were obtained from IOLMaster 700. Fourteen formulas were evaluated using the optimized A constants: Barrett Universal II (BUII), Kane, Emmetropia Verifying Optical (EVO) 2.0, PEARL-DGS, T2, SRK/T, Holladay 1, Holladay 2, Haigis and Wang-Koch AL adjusted formulas (SRK/Tmodified-W/K, Holladay 1modified-W/K, Holladay 1NP-modified-W/K, Holladay 2modified-W/K, Holladay 2NP-modified-W/K). The mean prediction error (PE) and standard deviation (SD), mean absolute errors (MAE), median absolute errors (MedAE), and the percentage of prediction errors (PEs) within ± 0.25 D, ± 0.50 D, ± 1.00 D were analyzed. The Kane formula had the smallest MAE (0.43 D) and MedAE (0.34 D). The highest percentage of PE within ± 0.25 D was for EVO 2.0 (37.91%) and the Holladay 1NP-modified-W/K formulas (37.91%). The Kane formula had the highest percentage of PEs in the range of ± 0.50, ± 0.75, ± 1.00, and ± 2.00 D. There was no significant difference in PEs within ± 0.25, ± 0.50 ± 0.75 and ± 1.00 D between BUII, Kane, EVO 2.0 and Wang-Koch AL adjusted formulas (P > .05) by using Cochran's Q test. The Holladay 2modified-W/K formula has the lowest percentage of hyperopic outcomes (29.38%). The BUII, Kane, EVO 2.0 and Wang-Koch AL adjusted formulas have comparable accuracy for IOL power calculation in eyes with ALs > 30.0mm.

Accuracy of 20 Intraocular Lens Power Calculation Formulas in Medium-Long Eyes.

The aim of this work is to compare 20 intraocular lens (IOL) power calculation formulas in medium-long eyes (24.50-25.99mm) in terms of root mean square absolute error (RMSAE), median absolute error (MedAE), and percentage of eyes with prediction error (PE) within ± 0.50 D. The data of patients who underwent uneventful phacoemulsification between January 2017 and September 2023 were reviewed. Pre-surgery IOL power was calculated using Holladay1, SRK/T, Hoffer Q, Holladay 2, and Haigis. Three months after phacoemulsification, refraction was measured. Post-surgery IOL power calculations were performed utilizing the following formulas: Barrett Universal II, Kane, K6, Olsen (OLCR), Olsen (standalone), PEARL-DGS, Ladas Super Formula AI (LSF AI), T2, EVO, VRF, Hoffer QST, Castrop, VRF-G, Karmona, and Naeser 2. RMSAE, MedAE, and percentage of eyes with PE within ± 0.25 D, ± 0.50 D, ± 0.75 D and ± 1.00 were calculated. One hundred twenty-four eyes with axial length ranges between 24.52 and 25.97mm were studied. The SRK/T formula yielded the lowest RMSAE (0.206) just before Holladay 1 (0.260) and T2 (0.261). In terms of MedAE, the best outcome was obtained by SRK/T (0.12) followed by Barrett Universal II (0.15) and LSF AI (0.15). The highest percentage of eyes with prediction error within ± 0.50 D was achieved by SRK/T, T2, and Holladay 1 (97.58, 93.55, and 93.55%, respectively). Third-generation formulas (SRK/T, Holladay 1) provided highly accurate outcomes in medium-long eyes and still can be wildly used to calculate IOL power.

Accuracy of new intraocular lens power calculation formula for short and long eyes using segmental refractive indices.

To evaluate the accuracy of a new intraocular lens power calculation formula using segmental refractive index-based axial length (AL). Chukyo Eye Clinic, Nagoya, Japan. Retrospective observational study. This study included patients undergoing preoperative examination for cataract surgery with the new Barrett True AL (BTAL) and Emmetropia Verifying Optical (EVO) formulas using segmental refractive index, and conventional Barrett Universal II (BU II) formula using equivalent refractive index. The predicted refractive error of each formula was compared with the postoperative subjective spherical equivalent. The mean prediction error (MPE) in the short AL group (≤ 22 mm; 44 eyes) was 0.32 ± 0.40 D for BU II, 0.22 ± 0.37 D for BTAL, and 0.10 ± 0.37 D for EVO (P < 0.0001). MPE in the long AL group (≥ 26 mm; 92 eyes) was 0.01 ± 0.32 D for BU II, 0.04 ± 0.32 D for BTAL, and 0.09 ± 0.32 D for EVO (P < 0.0001). In patients with an AL ≥ 28 mm, BU II showed a myopic trend in 57.1% of cases, while BTAL and EVO showed a hyperopic trend in 71.4%. The MPE for patients with an AL ≥ 28 mm was -0.16 ± 0.34 D for BU II, 0.18 ± 0.33 D for BTAL, and 0.16 ± 0.32 D for EVO (P < 0.0001). The new EVO and BTAL formulas showed higher accuracy than BU II in short eyes, whereas there was no difference in long eyes.

