Intraocular Lens Power Calculation Formulas Research Articles

Accuracy of intraocular lens calculation formulas based on swept-source OCT biometer in cataract patients with phakic intraocular lens

PurposeTo research the accuracy of intraocular lens (IOL) calculation formulas and investigate the effect of anterior chamber depth (ACD) and lens thickness (LT) measured by swept-source optical coherence tomography biometer (IOLMaster 700) in patients with posterior chamber phakic IOL (PC-pIOL).MethodsRetrospective case series. The IOLMaster 700 biometer was used to measure axial length (AL) and anterior segment parameters. The traditional formulas (SRK/T, Holladay 1 and Haigis) with or without Wang-Koch (WK) AL adjustment, and new-generation formulas (Barret Universal II [BUII], Emmetropia Verifying Optical [EVO] v2.0, Kane, Pearl-DGS) were utilized in IOL power calculation.ResultsThis study enrolled 24 eyes of 24 patients undergoing combined PC-pIOL removal and cataract surgery at Xiamen Eye Center of Xiamen University, Xiamen, Fujian, China. The median absolute prediction error in ascending order was EVO 2.0 (0.33), Kane (0.35), SRK/T-WKmodified (0.42), Holladay 1-WKmodified (0.44), Haigis-WKC1 (0.46), Pearl-DGS (0.47), BUII (0.58), Haigis (0.75), SRK/T (0.79), and Holladay 1 (1.32). The root-mean-square absolute error in ascending order was Haigis-WKC1 (0.591), Holladay 1-WKmodified (0.622), SRK/T-WKmodified (0.623), EVO (0.673), Kane (0.678), Pearl-DGS (0.753), BUII (0.863), Haigis (1.061), SRK/T (1.188), and Holladay 1 (1.513). A detailed analysis of ACD and LT measurement error revealed negligible impact on refractive outcomes in BUII and EVO 2.0 when these parameters were incorporated or omitted in the formula calculation.ConclusionThe Kane, EVO 2.0, and traditional formulas with WK AL adjustment displayed high prediction accuracy. Furthermore, the ACD and LT measurement error does not exert a significant influence on the accuracy of IOL power calculation formulas in highly myopic eyes implanted with PC-pIOL.

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 diopter (D) for BU II, 0.22 ± 0.37 D for BTAL, and 0.10 ± 0.37 D for EVO ( P < .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 < .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 < .0001). The new EVO and BTAL formulas showed higher accuracy than BU II in short eyes, whereas there was no difference in long eyes.

Evaluation of the Accuracy of Intraocular Lens Power Calculation Formulas in Phacovitrectomy.

The aim of this study was to evaluate the refractive error in patients undergoing combined phacovitrectomy with and without gas tamponade. This was a retrospective chart review including patients undergoing phacoemulsification alone (Group 1), combined phacovitrectomy for epiretinal membrane (Group 2), and combined phacovitrectomy with gas tamponade for rhegmatogenous retinal detachment (RRD) (Group 3). Axial length and keratometry were measured using an optical biometric system (Argos, Alcon Laboratories. Inc.), and a three-piece intraocular lens (IOL; NX-70S) was implanted in all groups. In each group, the prediction error at 3 months was calculated using IOL power calculation formulas (SRK/T, Hill-RBF, Kane, and Barrett Universal II) for each eye. Outcome measures included the mean prediction error (MPE), its standard deviation (SD), and the mean absolute error (MAE). The change in IOL position at 3 months was also assessed using anterior segment optical coherence tomography. A total of 104 eyes were included (Group 1: 30; Group 2: 34; Group 3: 40 eyes). The MPE was -0.08 ± 0.37 diopters (D), -0.26 ± 0.32 D, and -0.59 ± 0.34 D in Group 1, Group 2, and Group 3, respectively, using the Barrett Universal II formula (P < 0.01, ANOVA). The movement forward in the IOL position was 0.95 ± 0.16mm, 0.94 ± 0.12mm, and 1.07 ± 0.20mm in Group 1, Group 2, and Group 3, respectively (P < 0.01). No significant difference was shown in MPE among the four formulas after combined phacovitrectomy with gas (P = 0.531). Phacovitrectomy in RRD induced a significant myopic shift using any of the clinically available formulas. This suggests that myopic shift should be taken into consideration for better refractive outcomes in phacovitrectomy with gas tamponade in RRD.

Comparison of intraocular lens power prediction by American Society of Cataract and Refractive Surgery formulas and Barrett True-K TK in eyes with prior laser refractive surgery.

