Accuracy of intraocular lens calculation formulas using a swept-source optical coherence tomography biometer in high myopia

Background: To compare the accuracy of intraocular lens (IOL) calculation formulas in cataract patients with high myopia using the measurements of a swept-source optical coherence tomography (SS-OCT) biometer, the IOLMaster700. Methods: Patients with axial length (AL) equal to or longer than 26.00mm undergoing uneventful cataract surgery were enrolled. Kane, Hill-RBF3.0, EVO, Barrett Universal II, Haigis, and SRK/T formulas were evaluated with the measurements taken by IOLMaster700. The manifest refraction was measured at one month postoperatively. After the mean refractive errors were zeroed out, the mean absolute error (MAE), the median absolute error (MedAE), the standard deviation of prediction error (SD), and the percentage of eyes with refractive errors within ±0.25, ±0.50, ±0.75, and ±1.00 diopter (D) were calculated. A subgroup analysis was based on the axial length. Results: 65 eyes of 65 patients were included. There were signicant differences between the absolute refractive errors predicted by these formulas (P (cid:0) 0.05), but no signicant differences between the percentage of eyes within a certain range of refractive errors (P (cid:0) 0.05). The Kane formula achieved the lowest MAE (0.323D), SD (0.402D), followed by EVO, Hill-RBF3.0, Barrett Universal II, Haigis, and SRK/T formulas. The Kane formula also had the highest percentage of eyes with refractive errors within ±0.50D (80.0%) and ±1.00D (98.5%). The Hill-RBF3.0 formula achieved the lowest MedAE (0.240D). In eyes with an AL ≥ 30.00mm, the Kane formula had the lowest MAE (0.358D). Conclusion: Newer formulas such as Kane, EVO, Hill-RBF3.0, and Barrett Universal II show the highest accuracy in refractive prediction in eyes with high myopia while using the measurements of IOLMaster700. In extremely myopic eyes of six formulas with posthoc analysis showing a signicant difference between EVO

Accuracy of intraocular lens calculation formulas using a swept-source optical coherence tomography biometer in high myopia Chi  Background Today, cataract surgery has been shifted from a rehabilitation procedure to a refractive procedure. The accuracy of refractive prediction could be guaranteed in most emmetropic eyes. [1] However, in high myopic eyes with axial length longer than 26.00mm, the accuracy of refractive prediction remains a challenge, often leading to unexpected postoperative hyperopia. [1][2] The refractive outcome of cataract surgery is in uenced by the choice of IOL calculation formula and the accuracy of the various devices used to measure the eye. [3] IOLMaster700 is a new optical biometer based on swept-source optical coherence tomography. It provides a 1050nm laser infrared light with better penetration in eyes with less transparent ocular media or longer axial length (AL) and displays a retinal OCT image to detect xation status and avoid xation loss. [4][5] The SRK/T and Haigis formulas are relatively more accurate than other traditional third and fourth-generation formulas in eyes with high myopia, [6] and new generation formulas have been developed these years. The differences in the derivation method and metrics used are summarized in Table 1. Barrett Universal II is a 5-variable thick-lens vergence formula. [7] Hill-Radial Basis Function (Hill-RBF) is an arti cial intelligence formula and has been updated to version 3.0. [8] Kane formula is based on theoretical optics as well as regression and arti cial intelligence. [9] The Emmetropia Verifying Optical (EVO) formula is a thick-lens formula based on the theory of emmetropization. [9] The purpose of this study was to investigate the accuracy of IOL power calculation formulas (Barrett Universal II, Hill-RBF3.0, Kane, EVO, SRK/T, and Haigis) in eyes with axial length longer than 26.00mm using an SS-OCT biometer (IOLMaster700). We also evaluated clinical outcomes in subgroups based on axial length.

Ethical approval
This study was approved by the Chinese Ethics Committee of Registering Clinical Trials and was conducted in accordance with the Declaration of Helsinki. The need for written informed consent was waived because of the retrospective design and the use of de-identi ed patient data with approval from the General Hospital of PLA.
The study was registered with the Chinese Clinical Trial Registry.

Patient selection
Consecutive cataract patients with axial length longer than 26.00mm who had uneventful cataract surgery were enrolled. The right eye was selected if patients had bilateral cataract surgery. Patients with previous trauma or surgery, glaucoma, strabismus, corneal pathology, or severe fundus pathology that may affect the accurate biometry were excluded. Patients with a postoperative corrected distance visual acuity worse than 20/40 were excluded. Patients with missing postoperative refractive outcomes were also excluded.