Impact of segmented optical axial length on the performance of intraocular lens power calculation formulas.

To investigate the difference between the segmented axial length (AL) and the composite AL on a swept-source optical coherence tomography biometer and to evaluate the subsequent effects on artificial intelligence intraocular lens (IOL) power calculations: the Kane and Hill-RBF 3.0 formulas compared with established vergence formulas. National Hospital Organization, Tokyo Medical Center, Japan. Retrospective case series. Consecutive patients undergoing cataract surgery with a single-piece IOL were reviewed. The prediction accuracy of the Barrett Universal II, Haigis, Hill-RBF 3.0, Hoffer Q, Holladay 1, Kane, and SRK/T formulas based on 2 ALs were compared for each formula. The heteroscedastic test was used with the SD of prediction errors as the endpoint for formula performance. The study included 145 eyes of 145 patients. The segmented AL (24.83 ± 1.89) was significantly shorter than the composite AL (24.88 ± 1.96, P < .001). Bland-Altman analysis revealed a negative proportional bias for the differences between the segmented AL and the composite AL. The SD values obtained by Hoffer Q, Holladay 1, and SRK/T formulas based on the segmented AL (0.52 diopters [D], 0.54 D, and 0.50 D, respectively) were significantly lower than those based on the composite AL (0.57 D, 0.60 D, and 0.52 D, respectively, P < .01). The segmented ALs were longer in short eyes and shorter in long eyes than the composite ALs. The refractive accuracy can be improved in the Hoffer Q, Holladay 1, and SRK/T formulas by changing the composite ALs to the segmented ALs.

Precision in IOL Calculation for Cataract Patients with Prior History of Combined RK and LASIK Histories.

This study aimed to evaluate the accuracy of 12 intraocular lens (IOL) power calculation formulae for eyes that have undergone both radial keratotomy (RK) and laser assisted in situ keratomileusis (LASIK) surgery to determine the efficacy of various IOL calculations for this unique patient group. Currently, research on this surgical topic is limited. In this retrospective study, 11 eyes from 7 individuals with a history of RK and LASIK who underwent cataract surgery at Hoopes Vision were analyzed. Preoperative biometric and corneal topographic measurements were performed. Subjective refraction was obtained postoperatively. Twelve different intraocular lens (IOL) power calculations were used: Barrett True K No History, Barrett True K (prior LASIK, Prior RK history), Barrett Universal 2, Camellin-Calossi-Camellin (3C), Double K-Modified Holladay, Haigis-L, Galilei, OCT, PEARL-DGS, Potvin-Hill, Panacea, and Shammas. The rankings of mean arithmetic error (MAE), from least to greatest, were as follows: 3C (0.088), Haigis-L-L (-0.508), Shammas (-0.516), OCT Average (-0.538), Barrett True K (-0.557), OCT RK (-0.563), Galilei (-0.570), IOL Master (-0.571), OCT LASIK (-0.583), Barrett True K No History (-0.597), Pearl-DGS (-0.606), Potvin-Hill SF (-0.770), Potvin-Hill TNP (-0.778), Panacea (-0.876), and Barrett Universal 2 (-1.522). The 3C formula achieved the greatest percentage of eyes within ±0.25 D of target range (91%), while Haigis-L, Shammas, Galilei, Potvin Hill, Barrett True K, IOL Master, PEARL-DGS, and OCT formulae performed similarly, achieving 45% of eyes within ±0.75D of target refraction. This study demonstrates the accuracy of the lesser known 3C formula in IOL calculation, particularly for patients who have undergone both RK and LASIK. Well-known formulae, such as Haigis-L, Shammas, and Galilei, which are used by the American Society of Cataract and Refractive Surgery (ASCRS), are viable options, although 3C formulae should be considered in this patient population. Furthermore, larger studies can confirm the best IOL power formulas for post-RK and LASIK cataract patients.

