Intraocular Lens Power Calculation Formulas Research Articles

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.

Effect of Segmented Optical Axial Length on the Performance of New-Generation Intraocular Lens Power Calculation Formulas in Extremely Long Eyes.

To evaluate the performance of traditional vergence formulas with segmented axial length (AL) compared to traditional composite AL in extremely long eyes, and to determine whether the segmented AL can be extended to the new-generation formulas, including the Barrett Universal II, Emmetropia Verifying Optical 2.0 (EVO2), Hill-RBF 3.0 (Hill3), Kane, and Ladas Super formula (LSF) formulas in extremely long eyes. National Hospital. Organization, Tokyo Medical Center, Japan. Retrospective case series. Consecutive patients who underwent uncomplicated cataract surgery implanted with a three-piece intraocular lens between December 2015 and March 2021 were retrospectively reviewed. The composite AL was measured with a swept-source optical coherence tomography (SS-OCT) biometer using a mean refractive index. The segmented AL was calculated by summing the geometric lengths of the ocular segments (cornea, aqueous, lens, and vitreous) using multiple specific refractive indices based on the data obtained by the SS-OCT-based biometer. When refraction was measured at three months postoperatively, the median absolute errors (MedAEs) were calculated with two ALs for each formula. The study included 31 eyes of 22 patients. The segmented AL (30.45 ± 1.23 mm) was significantly shorter than the composite AL (30.71 ± 1.28 mm, p < 0.001). The MedAEs were significantly reduced when using segmented AL for SRK/T, Haigis, Hill3, and LSF, compared to those obtained using composite AL (0.38 vs. 0.62, 0.48 vs. 0.79, 0.50 vs. 0.90, 0.34 vs. 0.61, p < 0.001 for all formulas, respectively). On the contrary, the MedAE obtained by Kane with segmented AL was significantly worse compared to the one with composite AL (0.35 vs. 0.27, p = 0.03). In extremely high myopic eyes, the segmented AL improves the performance of SRK/T, Haigis, Hill3, and LSF formulas compared to the composite AL, while the segmented AL worsens the prediction accuracy of the Kane formula.

Comparative analysis of IOL power calculations in postoperative refractive surgery patients: a theoretical surgical model for FS-LASIK and SMILE procedures

BackgroundAs the two most prevalent refractive surgeries in China, there is a substantial number of patients who have undergone Femtosecond Laser-assisted In Situ Keratomileusis (FS-LASIK) and Small Incision Lenticule Extraction (SMILE) procedures. However, there is still limited knowledge regarding the selection of intraocular lens (IOL) power calculation formulas for these patients with a history of FS-LASIK or SMILE.MethodsA total of 100 eyes from 50 postoperative refractive surgery patients were included in this prospective cohort study, with 25 individuals (50 eyes) having undergone FS-LASIK and 25 individuals (50 eyes) having undergone SMILE. We utilized a theoretical surgical model to simulate the IOL implantation process in postoperative FS-LASIK and SMILE patients. Subsequently, we performed comprehensive biological measurements both before and after the surgeries, encompassing demographic information, corneal biometric parameters, and axial length. Various formulas, including the Barrett Universal II (BUII) formula, as a baseline, were employed to calculate IOL power for the patients.ResultsThe Barrett True K (BTK) formula, demonstrated an mean absolute error (AE) within 0.5 D for both FS-LASIK and SMILE groups (0.28 ± 0.25 D and 0.36 ± 0.24 D, respectively). Notably, the FS-LASIK group showed 82% of results differing by less than 0.25 D compared to preoperative BUII results. The Barrett True K No History (BTKNH) formula, which also incorporates measured posterior corneal curvature, performed similarly to BTK in both groups. Additionally, the Masket formula, relying on refractive changes based on empirical experience, displayed promising potential for IOL calculations in SMILE patients compared with BTK (p = 0.411).ConclusionThe study reveals the accuracy and stability of the BTK and BTKNH formulas for IOL power calculations in myopic FS-LASIK/SMILE patients. Moreover, the Masket formula shows encouraging results in SMILE patients. These findings contribute to enhancing the predictability and success of IOL power calculations in patients with a history of refractive surgery, providing valuable insights for clinical practice. Further research and larger sample sizes are warranted to validate and optimize the identified formulas for better patient outcomes.