To evaluate the prediction accuracy of various intraocular lens (IOL) power calculation formulas on American Society of Cataract and Refractive Surgery (ASCRS) calculator and Barrett True-K total keratometry (TK) in eyes with previous laser refractive surgery for myopia. This retrospective study included eyes with history of myopic laser refractive surgery, which have undergone clear or cataractous lens extraction by phacoemulsification followed by IOL implantation. Those who underwent uneventful crystalline lens extraction were included. Eyes with any complication of refractive surgery or those with eventful lens extraction procedure and those who were lost to follow-up were excluded. Formulas compared were Wang-Koch-Maloney, Shammas, Haigis-L, Barrett True-K no-history formula, ASCRS average power, ASCRS maximum power on the ASCRS post-refractive calculator and the IOLMaster 700 Barrett True-K TK. Prediction error was calculated as the difference between the implanted IOL power and the predicted power by various formulae available on ASCRS online calculator. Forty post-myopic laser-refractive surgery eyes of 26 patients were included. Friedman's test revealed that Shammas formula, Barrett True-K, and ASCRS maximum power were significantly different from all other formulas (P < 0.00001 for each). Median absolute error (MedAE) was the least for Shammas and Barrett True-K TK formulas (0.28 [0.14, 0.36] and 0.28 [0.21, 0.39], respectively) and the highest for Wang-Koch-Maloney (1.29 [0.97, 1.61]). Shammas formula had the least variance (0.14), while Wang-Koch-Maloney formula had the maximum variance (2.66). In post-myopic laser refractive surgery eyes, Shammas formula and Barrett True-K TK no-history formula on ASCRS calculator are more accurate in predicting IOL powers.

Spherical Equivalent Prediction Analysis in IOL Power Calculations Using Eyetemis, A Comprehensive Approach.

To compare two different datasets, using Eyetemis, an online analytical tool designed for assessing the spherical equivalent prediction errors (SEQ-PE) of intraocular lens (IOL) power calculation formulas following cataract surgery. Institutional. Retrospective case series. The study was comprised of two distinct datasets of patients who had undergone successful cataract surgery. Dataset-1 includes standard eyes whereas Dataset-2 includes eyes with keratoconus. An online tool was used for SEQ-PE analysis across the 2 datasets, adhering to ISO standards for evaluating accuracy based upon trueness and precision. The tool incorporates robust t-tests for comparing the trimmed-mean of the data, adjusting for heteroscedasticity. IOL constants in Dataset-1 were optimized for the comparison of Hoffer Q, Holladay1, SRK/T, Haigis and Barrett Universal II (BUII) formulas. In Dataset-2, IOL constants from the IOLCon website, were used for the comparison of the BUII and its designated KCN-version: Barrett TrueK Keratoconus (TrueK [KCN]). For Dataset-1: the trimmed-mean SEQ-PE values of all formulas were not significantly different from zero. BUII had superior precision and accuracy compared to all other formulas except from Haigis (P≤ 0.04). For Dataset-2: BUII's trimmed-mean SEQ-PE was significantly different from zero (0.59D, P< 0.01), unlike the TrueK [KCN] (0.12D, P= 0.10). Additionally, TrueK [KCN] exhibited enhanced precision and accuracy relative to BUII (P< 0.01). The online analysis tool provides a streamlined approach for assessing the prediction accuracy of SEQ refraction following cataract surgery, effectively evaluating trueness, precision, and overall accuracy through the use of advanced statistical methods.

Comparing the accuracy of intraocular lens power calculation formulas using artificial intelligence and traditional formulas in highly myopic patients: a meta-analysis.

The accuracy of intraocular lens (IOL) calculations is one of the key indicators for determining the success of cataract surgery. However, in highly myopic patients, the calculation errors are relatively larger than those in general patients. With the continuous development of artificial intelligence (AI) technology, there has also been a constant emergence of AI-related calculation formulas. The purpose of this investigation was to evaluate the accuracy of AI calculation formulas in calculating the power of IOL for highly myopic patients. We searched the relevant literature through August 2023 using three databases: PubMed, EMBASE, and the Cochrane Library. Six IOL calculation formulas were compared: Kane, Hill-RBF, EVO, Barrett II, Haigis, and SRK/T. The included metrics were the mean absolute error (MAE) and percentage of errors within ± 0.25 D, ± 0.50 D, and ± 1.00 D. The results showed that the MAE of Kane was significantly lower than that of Barrett II (mean difference = - 0.03 D, P = 0.02), SRK/T (MD = - 0.08 D, P = 0.02), and Haigis (MD = - 0.12 D, P < 0.00001). The percentage refractive prediction errors for Kane at ± 0.25 D, ± 0.50 D, and ± 1.00 D were significantly greater than those for SRK/T (P = 0.007, 0.003, and 0.01, respectively) and Haigis (P = 0.009, 0.0001, and 0.001, respectively). No statistically significant differences were noted between Hill-RBF and Barret, but Hill-RBF was significantly better than SRK/T and Haigis. The AI calculation formulas showed more accurate results compared with traditional formulas. Among them, Kane has the best performance in calculating IOL degrees for highlymyopic patients.