Predictability of Existing IOL Formulas After Cataract Surgery in Patients with a Previous History of Radial Keratotomy: A Retrospective Cohort Study and Literature Review.

This study aims to evaluate the accuracy of 12 different intraocular lens (IOL) power calculation formulas for post-radial keratotomy (RK) eyes. The investigation utilizes recent advances in topography/tomography devices and artificial intelligence (AI)-based calculators, comparing the results to those reported in current literature to assess the efficacy and predictability of IOL calculations for this patient group. In this retrospective study, 37 eyes from 24 individuals with a history of RK who underwent cataract surgery at Hoopes Vision Center were analyzed. Biometry and corneal topography measurements were taken preoperatively. Subjective refraction was obtained 6 months postoperatively. Twelve different IOL power calculations were used, including the American Society of Cataract and Refractive Surgery (ASCRS) post-RK online formula, and the Barrett True K, Double K modified-Holladay 1, Haigis-L, Panacea, Camellin-Calossi, Emmetropia Verifying Optical (EVO) 2.0, Kane, and Prediction Enhanced by Artificial Intelligence and output Linearization-Debellemanière, Gatinel, and Saad (PEARL-DGS) formulas. Outcome measures included median absolute error (MedAE), mean absolute error (MAE), arithmetic mean error (AME), and percentage of eyes achieving refractive prediction errors (RPE) within ± 0.50 D, ± 0.75 D, and ± 1 D for each formula. A search of the literature was also performed by two independent reviewers based on relevant formulas. Overall, the best performing IOL power calculations were the Camellin-Calossi (MedAE = 0.515 D), the ASCRS average (MedAE = 0.535 D), and the EVO (MedAE = 0.545 D) and Kane (MedAE = 0.555 D) AI-based formulas. The EVO and Kane formulas along with the ASCRS calculation performed similarly, with 48.65% of eyes scoring within ± 0.50 D of the target range, while the Equivalent Keratometry Reading (EKR) 65 Holladay formula achieved the greatest percentage of eyes scoring within ± 0.25 D of the target range (35.14%). Additionally, the EVO 2.0 formula achieved 64.86% of eyes scoring within the ± 0.75 D RPE category, while the Kane formula achieved 75.68% of eyes scoring within the ± 1 D RPE category. There was no significant difference in MAE between the established and newer generation formulas (P > 0.05). The Panacea formula consistently underperformed when compared to the ASCRS average and other high-performing formulas (P < 0.05). This study demonstrates the potential of AI-based IOL calculation formulas, such as EVO 2.0 and Kane, for improving the accuracy of IOL power calculation in post-RK eyes undergoing cataract surgery. Established calculations, such as the ASCRS and Barrett True K formula, remain effective options, while under-utilized formulas, like the EKR65 and Camellin-Calossi formulas, show promise, emphasizing the need for further research and larger studies to validate and enhance IOL power calculation for this patient group.

Retrospective assessment of accuracy of nine intraocular lens power calculation formulae in eyes with axial myopia.

To compare the accuracy of nine conventional and newer-generation formulae in calculating intraocular lens power in eyes with axial myopia. Tertiary eye care center, Bengaluru, India. Retrospective cross-sectional, comparative study conducted in India. Patients undergoing uneventful phacoemulsification in eyes with axial length >26 mm were included. Preoperative biometry was done using Lenstar LS 900 (Haag-Streit AG, Switzerland). Single eye of patients undergoing bilateral implantation was randomly selected. Optimized lens constants were used to calculate the predicted postoperative refraction of each formula, which was then compared with the actual refractive outcomes to give the prediction errors, following which subgroup analysis was performed. The Kane formula, Barrett universal II, Emmetropia Verifying Optical (EVO) 2.0, Hill Radial Basis Function (Hill RBF) 3.0, Olsen formula, along with Wang Koch-adjusted four formulae, that is, Sanders Retzlaff Kraff/Theoretical (SRK/T), Holladay 1, Haigis, and Hoffer Q formula, were compared for intraocular lens power calculations. One hundred and sixty-five eyes that fulfilled all the inclusion criteria were studied. Hill RBF 3.0 had the lowest mean and median absolute prediction errors (0.355 and 0.275, respectively) compared to all formulas. In subgroup analysis (26-28, >28-30, and >30 mm), significant difference was seen only in extremely long eyes (>30 mm). The Hill RBF 3.0 formula generated the maximum percentage of eyes with refractive errors within ±0.25, ±0.5, ±0.75, and ±1 D (46%, 76.2%, 89.9%, and 95.8%, respectively). This is the first study evaluating all the formulas exclusively in the myopic eyes. Hill RBF 3 was found to be superior in accuracy to all other formulas.