Refractive Outcomes of Cataract Surgery in Patients With Intrastromal Femtosecond Laser Treatment of Presbyopia (INTRACOR).

To evaluate the outcomes of cataract surgery with intraocular lens (IOL) implantation in patients who underwent intrastromal femtosecond laser treatment of presbyopia (INTRACOR). This was an interventional case series of 8 patients (10 eyes) who presented for cataract surgery 6.1 ± 3.2 years (mean ± standard deviation [SD]) after INTRACOR (Technolas Perfect Vision GmbH) treatment. A monofocal IOL was implanted in 9 eyes (7 patients) and a small-aperture IOL was implanted in 1 eye. The IOL power was calculated without adjustments using biometry obtained after the INTRACOR treatment. For additional calculations, keratometry obtained before the INTRACOR treatment was used. Postoperative examinations included visual acuity testing, manifest refraction, defocus curve, ocular biometry, corneal tomography, aberrometry, anterior segment optical coherence tomography, and slit-lamp examination. After the cataract surgery, the mean ± SD uncorrected distance visual acuity was 0.37 ± 0.17 logMAR, the corrected distance visual acuity was 0.10 ± 0.10 logMAR, and the manifest refraction spherical equivalent, adjusted to infinity, was +0.39 ± 0.63 diopters (D). Intermediate and near visual acuity, both uncorrected and distance-corrected, and distance-corrected defocus curves varied considerably among patients. Using biometry performed after INTRACOR, the traditional IOL power calculation formulas produced hyperopic outcomes, with the mean ± SD prediction error ranging from +0.72 ± 0.34 to +0.96 ± 0.41 D. Although the mean ± SD prediction error decreased (range: -0.34 ± 0.56 to -0.15 ± 0.53 D) when using keratometry obtained before INTRACOR, the accuracy remained low due to high variability. In patients with cataract who had previous INTRACOR treatment, IOL power calculation could be inaccurate, with a tendency toward hyperopic outcomes. These results require confirmation in more extensive studies. [J Refract Surg. 2023;39(10):676-682.].

Network Meta-analysis of Intraocular Lens Power Calculation Formula Accuracy in 1016 Eyes With Long Axial Length

To systematically review the literature and quantitatively synthesize the currently available evidence to compare the accuracy of different intraocular lens calculation formulas in eyes with long axial length (AL). Network meta-analysis. PubMed, Embase, Web of Science, and the Cochrane Library were systematically searched for studies published between January 2000 and June 2022. Included were prospective or retrospective clinical studies reporting the following outcomes in cataract patients with long AL (ie, ≥26 mm): percentage of eyes with a prediction error (PE) within ±0.25, ±0.50, and ±1.00 diopters (D). Network meta-analysis was conducted using R software (version 4.2.1). Ten prospective or retrospective clinical studies, including 1016 eyes and 11 calculation formulas, were identified. A traditional meta-analysis showed that for the percentage of eyes with PE within ±0.25 and ±0.50 D, the Olsen, Kane, and Emmetropia Verifying Optical (EVO) all had insignificantly higher percentages compared with others. Considering the percentage of eyes with PE within ±1.00 D, the original and modified Wang-Koch adjustment formulas for Holladay 1 (H1-WK and H1-MWK) and EVO formulas showed superiority, but the difference was insignificant. This network meta-analysis revealed that compared with the widely used Barrett Universal II (BUII) formula, the Olsen, Kane, and EVO formulas had higher percentages of eyes with PE within ±0.25, ±0.50, and ±1.00 D (all odds ratios >1 but P >.05). Based on the surface under the cumulative ranking area (SUCRA) values for the percentage of eyes with PE within ±0.25 D, the Olsen (96.4%), Kane (77.5%), and EVO (75.9%) formulas had the highest probability of being in the top 3 of the 11 formulas. The Olsen, Kane, and EVO formulas may perform better than others in calculating IOL power in eyes with long AL. Nevertheless, there is still considerable uncertainty in this regard and the accuracy of these formulas in highly myopic eyes should be confirmed in studies based on large multicenter registries.

Intraocular Lens Power Calculation Formulas-A Systematic Review.