Preoperative examinations
Standard routine preoperative examinations including a slit-lamp examination, ultrasound biometry, fundoscopy, corneal topography, intraocular pressure, and corneal endothelium calculation were performed. The axial length was measured by one experienced technician using a swept-source optical coherence tomography biometer (IOLMaster700, Carl Zeiss Meditec AG). Keratometry (K), anterior chamber depth (ACD), white to white (WTW), and lens thickness (LT) were also measured.

Surgical technique
Phacoemulsi cation cataract surgery with a temporal 3.0mm clear corneal incision was performed by the same

IOL power calculation
Six formulas were calculated through their respective websites. [8][9][10][11][12] The Hill-RBF3.0 allows users to enter target refraction between -2.5D to +1.0D. For IOLs with target refraction less than -2.5D, the predicted refraction was obtained by extrapolation. The manufacturer provided or User Group for Laser Interference (ULIB) optimized constants were used for Akreos Adapt AO, Akreos Adapt, Tecnis ZCB00, and Softec HD IOLs. [13] The constants optimized by our hospital were used for Bigbag and Proming A1-UV IOLs.
Postoperative examinations Manifest refraction was tested by the same experienced technician at least one month after surgery. The postoperative refractive error was de ned as the actual postoperative refraction minus the predicted postoperative refraction. A negative value represented a myopic outcome, whereas a positive value indicated a hyperopic outcome. The mean refractive errors of each formula were adjusted to zero by subtracting an amount equal to the mean refractive error from the postoperative refractive error for each eye. After the mean refractive errors were zeroed out, the mean absolute error (MAE), median absolute error (MedAE), and standard deviation of prediction error (SD) were calculated. For each formula, the percentage of eyes with refractive errors within ±0.25D, ±0.50D, ±0.75D, and ±1.00D were also calculated. The subgroup analysis was performed based on the AL for 26.00≤AL 28.00mm, 28.00≤AL 30.00mm, and AL≥30.00mm.

Statistical analysis
Statistical analyses were performed using SPSS (version 26.0, SPSS Inc) and GraphPad Prism 8 (version 8.2.0, GraphPad Inc). Kolmogorov-Smirnov test was used to assess the normality of data. The single-sample t test or Wilcoxon signed rank-sum test was used to determine whether the mean refractive errors were different from zero. Friedman's nonparametric test was performed to compare the difference in absolute refractive errors. The posthoc test of Wilcoxon signed-rank test with Bonferroni correction was adopted for multiple comparisons.
Cochran's Q test was used to compare the percentage of eyes within a speci c range of refraction errors.
Adjusted P values (by Bonferroni correction) less than 0.05 were considered statistically signi cant.
Demographic characteristics are shown in Table 2. The mean AL was 28.95 ± 2.28 mm, mean corneal power was 43.61 ± 1.34 D, the mean ACD was 3.50 ± 0.43 mm, and the mean LT was 4.31 ± 0.55 mm. The mean IOL power  Table 3, and the box-and-whisker plots of absolute errors are shown in Figure 1. The percentage of eyes within a speci c range of refractive errors is shown in Table 3, and the distribution of refractive errors is shown in Figure 2. The highest percentage within ±0.50D was achieved with Kane (80.0%), followed by Hill-RBF3.0 (78.5%), EVO (78.4%), Barrett Universal II (75.4%), Haigis (66.2%), and SRK/T (60.0%).
With all formulas, the percentage of eyes within ±1.00D was higher than 90.0%, and the highest percentage of eyes with refractive errors within ±1.00D was achieved by the Kane formula (98.5%). The Cochran's Q test con rmed no statistical difference between the percentage of eyes within ±0.25 D, ±0.50 D, and ±1.00 D of refractive errors (P 0.05).
Clinical outcomes of the subgroup The MAE and MedAE for each formula by axial length are shown in Table 4