Systematic evaluation of machine learning-enhanced trifocal IOL power selection for axial myopia cataract patients

PurposeThis study aimed to evaluate and optimize intraocular lens (IOL) power selection for cataract patients with high axial myopia receiving trifocal IOLs. DesignA multi-center, retrospective observational case series was conducted. Patients having an axial length ≥26 mm and undergoing cataract surgery with trifocal IOL implanted were studied. MethodsPreoperative biometric and postoperative outcome data from 139 eyes were collected to train and test various machine learning (ML) models (support vector machine, linear regression, and stacking regressor) using five-fold cross-validation. The models' performance was further validated externally using data from 48 eyes enrolled from other hospitals. Performance of seven IOL calculation formulas (BUII, Kane, EVO, K6, DGS, Holladay I, and SRK/T) were examined with and without ML models. ResultsThe results of cross-validation revealed improvements across all IOL calculation formulas, especially for K6 and Holladay I. The model increased the percentage of eyes with a prediction error (PE) within ±0.50 D from 71.94% to 79.14% for K6, and from 35.25% to 51.80% for Holladay I. In external validation involving 48 patients from other centers, six out of seven formulas demonstrated a reduction in the mean absolute error (MAE). K6's PE within ±0.50 D improved from 62.50% to 77.08%, and Holladay I from 16.67% to 58.33%. ConclusionsIn this study, we conducted a comprehensive evaluation of seven IOL power calculation formulas in high axial myopia cases and explored the effectiveness of the Stacking Regressor model in augmenting their accuracy. Of these formulas, K6 and Holladay I exhibited the most significant improvements, suggesting that integrating ML may have varying levels of effectiveness across different formulas but holds substantial promise in improving the predictability of IOL power calculations in patients with long eyes.

Limitations of constant optimization with disclosed intraocular lens power formulae.

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. Tertiary care center. Retrospective single-center consecutive case series. This analysis is based on a dataset of 888 eyes before and after cataract surgery with IOL implantation (Hoya Vivinex). Spherical equivalent refraction predSEQ was predicted using IOLMaster 700 data, IOL power, and formula constants from IOLCon ( https://iolcon.org ). The formula prediction error (PE) was derived as predSEQ minus achieved spherical equivalent refraction for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulae. The gradient of predSEQ (gradSEQ) as a measure for the effect of the constants on refraction was calculated and used for constant optimization. Using initial formula constants, the mean PE was -0.1782 ± 0.4450, -0.1814 ± 0.4159, -0.1702 ± 0.4207, -0.1211 ± 0.3740, and -0.1912 ± 0.3449 diopters (D) for the SRKT, Hoffer Q, Holladay, Haigis, and Castrop formulas, respectively. gradSEQ for all formula constants (except gradSEQ for the Castrop R) decay with axial length because of interaction with the effective lens position (ELP). Constant optimization for a zero mean PE (SD: 0.4410, 0.4307, 0.4272, 0.3742, 0.3436 D) results in a change in the PE trend over axial length in all formulae where the constant acts directly on the ELP. With IOL power calculation formulae where the constant(s) act directly on the ELP, a change in constant(s) always changes the trend of the PE according to gradSEQ. Formulae where at least 1 constant does not act on the ELP have more flexibility to zero the mean or median PE without coupling with a PE trend error over axial length.