The proper choice of an intraocular lens (IOL) power calculation formula is an important aspect of phacoemulsification. In this study, the formulas most commonly used today are described and their accuracy is evaluated. This review includes papers evaluating the accuracy of IOL power calculation formulas published during the period from January 2015 to December 2022. The articles were identified by a literature search of medical and other databases (PubMed/MEDLINE, Crossref, Web of Science, SciELO, Google Scholar, and Cochrane Library) using the terms "IOL formulas," "Barrett Universal II," "Kane," "Hill-RBF," "Olsen," "PEARL-DGS," "EVO," "Haigis," "SRK/T," and "Hoffer Q." Twenty-nine of the most recent peer-reviewed papers in English with the largest samples and largest number of formulas compared were considered. Outcomes of mean absolute error and percentage of predictions within ±0.5 D and ±1.0 D were used to evaluate the accuracy of the formulas. In most studies, Barrett achieved the smallest mean absolute error and PEARL-DGS the highest percentage of patients with ±0.5 D in short eyes, while Kane obtained the highest percentage of patients with ±0.5 D in long eyes. The third- and fourth-generation formulas are gradually being replaced by more accurate ones. The Barrett Universal II among vergence formulas and Kane and PEARL-DGS among artificial intelligence-based formulas are currently most often reported as the most precise.

Accuracy of Different Intraocular Lens Calculation Formulas in Patients with High Axial Myopia

Background The two main problems encountered in calculation of intra ocular lens power are the measurement of the proper axial length (AL), and the lack of accuracy of the available formulas that calculate the power of the intra ocular lens in cases of eyes with high axial length. Aim of the Work To compare the accuracy of intraocular lens (IOL) calculation formulae (Holladay I, Haigis, SRK/T, Hoffer Q, Holladay II, and Barrett Universal II) in the prediction of postoperative refraction for eyes with AL 26.0 mm or more. Patients and Methods A prospective study was carried on forty-seven eyes of forty-seven patients. All the patients were managed at Ain Shams University Hospitals in cooperation with a specialized centre between April 2019 and March 2020. Results Mean absolute error (MAE) was calculated for each formula showed that the least MAE is for Barrett Universal II formula. SRK/T formula is the 2nd lower MAE followed by Haigis formula and the last is Holladay II formula. The scatter plots between AL and absolute error from each of the six calculations formulae was done and showed that Barrett universal II has negative correlation with AL. As for SRK/T and Haigis formulae there is a linear correlation. Numerical Predictive Error showed that SRK/T formula had the lowest mean numerical error followed by Haigis formula then Barrett Universal II and last came Holladay II formula. Conclusion for high axial myopic eyes, the Barrett Universal II formula is the best in this group of patients and provide the lowest mean absolute error, highest percentage of eyes within ≤ ± 0.50 D and the lowest risk of refractive surprise compared to other IOL power calculation formulae. Then comes Haigis and SRK/T formulae which performed similarly and provide a good predictable outcome then at last came Holladay II formula.

Comparison of Accuracy of 6 Modern Intraocular Lens Power Calculation Formulas.

To compare the accuracy of modern intraocular lens (IOL) power calculation formulas in predicting refractive outcomes after standard cataract surgery. The medical records of 203 eyes of 203 patients that received phacoemulsification and IOL implantation were retrospectively reviewed. Partial coherence interferometry was used to obtain the biometric values. The refractive outcomes of Barrett Universal II (BUII), Emmetropia Verifying Optical (EVO) 2.0, Hill-RBF 3.0, Hoffer QST, Kane, and PEARL-DGS formulas were evaluated. Axial length subgroup analysis was done separately. The correlations between the prediction error calculated by each formula and axial length (AL) and corneal power were also analyzed. Overall, there was no significant difference between the absolute prediction errors predicted by the six formulas after adjusting the mean prediction error (p = 0.058). AL subgroup analysis of absolute error also showed that there is no significant difference between the formulas. The BUII and Hill-RBF 3.0 formulas showed a higher percentage of eyes with PE within ±0.50 D compared to the Hoffer QST formula (p = 0.022 and p = 0.035). However, there was no significant difference after Bonferroni correction was applied. The BUII formula showed the highest IOL Formula Performance Index (FPI) and therefore the highest accuracy, followed by PEARL-DGS, EVO 2.0, Kane, Hill-RBF 3.0 and Hoffer QST formulas. Out of the six formulas, the prediction error calculated by the Hoffer QST was significantly correlated with the AL (p = 0.011). None of the prediction errors calculated by the six formulas showed correlation to the corneal power. Analysis of the prediction error showed that the 6 modern IOL power calculation formulas have comparable accuracy overall and across different ranges of axial length.