Discussion
In this study, we investigated the accuracy of IOL calculation formulas in high myopia using the measurements provided by IOLMaster700. Barrett Universal II, Hill-RBF3.0, Kane, EVO, SRK/T, and Haigis formulas were evaluated.
The benchmark standards for refractive outcomes after cataract surgery was established in the UK National Health Service in 2009, that using optimized A constants and partial coherence interferometry, 55% of patients achieving a refractive error within ±0.50D, and 85% of patients achieving a refractive error within ±1.00D. [14] The outcomes of our study outperformed the benchmark standards, with a refractive error within ±0.50D and ±1.00D achieved by at least 60% and 92.3% of patients. For newer generation formulas such as Barrett Universal II, Hill-RBF3.0, Kane, and EVO formulas, the refractive error within ±0.50D and ±1.00D were achieved by at least 75.4% and 95.4% of patients, indicating an improved outcome.
Accurate refractive prediction remains challenging in cataract patients with high myopia. The largest studies analyzed 2060 high myopic eyes. [1] In 2018, Melles et al. [1] compared 1548 eyes with SN60WF (Alcon) and 512 eyes with SA60AT (Alcon) of AL longer than 25.50mm with the Lenstar LS900, the accuracy of formulas including Barrett Universal II, SRK/T, and Haigis. The Barrett Universal II formula had the best outcome and was less in uenced by long axial length. The SRK/T and Haigis performed better than other traditional third and fourth generation formulas. In 2019, Melles et al. [15] evaluated newer formulas including Kane, EVO, and Hill-RBF2.0 using the same dataset, and the Kane formula achieved the lowest MAE, MedAE, and SD in long and extremely long axial length eyes. The Hill-RBF2.0 and EVO formulas were less accurate than Barrett Universal II.
Darcy et al. [16] compared in 637 eyes of AL longer than 26.00mm with the IOLMaster500, the accuracy of formulas including Kane, Barrett Universal II, Hill-RBF2.0, Haigis, and SRK/T. The best formula was Kane with a MAE of 0.329D, followed by Barrett Universal II (0.338D), Hill-RBF2.0 (0.352D), Haigis (0.359D), and SRK/T (0.363D). Similarly, Cheng et al. [17] compared the use of formulas including Kane, Barrett Universal II, Hill-RBF2.0, EVO, and Haigis in 370 eyes of AL longer than 26.00mm with IOLMaster500, and found that the Kane formula yielded the lowest MAE of 0.34D, followed by Barrett Universal II (0.37D), Hill-RBF2.0 (0.38D), EVO (0.40D) and Haigis (0.40D). The Kane formula was comparable to Hill-RBF2.0 and Barrett Universal II in the whole group and was better than Hill-RBF2.0 and Barrett Universal II in extremely myopic eyes with an AL ≥30.00mm. In a study of 79 eyes of AL longer than 26.00mm with OA2000, Rong et al. [18] noted that the MedAE of Barrett Universal II (0.37D) was lower than Haigis (0.46D), and the percentage of eyes within ±0.50D of Barrett Universal II (70%) was higher than Haigis (54%). The refractive errors of the two formulas were lowest in eyes of AL between 28.00mm and 30.00mm. In 2020, several studies with measurements taken by IOLMaster700 were published. In a study of 164 eyes of AL longer than 26.00mm by Zhang et al., [19] EVO was found to have a MAE of 0.35D and 79.27% of patients achieving a refractive error within ±0.50D, better than Barrett Universal II (0.38D, 73.17%).
Carmona-González et al. [20] compared in 115 eyes of AL longer than 25.00mm, the accuracy of formulas including all six formulas analyzed in our study. The lowest MAE was achieved by Barrett Universal II (0. in short, medium, and long eyes have been reported in several studies. [15][16]21] The EVO formula is a thick lens formula based on the theory of emmetropization. In our study, the EVO formula achieved the second-lowest MAE of 0.335D, a MedAE of 0.285D, 78.4% and 96.9% of eyes within ±0.50D and ±1.00D respectively, which was comparable to the results of previous studies. [16,19] In eyes of AL within 26.00mm and 28.00mm, EVO was ranked rst with an MAE of 0.328D, while in eyes of AL longer than 28.00mm, EVO had a higher MAE than Kane and Hill-RBF3.0 formulas. This is consistent with the viewpoint of Melles et al. [15] that the emmetropization concept may break down at the extremes of the axial lengths.
The Hill-RBF is the rst IOL calculation formula based purely on arti cial intelligence and has been updated to version 3.0 in December 2020. To our knowledge, no published study on version 3.0 of the Hill-RBF formula exists to compare our results. Previous studies reported that Hill-RBF2.0 was less accurate than Kane and Barrett Universal II formulas in high myopic eyes. [15][16][17] In our study, Hill-RBF3.0 had a MAE of 0.346D, the lowest MedAE of 0.240D, 78.5% and 95.4% of eyes within ±0.50D and ±1.00D respectively. Hill-RBF3.0 nished behind the Kane formula, but ahead of Barrett Universal II, indicating that it has improved compared with the previous version. The Hill-RBF3.0 allows users to enter target refraction between -2.5D to +1.0D. For high myopic eyes with target refraction less than -2.5D, refractive predictions were obtained by arti cial extrapolation, which led to inconvenience in clinical use. Nevertheless, we still included the dataset obtained by extrapolation in our analysis and achieved a good outcome.