Modified intraocular lens power selection method according to biometric subgroups Eom IOL power calculator

This study evaluates the accuracy of a newly developed intraocular lens (IOL) power calculation method that applies four different IOL power calculation formulas according to 768 biometric subgroups based on keratometry, anterior chamber depth, and axial length. This retrospective cross-sectional study was conducted in at Korea University Ansan Hospital. A total of 1600 eyes from 1600 patients who underwent phacoemulsification and a ZCB00 IOL in-the-bag implantation were divided into two datasets: a reference dataset (1200 eyes) and a validation dataset (400 eyes). Using the reference dataset and the results of previous studies, the Eom IOL power calculator was developed using 768 biometric subgroups. The median absolute errors (MedAEs) and IOL Formula Performance Indexes (FPIs) of the Barrett Universal II, Haigis, Hoffer Q, Holladay 1, Ladas Super, SRK/T, and Eom formulas using the 400-eye validation dataset were compared. The MedAE of the Eom formula (0.22 D) was significantly smaller than that of the other four formulas, except for the Barrett Universal II and Ladas Super formulas (0.24 D and 0.23 D, respectively). The IOL FPI of the Eom formula was 0.553, which ranked first, followed by the Ladas Super (0.474), Barrett Universal II (0.470), Holladay 1 (0.444), Hoffer Q (0.396), Haigis (0.392), and SRK/T (0.361) formulas. In conclusion, the Eom IOL power calculator developed in this study demonstrated similar or slightly better accuracy than the Barrett Universal II and Ladas Super formulas and was superior to the four traditional IOL power calculation formulas.

How to choose the intraocular lens power calculation formulas in eyes with extremely long axial length? A systematic review and meta-analysis.

To evaluate the accuracy of 10 formulas for calculating intraocular lens (IOL) power in cataract eye with an axial length (AL) of more than 28.0 mm. We searched scientific databases including PubMed, EMBASE, Web of Science and Cochrane Library for research published over the past 5 years, up to Sept 2023. The inclusion criteria were case series studies that compared different formulas (Barrett II, EVO, Kane, Hill-RBF, Haigis, Hoffer Q, Holladay 1, SRK/T, Holladay 1 w-k and SRK/T w-k), in patients with extremely long AL undergoing uncomplicated cataract surgery with IOL implantation. The mean difference (MD) of mean absolute error (MAE) and the odds ratio (OR) of both the percentage of eyes within ±0.50D of prediction error (PPE±0.50D) and the percentage of eyes within ±1.00D of prediction error (PPE±1.00D) among different formulas were pooled using meta-analysis. A total of 11 studies, involving 1376 eyes, were included to evaluate the 10 formulas mentioned above. Among these formulas, Barrett II, EVO, Kane, and Hill-RBF demonstrated significantly lower MAE values compared to SRK/T. Furthermore, Kane and Hill-RBF had lower MAE values than EVO. Additionally, Barrett II and Kane yielded significantly lower MAE values than Haigis while Hill-RBF showed significantly lower MAE values than Holladay 1. Moreover, Hill-RBF showed the highest values for both PPE±0.50D and PPE±1.00D, followed by Kane. Both EVO and Kane had higher values of PPE±0.50D and PPE±1.00D compared to Haigis and SRK/T. The Wang-Koch adjusted formulas and new-generation formulas have shown potential for higher accuracy in predicting IOL power for cataract patients with extremely long AL compared to traditional formulas. Based on the current limited clinical studies, Hill-RBF and Kane formulas seem to be a better choice for eyes with extremely long AL.

A Review of Intraocular Lens Power Calculation Formulas Based on Artificial Intelligence.

The proper selection of an intraocular lens power calculation formula is an essential aspect of cataract surgery. This study evaluated the accuracy of artificial intelligence-based formulas. Systematic review. This review comprises articles evaluating the exactness of artificial intelligence-based formulas published from 2017 to July 2023. The papers were identified by a literature search of various databases (Pubmed/MEDLINE, Google Scholar, Crossref, Cochrane Library, Web of Science, and SciELO) using the terms "IOL formulas", "FullMonte", "Ladas", "Hill-RBF", "PEARL-DGS", "Kane", "Karmona", "Hoffer QST", and "Nallasamy". In total, 25 peer-reviewed articles in English with the maximum sample and the largest number of compared formulas were examined. The scores of the mean absolute error and percentage of patients within ±0.5 D and ±1.0 D were used to estimate the exactness of the formulas. In most studies the Kane formula obtained the smallest mean absolute error and the highest percentage of patients within ±0.5 D and ±1.0 D. Second place was typically achieved by the PEARL DGS formula. The limitations of the studies were also discussed. Kane seems to be the most accurate artificial intelligence-based formula. PEARL DGS also gives very good results. Hoffer QST, Karmona, and Nallasamy are the newest, and need further evaluation.