Accuracy of Traditional and Modern Formulas for Intraocular Lens Power Calculation After Radial Keratotomy Using Standard Keratometry.

To compare the accuracy of multiple traditional and modern intraocular lens (IOL) power calculation formulas in post-radial keratotomy (RK) patients undergoing cataract surgery. This retrospective case series included 50 eyes with prior RK who underwent routine phacoemulsification surgery with single-piece acrylic IOL implantation (A constant = 118.8). Outcomes of multiple formulas were calculated. Included formulas were SRK/T, Holladay 1, Holladay 2, Haigis, Barrett True-K, Haigis and Barrett True-K (target refraction of 0.50 D), Barrett Universal II, Kane, PEARL-DGS, Shammas no history, DK SRK/T, DK SRK/T (target refraction of 0.50 D), Double K (DK) Holladay 1, and DK Holladay 1 (target refraction of 0.50 D). Averages of multiple combinations of best-performing single formulas were calculated. Primary outcome is mean absolute error (MAE). Haigis (with -0.50 D target refraction) and DK SRK/T showed the lowest mean and median absolute errors (MedAE) followed by Haigis, Barrett True-K, and Barrett True-K (with -0.50 D target refraction). Combinations of 3, 4, or 5 of best performing single formulas yielded good results with >60% of cases within +0.50 D of intended refraction and MAE around 0.50 D. The best performing formulas with flatter K readings were PEARL-DGS and Haigis (with additional -0.50 D target refraction) with MAE of 0.72 + 0.71 D and 0.70 + 0.70 D, respectively, followed by Barrett True-K (with intended -0.50 D target refraction) with MAE of 0.75 + 0.63 D. Using an average of three or more Haigis (with -0.50 D target refraction), the Barrett True-K, DK Holladay 1, and DK SRK/T formulas showed better outcomes than using a single formula for IOLMaster 700 standard K readings. The PEARL-DGS formula showed better accuracy in eyes with flatter K readings (<38 D).

Efficacy of segmented axial length and artificial intelligence approaches to intraocular lens power calculation in short eyes.

In short eyes, to compare the predictive accuracy of newer intraocular lens (IOL) power calculation formulas using traditional and segmented axial length (AL) measurements. Cullen Eye Institute, Baylor College of Medicine, Houston, Texas and East Valley Ophthalmology, Mesa, Arizona. Multi-center retrospective case series. Measurements from an optical biometer were collected in eyes with AL <22 mm. IOL power calculations were performed with 15 formulas using 2 AL values: (1) machine-reported traditional AL (Td-AL) and (2) segmented AL calculated with the Cooke-modified AL nomogram (CMAL). 1 AL method and 7 formulas were selected for pairwise analysis of mean absolute error (MAE) and root mean square absolute error (RMSAE). The study comprised 278 eyes. Compared with the Td-AL, the CMAL produced hyperopic shifts without differences in RMSAE. The ZEISS AI IOL Calculator (ZEISS AI), K6, Kane, Hill-RBF, Pearl-DGS, EVO, and Barrett Universal II (Barrett) formulas with Td-AL were compared pairwise. The ZEISS AI demonstrated smaller MAE and RMSAE than the Barrett, Pearl-DGS, and Kane. K6 had a smaller RMSAE than the Barrett formula. In 73 eyes with shallow anterior chamber depth, the ZEISS AI and Kane had a smaller RMSAE than the Barrett. ZEISS AI outperformed Barrett, Pearl-DGS, and Kane. The K6 formula outperformed some formulas in selected parameters. Across all formulas, use of a segmented AL did not improve refractive predictions.

Refractive outcome and lens power calculation after intrascleral intraocular lens fixation: a comparison of three-piece and one-piece intrascleral fixation technique