Barrett Universal II is a paraxial ray-tracing thick-lens formula, which accounts for the varying principal planes among different-powered IOLs. It considers the effective lens position (ELP) to be a result of the ACD and a lens factor related to the physical position and the location of the principal planes of the IOL. [2] Barrett Universal II was ranked among the most accurate formulas for high myopic eyes in many studies. [1,22] In our study, Barrett Universal II, with a MAE of 0.361D, a MedAE of 0.313D, 75.4% and 96.9% of eyes within ±0.50D and ±1.00D, was ranked fourth behind newer formulas including Kane, EVO, and Hill-RBF3.0.
SRK/T and Haigis formulas are traditional vergence formulas, which use different numbers of variables to estimate ELP. SRK/T and Haigis formulas were reported superior accuracy over Holladay1, and HofferQ formulas for high myopic eyes. [6] In our study, Haigis achieved a MAE of 0.415D, a MedAE of 0.360D, 66.2% and 92.3% of eyes within ±0.50D and ±1.00D, while SRK/T had a MAE of 0.450D, a MedAE of 0.370D, 60% and 95.4% of eyes within ±0.50D and ±1.00D. The refractive outcomes of the two formulas were comparable to previous studies. [23][24] SRK/T and Haigis formulas were less accurate than other new formulas as we expected. The advantage is that IOL constants of two formulas could be optimized independently, which is convenient for clinicians.
Based on AL subgroups, Kane was comparable to Hill-RBF3.0, EVO, Barrett Universal II formulas in eyes with an AL between 26.00mm and 30.00mm, and had a superior behavior over other formulas in eyes with an AL longer than 30.00mm. The excellent outcome of the Kane formula in extremely high myopic eyes was also detected in a previous study by Cheng et al.. [17] Furthermore, the MAEs and MedAEs were lowest in eyes with an AL within 28.00mm to 30.00mm, as in two previous studies by Rong et al. [18] and Cheng et al.. [17] Rong et al. [18] explained that it is the point at which refractive errors change between myopic and hyperopic. In our study, the refractive errors of Hill-RBF3.0 and Kane formulas changed from hyperopia to myopia, and the refractive errors of the other four formulas changed from myopia to hyperopia as axial length got longer, which supported the viewpoint mentioned before. To avoid hyperopic shift, EVO and Barrett Universal II formulas were preferred in eyes with an AL between 26.00mm and 28.00mm, while Kane and Hill-RBF3.0 formulas were the rst choices in eyes with an AL longer than 30.00mm.
In our study, preoperative measurements were taken by a swept-source optical coherence tomography optical biometer. IOLMaster700, with a longer wavelength, is more successful at measuring AL through dense cataracts and extremely long eyes. [5] The device provides cross retinal OCT images to detect xation status and is expected to produce more precise AL measurement in myopic eyes with posterior staphyloma. [4] Moreover, the device measures LT and WTW, which are optional variables in Kane (LT), Barrett Universal II (LT, WTW), Hill-RBF3.0 (LT, WTW), and EVO (LT), and is expected to further re ne the accuracy of IOL formulas.
Nevertheless, the refractive outcomes achieved in our study are consistent with results based on other biometers. [17,21,24] The reason could be that any clinical differences, such as the range of AL included, the type of IOLs, and the selection of IOL constants, affect the refractive prediction of IOL calculation formulas. When comparing the differences in refractive prediction of different devices, biometric measurements should be carried out on the same group of patients and reduce the in uence of any other clinical factors.
Our study had several limitations. 1.Lens constant optimization for new generation formulas was limited because they were not published; instead, the mean refractive errors were simply zeroed out to eliminate systematic errors. Although different from traditional lens constant optimization, that was suggested by protocols of IOL formula accuracy provided by Wang et al.. [25] 2. Data from multiple IOL models were included, which might introduce bias due to different IOL models. However, in modern surgery, multiple IOLs are used, and the results may have greater generalizability. 3. A small number of eyes were evaluated in our study compared to other studies, and further studies with a larger sample size are needed to investigate the difference in each subgroup.

Conclusions
In conclusion, newer formulas such as Kane, EVO, Hill-RBF3.0, and Barrett Universal II yielded accurate refractive prediction in eyes with high myopia while using the measurements of IOLMaster700. In eyes with AL ≥30.00mm, Availability of data and materials The datasets used and/or analysed during the current study are available from the corresponding author upon reasonable request.
CZ and ZY contributed to this work equally. CZ collected and analyzed the data, drafted the initial manuscript, and revised the manuscript. ZY coordinated and supervised data collection, drafted the initial manuscript, and revised the manuscript. WQC, YG, and TJM collected the data. ZHL conceptualized and designed the study, critically reviewed the manuscript, and revised the manuscript. All authors read and approved the nal manuscript. Tables   Table 1. Summary of intraocular lens formulas   Figure 1 Box-and-whisker plots of absolute errors (in diopters) for each formula Comparison of prediction errors (in diopters) for each formula (axial length)

Supplementary Files
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