Effect of Posterior Keratometry on the Accuracy of 10 Intraocular Lens Calculation Formulas: Standard Keratometry versus Total Keratometry.

To investigate the effect of posterior keratometry (PK) on the accuracy of 10 intraocular lens (IOL) power calculation formulas using standard keratometry (K) and total keratometry (TK). This is a retrospective consecutive case-series study. The IOL power was calculated using K and TK measured by IOLMaster 700 in 6 new-generation formulas (Barrett Universal II, Emmetropia Verifying Optical (EVO) 2.0, RBF Calculator 3.0, Hoffer QST, Kane, and Ladas Super Formula) and 4 traditional formulas (Haigis, Hoffer Q, Holladay 1, and SRK/T). The arithmetic prediction error (PE) and mean absolute PE (MAE) were evaluated. The locally-weighted scatterplot smoothing was performed to assess the relationship between PE and PK. A total of 576 patients (576 eyes) who underwent cataract surgery were included. Compared with using K, all formulas using TK showed a hyperopic shift in the whole group. Specifically, for eyes with PK exceeding -5.90 D, all formulas using TK exhibited a hyperopic shift (all P < 0.001), while eyes with PK less than -5.90 D showed a myopic shift (all P < 0.001). The MAE of new-generation formulas calculated with TK and K showed no statistical differences, while the MAE of traditional formulas with TK was larger (TK: 0.34 ~ 0.43 D; K: 0.33 ~ 0.42 D, all P < 0.05). The prediction bias of formulas with TK increased as PK deviated from -5.90 D. TK did not improve the prediction accuracy of new-generation formulas, and even performed worse in traditional formulas.

Intraocular lens power calculation formulas: a scientometric analysis.

The most accurate method of intraocular lens (IOL) power calculation in cataract surgery has not been determined, and further studies are needed to reach a consensus. The aim of this study was to assess publications related to IOL power calculation formulas, mapping their yearly trends, most productive authors, top publishing countries and institutions, and areas of specialization for IOL power formulas. We conducted a comprehensive analysis of research articles published on the topic of IOL power calculation formulas. Using PubMed, we employed appropriate search terms and filtered the results for the period of January 1, 1946, to June 28, 2023. Data were analyzed using CiteSpace, VOSviewer, and Microsoft Excel programs. The visual representations of the collected data through the use of figures was provided to demonstrate the aspects of IOL power calculation research. We retrieved 5475 documents in the initial search. Analysis of these documents revealed an increase in the number of publications, from one publication in 1946 to 201 publications in 2023. The top three countries contributing to these publications were the United States, China, and Japan, collectively accounting for over 27% of the total articles. However, the two institutions with the highest contributions were located in the United Kingdom and Hungary, neither of which was among the top 10 countries in overall contributions. Overall 15 326 authors contributed to publications pertaining to IOL power calculation formulas. Among these authors, the most prolific contributors included Achim Langenbucher from Saarland University (Germany), Giacomo Savini from G.B. Bietti Foundation I.R.C.C.S. (Italy), and Kenneth J Hoffer from the University of California (United States). Saarland University emerged as the most productive institution, contributing equally to two distinct departments: the Dr. Rolf M. Schwiete Center for Limbal Stem Cell Research and Congenital Aniridia, as well as the Department of Experimental Ophthalmology. The School of Physical Science at the Open University in the United Kingdom engaged in partnership with various institutions including Eye & Laser Clinic Castrop Rauxel in Germany and Johannes Kepler University Linz in Austria. Among the top 10 keywords found in the publications were "cataract", "cataract surgery", and "intraocular lens". This study represents the first scientometric analysis of publications related to IOL power calculation formulas. The study offers valuable insights into the geographic distribution, contributing authors, and emphasis of research on the IOL power calculation formulas. Further cooperation is essential to pinpoint the most suitable formula and to address gaps in our current understanding.

The effect of patient age on some new and older IOL power calculation formulas.