PurposeTo evaluate the refractive prediction error of common intraocular lens (IOL) power calculation formulae in patients who underwent intrascleral IOL fixation using two different techniques.MethodsThis is a prospective, randomized, longitudinal, single-site, single-surgeon study. Patients who underwent intrascleral IOL implantation using the Yamane or the Carlevale technique were followed up for a period of six months postoperatively. Refraction was measured using the best-corrected visual acuity at 4 m (EDTRS chart). Lens decentration, tilt and effective lens position (ELP) were assessed using an anterior segment optical coherence tomography (AS-OCT). The prediction error (PE) and the absolute error (AE) were evaluated for the SRK/T, Hollayday1 and Hoffer Q formula. Subsequently, correlations between the PE and axial length, keratometry, white to white and ELP were assessed.ResultsIn total, 53 eyes of 53 patients were included in the study. Twenty-four eyes of 24 patients were in the Yamane group (YG) and 29 eyes of 29 patients were in the Carlevale group (CG). In the YG, the Holladay 1 and Hoffer Q formulae resulted in a hyperopic PE (0.02 ± 0.56 D, and 0.13 ± 0.64 D, respectively) while in the SRK/T formula the PE was slightly myopic (− 0.16 ± 0.56 D). In the CG, SRK/T and Holladay 1 formulae led to a myopic PE (− 0.1 ± 0.80 D and − 0.04 ± 0.74 D, respectively), Hoffer Q to a hyperopic PE (0.04 ± 0.75 D). There was no difference between the PE of the same formulae across both groups (P > 0.05). In both groups the AE differed significantly from zero in each evaluated formula. The AE error was within ± 0.50 D in 45%–71% and was within ± 1.00 D in 72%–92% of eyes depending on the formula and surgical method used. No significant differences were found between formulae within and across groups (P > 0.05). Intraocular lens tilt was lower in the CG (6.45 ± 2.03°) compared to the YG (7.67 ± 3.70°) (P < 0.001). Lens decentration was higher in the YG (0.57 ± 0.37 mm) than in the CG (0.38 ± 0.21 mm), though the difference was not statistically significant (P = 0.9996).ConclusionsRefractive predictability was similar in both groups. IOL tilt was better in the CG, however this did not influence the refractive predictability. Though not significant, Holladay 1 formula seemed to be more probable than the SRK/T and Hoffer Q formulae. However, significant outliers were observed in all three different formulae and therefore remain a challenging task in secondary fixated IOLs.

The Zhu-Lu formula: a machine learning-based intraocular lens power calculation formula for highly myopic eyes

BackgroundTo develop a novel machine learning-based intraocular lens (IOL) power calculation formula for highly myopic eyes.MethodsA total of 1828 eyes (from 1828 highly myopic patients) undergoing cataract surgery in our hospital were used as the internal dataset, and 151 eyes from 151 highly myopic patients from two other hospitals were used as external test dataset. The Zhu-Lu formula was developed based on the eXtreme Gradient Boosting and the support vector regression algorithms. Its accuracy was compared in the internal and external test datasets with the Barrett Universal II (BUII), Emmetropia Verifying Optical (EVO) 2.0, Kane, Pearl-DGS and Radial Basis Function (RBF) 3.0 formulas.ResultsIn the internal test dataset, the Zhu-Lu, RBF 3.0 and BUII ranked top three from low to high taking into account standard deviations (SDs) of prediction errors (PEs). The Zhu-Lu and RBF 3.0 showed significantly lower median absolute errors (MedAEs) than the other formulas (all P < 0.05). In the external test dataset, the Zhu-Lu, Kane and EVO 2.0 ranked top three from low to high considering SDs of PEs. The Zhu-Lu formula showed a comparable MedAE with BUII and EVO 2.0 but significantly lower than Kane, Pearl-DGS and RBF 3.0 (all P < 0.05). The Zhu-Lu formula ranked first regarding the percentages of eyes within ± 0.50 D of the PE in both test datasets (internal: 80.61%; external: 72.85%). In the axial length subgroup analysis, the PE of the Zhu-Lu stayed stably close to zero in all subgroups.ConclusionsThe novel IOL power calculation formula for highly myopic eyes demonstrated improved and stable predictive accuracy compared with other artificial intelligence-based formulas.

A Simplified Method to Minimize Systematic Bias of Single-Optimized Intraocular Lens Power Calculation Formulas