Comparative accuracy of intraocular lens power calculation formulas when targeting myopia

PurposeThis study aims to compare the accuracies of intraocular lens (IOL) power calculation formulas when targeting myopia versus emmetropia. MethodsA total of 450 patients were included, with 225 patients targeting emmetropia and 225 patients aiming for approximately −2.0 diopters of myopia. This retrospective analysis utilized data from a single eye of each patient, with preoperative biometric measurements obtained using the IOL Master 700. The study considered established formulas such as Haigis, Hoffer Q, Holladay 1, Holladay 2, and SRK/T, as well as modern formulas including Barrett Universal II, Cooke K6, EVO 2.0, Hill-RBF, Hoffer QST, Kane, Olsen, and PEARL-DGS. Statistical analyses, including Friedman test and post hoc analysis, were employed to compare the accuracy of each IOL power calculation formula between the two groups. Additionally, a multiple regression analysis was conducted to identify variables influencing the accuracy of intraocular lens power calculation formulas. ResultsIn targeting myopia, all IOL formulas tended to exhibit a greater refractive error compared to when targeting emmetropic eyes. Notably, the Haigis, SRK/T, and Holladay 2 formulas were found to be highly influenced by this trend, while the modern formulas were less affected. ConclusionThe accuracy of IOL power calculation formulas diminishes when targeting myopia in comparison to emmetropia. However, the modern formulas appear less susceptible to this trend. Consequently, when aiming for myopia, the use of the modern formulas is recommended for enhanced accuracy in IOL power calculation.

A New Method to Minimize the Standard Deviation and Root Mean Square of the Prediction Error of Single-Optimized IOL Power Formulas.

The purpose of this study was to develop a simplified method to approximate constants minimizing the standard deviation (SD) and the root mean square (RMS) of the prediction error in single-optimized intraocular lens (IOL) power calculation formulas. The study introduces analytical formulas to determine the optimal constant value for minimizing SD and RMS in single-optimized IOL power calculation formulas. These formulas were tested against various datasets containing biometric measurements from cataractous populations and included 10,330 eyes and 4 different IOL models. The study evaluated the effectiveness of the proposed method by comparing the outcomes with those obtained using traditional reference methods. In optimizing IOL constants, minor differences between reference and estimated A-constants were found, with the maximum deviation at -0.086 (SD, SRK/T, and Vivinex) and -0.003 (RMS, PEARL DGS, and Vivinex). The largest discrepancy for third-generation formulas was -0.027mm (SD, Haigis, and Vivinex) and 0.002mm (RMS, Hoffer Q, and PCB00/SN60WF). Maximum RMS differences were -0.021 and +0.021, both involving Hoffer Q. Post-minimization, the largest mean prediction error was 0.726 diopters (D; SD) and 0.043 D (RMS), with the highest SD and RMS after adjustments at 0.529 D and 0.875 D, respectively, indicating effective minimization strategies. The study simplifies the process of minimizing SD and RMS in single-optimized IOL power predictions, offering a valuable tool for clinicians. However, it also underscores the complexity of achieving balanced optimization and suggests the need for further research in this area. The study presents a novel, clinically practical approach for optimizing IOL power calculations.

Investigation of the myopic outcomes of the newer intraocular lens power calculation formulas in Korean patients with long eyes

This study investigated the underlying causes of the myopic outcomes of the optic-based newer formulas (Barrett Universal II, EVO 2.0, Kane, Hoffer-QST and PEARL-DGS) in long Korean eyes with Alcon TFNT intraocular lens (IOL) implantation. Postoperative data from 3100 randomly selected eyes of 3100 patients were analyzed to compare the reference back-calculated effective lens positions (ELPs) based on the Haigis formula using conventional axial length (AL) and Cooke-modified AL (CMAL) with the predicted ELP of each single- and triple-optimized Haigis formula applied to AL- and CMAL. Contrary to the AL-applied Haigis formula, the predicted ELP curve of the CMAL-applied, single-optimized Haigis formula, simulating the methods of the newer formulas, exhibited a significant upward deviation from the back-calculated ELP in long eyes. The relationship between the AL and anterior chamber depth in our long-eyed population differed from that in the base population of the PEARL-DGS formula. The myopic outcomes in long eyes appeared to stem from the substantial overestimation of the postoperative IOL position with AL modification, leading to the implantation of inappropriately higher-powered IOLs. This discrepancy may be attributed to the ethnic differences in ocular biometrics, particularly the relatively smaller anterior segment in East Asian patients with long AL.

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.

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.