To assess the accuracy of intraocular lens (IOL) power calculation in different age groups using various IOL calculation formulas. Data from 421 eyes of 421 patients ≥60 years old (ages: 60-69, n = 131; 70-74, n = 105; 75-84, n = 158 and ≥85, n = 27), who underwent uneventful cataract surgery with SN60WF IOL implantation at John A. Moran Eye Center, Salt Lake City, USA, were retrospectively obtained. The SD of the prediction error (PE), median and mean absolute PEs and the percentage of eyes within ±0.25, ±0.50, ±0.75 and ±1.00 D were calculated after constant optimizations for the following formulas: Barrett Universal II (BUII), Emmetropia Verifying Optical (EVO) 2.0, Haigis, Hoffer Q, Hoffer QST, Holladay 1, Kane, Radial Basis Function (RBF) 3.0 and SRK/T. Results were compared between the different age groups. Predictability rates within 0.25D were lower for the eldest age group compared with the other groups using the EVO 2.0 (33% vs. 37%-53%, p = 0.045), Kane (26% vs. 35%-50%, p = 0.034) and SRK/T (22% vs. 31%-49%, p = 0.002). Higher median absolute refractive errors for all formulas were observed in the oldest group [range: 0.39 D (Haigis, Hoffer QSR)-0.48 D (Kane)], followed by the youngest group [range: 0.30 D (RBF 3.0)-0.39 D (Holladay 1, SRK/T)] but did not reach statistical significance. No significant differences between the groups in the distribution parameter were seen. Current IOL power calculation formulas may have variable accuracy for different age groups. This should be taken into account when planning cataract surgery to improve refractive outcomes.

Efficacy of corneal curvature on the accuracy of 8 intraocular lens power calculation formulas in 302 highly myopic eyes.

To investigate the effect of corneal curvature (K) on the accuracy of 8 intraocular lens formulas in highly myopic eyes. Eye Hospital and School of Ophthalmology and Optometry, Wenzhou Medical University, Wenzhou, China. Retrospective consecutive case series. 302 eyes (302 patients) were analyzed in subgroups based on the K value. The mean refractive error, mean absolute error (MAE), median absolute error (MedAE), root-mean-square absolute prediction error (RMSAE) and proportions of eyes within ±0.25 diopter (D), ±0.50 D, ±0.75 D, ±1.00 D were statistical analyzed. Emmetropia Verifying Optical (EVO) 2.0, Kane, and Radial Basis Function (RBF) 3.0 had the lower MAE (≤0.28) and RMSAE (≤0.348) and highest percentage of eyes within ±0.50 D (≥83.58%) in the flat (K ≤ 43 D) and steep K (K > 45 D) groups. Hoffer QST had the lowest MedAE (0.19), RMSAE (0.351) and the highest percentage of eyes within ±0.50 D (82.98%) in the normal K group (43 < K ≤ 45 D). When axial length (AL) ≤28 mm, all formulas showed close RMSAE values (0.322 to 0.373) in flat K group. When AL >28 mm, RBF 3.0 achieved the lowest MAE (≤0.24), MedAE (≤0.17) and RMSAE (≤0.337) across all subgroups. EVO 2.0, Kane, and RBF 3.0 were the most accurate in highly myopic eyes with a flat or steep K. Hoffer QST is recommended for long eyes with normal K values. RBF 3.0 showed the highest accuracy when AL >28 mm, independent of corneal curvature.

Comparison of intraocular lens power calculation formulas in patients with a history of acute primary angle-closure attack

BackgroundTo compare the accuracy of nine intraocular lens (IOL) power calculation formulas, including three traditional formulas (SRK/T, Haigis, and Hoffer Q) and six new-generation formulas (Barrett Universal II [BUII], Hill-Radial Basis Function [RBF] 3.0, Kane, Emmetropia verifying optical [EVO], Ladas Super, and Pearl-DGS) in patients who underwent cataract surgery after acute primary angle closure (APAC).MethodsIn this retrospective cross-sectional study, 44 eyes of 44 patients (APAC) and 60 eyes of 60 patients (control) were included. We compared the mean absolute error, median absolute error (MedAE), and prediction error after surgery. Subgroup analyses were performed on whether axial length (AL) or preoperative laser peripheral iridotomy affected the postoperative refractive outcomes.ResultsIn the APAC group, all formulas showed higher MedAE and more myopic shift than the control group (all P < 0.05). In APAC eyes with AL ≥ 22 mm, there were no differences in MedAEs according to the IOL formulas; however, in APAC eyes with AL < 22 mm, Haigis (0.49 D) showed lower MedAE than SRK/T (0.82 D) (P = 0.036) and Hill-RBF 3.0 (0.54 D) showed lower MedAE than SRK/T (0.82 D), Hoffer Q (0.75 D) or Kane (0.83 D) (P = 0.045, 0.036 and 0.027, respectively). Pearl-DGS (0.63 D) showed lower MedAE than Hoffer Q (0.75 D) and Kane (0.83 D) (P = 0.045 and 0.036, respectively). Haigis and Hill-RBF 3.0 showed the highest percentage (46.7%) of eyes with PE within ± 0.5 D in APAC eyes with AL < 22 mm. Iridectomized eyes did not show superior precision than the non-iridotomized eyes in the APAC group.ConclusionsRefractive errors in the APAC group were more myopic than those in the control group. Haigis and Hill-RBF 3.0 showed high precision in the eyes with AL < 22 mm in the APAC group.