To provide a simplified method to optimize lens constants to zero the mean prediction error (ME) of an intraocularlens (IOL) calculation formula, without the need to program the formula itself, by exploring the influence of IOL and corneal power on the refractive impact of variations in effective lens position. Theoretical development of an optimized formula and retrospective clinical evaluation on documented datasets. Retrospective data from 8878 patients with cataracts with pre- and postoperative measurements available using 4 IOL models and 6 IOL power calculation formulas were examined. A schematic eye model was used to study the impact of small variations in effective lens position (ELP) on the postoperative spherical equivalent (SE) refraction. The impact of keratometry (K) and IOL power (P) on SE was investigated. A theoretical thick lens model was used to devise a formula to zero the average prediction error of an IOL power calculation formula. This was achieved by incrementing the predicted ELP, which could then be translated into an increment in the IOL constant. This method was tested on documented real-life postoperative datasets, using different IOL models and single-constant optimized IOL calculation formulas. For small variations in ELP, there was an exponential relationship between IOL power and the resultant postoperative refractive variation. The ELP adjustment necessary to zero the ME equated to a ratio between the ME and the mean of the following expression: 0.0006*(P2+2K*P) on the considered datasets. The accuracy of the values obtained using this formula was confirmed on documented postoperative datasets, and on published and nonpublished formulas. The proposed method allows surgeons without special expertise to optimize an IOL constant to nullify the ME on a documented dataset without coding the different formulas. The influence of individual eyes is proportional to the squared power of the implanted IOL.

Visual Outcomes of Cataract Surgery in Patients With Keratoconus Using Toric and Non-toric Lenses

To compare the accuracy and outcomes of different intraocular lens (IOL) power calculation formulas in eyes with keratoconus undergoing cataract surgery with toric and non-toric IOLs. This was a consecutive retrospective case series study including patients from the Cornea Service at the Department of Ophthalmology and Visual Sciences at the University of British Columbia, Vancouver, Canada, from 2000 to 2020. Keratoconus was diagnosed based on corneal topography and clinician opinion. Patients who underwent topography-guided photorefractive keratectomy, intracorneal ring segments implantation, or corneal transplant were excluded. The manifest spherical equivalent, prediction errors, and median absolute errors were calculated. Descriptive statistics were expressed as mean ± standard deviation. There were 160 eyes from 101 patients; 136 eyes received non-toric lenses and 24 eyes received toric lenses. Most patients had mild disease (< 48.00 diopters [D]) when stratified by steep keratometry values. Patients with severe disease (> 53.00 D) were significantly more hyperopic following surgery (P < .05). The Barrett Universal II (0.26 D, inter-quartile range [IQR] = 0.4), Holladay 2 (0.31, IQR = 1.2), and SRK/T (0.42, IQR = 0.86) formulas had the lowest median absolute error. The postoperative prediction error following toric lens insertion was not significantly different than following non-toric lens insertion, and the mean absolute astigmatism was significantly reduced with toric lenses. The Barrett Universal II, Holladay 2, and SRK/T were the most accurate IOL power calculation formulas in patients with keratoconus undergoing cataract surgery. Hyperopic surprise was increased in severe keratoconus. Toric IOLs may be considered in patients with mild keratoconus. [J Refract Surg. 2023;39(5):319-325.].

Comparison of Intraocular Lens Power Calculation formulas with and without Total Keratometry and Ray tracing in patients with previous myopic SMILE.

This study evaluated the prediction error (PE) variance and absolute median PE of different IOL calculation formulae including last generation formulae such as Barrett True-K with K, Okulix and Total Keratometry (TK) based calculations with Haigis and Barrett True-K in a simulation model in post-SMILE eyes. Department of Ophthalmology, University Hospital Marburg, Germany. Design: Prospective study. Preoperative measurements included IOL power calculation before and after SMILE surgery. The target refraction was set to be the lowest myopic refractive error in pre-SMILE eyes. The IOL power targeting at the lowest myopic refractive error in pre-SMILE eyes was selected for the post-SMILE IOL calculation of the same eye. The difference between the predicted refraction of pre- and post-SMILE eyes with the same IOL power was defined as IOL-Difference (IOL-Diff). The refractive change induced by SMILE was defined as the difference between preoperative and postoperative manifest refraction (SMILE-Diff). 98 eyes from 49 patients underwent bilateral myopic SMILE. The PE variance of Okulix was not significantly different compared to Barrett True-K with TK (P=0.471). The standard deviation (SD) of the mean PEs were ±0.413 D (Haigis-TK), ±0.453 D (Okulix), ±0.471 D (Barrett True-K with TK), ±0.556 D (Haigis-L) and ±0.576 D (Barrett True-K with K). The mean absolute PE were 0.340 D, 0.353 D, 0.404 D, 0.511 D and 0.715 D for Haigis-TK, Okulix, Barrett True-K with TK, Barrett True-K with K and Haigis-L respectively. The highest percentage of eyes within ± 0.50 D was achieved by Okulix followed by Haigis TK, Barrett True-K with TK, Barrett True-K with K and Haigis-L. Our results suggest that Haigis in combination with TK, Okulix and Barrett True-K with and without TK offer good options for accurate IOL power calculation after SMILE. Haigis-L showed a tendency for myopic shift in eyes after previous SMILE.