Comparison of the accuracy of 9 intraocular lens power calculation formulas after SMILE in Chinese myopic eyes

As of 2021, over 2.8 million small-incision lenticule extraction (SMILE) procedures have been performed in China. However, knowledge regarding the selection of intraocular lens (IOL) power calculation formula for post-SMILE cataract patients remains limited. This study included 52 eyes of 26 myopic patients from northern China who underwent SMILE at Tianjin Eye Hospital from September 2022 to February 2023 to investigate the suitability of multiple IOL calculation formulas in post-SMILE patients using a theoretical surgical model. We compared the postoperative results obtained from three artificial intelligence (AI)-based formulas and six conventional formulas provided by the American Society of Cataract and Refractive Surgery (ASCRS). These formulas were applied to calculate IOL power using both total keratometry (TK) and keratometry (K) values, and the results were compared to the preoperative results obtained from the Barrett Universal II (BUII) formula for the SMILE patients. Among the evaluated formulas, the results obtained from the Emmetropia Verifying Optical 2.0 Formula with TK (EVO-TK) (0.40 ± 0.29 D, range 0–1.23 D), Barrett True K with K formula (BTK-K, 0.41 ± 0.26 D, range 0.01–1.19 D), and Masket with K formula (Masket-K, 0.44 ± 0.33 D, range 0.02–1.39 D) demonstrated the closest proximity to BUII. Notably, the highest proportion of prediction errors within 0.5 D was observed with the BTK-K (71.15%), EVO-TK (69.23%), and Masket-K (67.31%), with the BTK-K showing a significantly higher proportion than the Masket-K (p < 0.001). Our research indicates that in post-SMILE patients, the EVO-TK, BTK-K, and Masket-K may yield more accurate calculation results. At their current stage in development, AI-based formulas do not demonstrate significant advantages over conventional formulas. However, the application of historical data can enhance the performance of these formulas.

The accuracy of intraocular lens power calculation formulas based on artificial intelligence in highly myopic eyes: a systematic review and network meta-analysis.

To systematically compare and rank the accuracy of AI-based intraocular lens (IOL) power calculation formulas and traditional IOL formulas in highly myopic eyes. We screened PubMed, Web of Science, Embase, and Cochrane Library databases for studies published from inception to April 2023. The following outcome data were collected: mean absolute error (MAE), percentage of eyes with a refractive prediction error (PE) within ±0.25, ±0.50, and ±1.00 diopters (D), and median absolute error (MedAE). The network meta-analysis was conducted by R 4.3.0 and STATA 17.0. Twelve studies involving 2,430 adult myopic eyes (with axial lengths >26.0 mm) that underwent uncomplicated cataract surgery with mono-focal IOL implantation were included. The network meta-analysis of 21 formulas showed that the top three AI-based formulas, as per the surface under the cumulative ranking curve (SUCRA) values, were XGBoost, Hill-RBF, and Kane. The three formulas had the lowest MedAE and were more accurate than traditional vergence formulas, such as SRK/T, Holladay 1, Holladay 2, Haigis, and Hoffer Q regarding MAE, percentage of eyes with PE within ±0.25, ±0.50, and ±1.00 D. The top AI-based formulas for calculating IOL power in highly myopic eyes were XGBoost, Hill-RBF, and Kane. They were significantly more accurate than traditional vergence formulas and ranked better than formulas with Wang-Koch AL modifications or newer generations of formulas such as Barrett and Olsen. https://www.crd.york.ac.uk/PROSPERO/, identifier: CRD42022335969.