Comparison of the prediction accuracy of 13 formulas in long eyes.

To investigate the accuracy of modern intraocular lens (IOL) power calculation formulas in eyes with axial length (AL) ≥ 26.00mm. A total of 193 eyes with one type of lens were analysed. An IOL Master 700 (Carl Zeiss Meditec, Jena, Germany) was used for optical biometry. Thirteen formulas and their modifications were evaluated: Barrett Universal II, Haigis, Hoffer QST, Holladay 1 MWK, Holladay 1 NLR, Holladay 2 NLR, Kane, Naeser 2, SRK/T, SRK/T MWK, T2, VRF and VRF-G. The User Group for Laser Interference Biometry lens constants were used for IOL power calculation. The mean prediction error (PE) and its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE) and the percentage of eyes with PEs within ± 0.25 D, ± 0.50 D and < ± 1.00 D were calculated. The modern formulas (Barrett Universal II, Hoffer QST, Kane, Naeser 2 and VRF-G) produced the smallest MedAE among all methods (0.30 D, 0.30 D, 0.30 D, 0.29 D and 0.28 D, respectively). The percentage of eyes with a PE within ± 0.50 D ranged from 67.48% to 74.85% for SRK/T and Hoffer QST, Naeser 2 and VRF-G, respectively. Dunn's post hoc test of the absolute errors revealed statistically significant differences (P < 0.05) between some of the newer formulas (Naeser 2 and VRF-G) and the remaining ones. From a clinical perspective the Hoffer QST, Naeser 2 and VRF-G formulas were more accurate predictors of postoperative refraction with the largest proportion of eyes within ± 0.50 D.

Comparison of the accuracy of nine intraocular lens power calculation formulas using partial coherence interferometry.

Cataract surgery is the most performed procedure in the world. To achieve the target refraction, several intraocular lens (IOL) power calculation formulas have been developed to improve the accuracy of IOL power predictions. We compared the accuracy of 9 IOL power calculation formulas (SRK/T, Hoffer Q, Holladay 1, Haigis, Barrett Universal II, Kane, EVO 2.0, Ladas Super formula and Hill-RBF 3.0) using partial coherence interferometry (PCI). We collected data from patients who underwent uncomplicated cataract surgery with implantation of 1 of 3 IOL types currently used in our center. All preoperative biometric measurements were performed using PCI. Prediction errors (PE) were deduced from refractive outcomes evaluated 3 months after surgery. The mean prediction error (ME), mean absolute prediction error (MAE), median absolute prediction error (MedAE), and standard deviation of prediction error (SD) were calculated, as well as the percentage of eyes with a PE within ±0.25, ±0.50, ±0.75 and ±1.00D for each formula. We included 126 eyes of 126 patients. Kane achieved the lowest MAE and SD across the entire sample as well as the highest percentage of PE within ±0.50D and was shown to be more accurate than Haigis and Hoffer Q (P<001). For an axial length of more than 26.0mm, EVO 2.0 and Barrett obtained the lowest MAEs, with EVO 2.0 and Kane showing a higher percentage of prediction at ±0.50D compared to old generation formulas except for SRK/T (P=04). All investigated formulas achieved good results; there was a tendency toward better outcomes with new generation formulas, especially in atypical eyes.

Accuracy of 24 IOL Power Calculation Methods.

To scrutinize the accuracy of 24 intraocular lens (IOL) power calculation formulas in unoperated eyes. In a series of consecutive patients undergoing phacoemulsification and implantation of the Tecnis 1 ZCB00 IOL (Johnson & Johnson Vision), the following formulas were evaluated: Barrett Universal II, Castrop, EVO 2.0, Haigis, Hoffer Q, Hoffer QST, Holladay 1, Holladay 2, Holladay 2 (AL Adjusted), K6 (Cooke), Kane, Karmona, LSF AI, Naeser 2, OKULIX, Olsen (OLCR), Olsen (standalone), Panacea, PEARL-DGS, RBF 3.0, SRK/T, T2, VRF, and VRF-G. The IOLMaster 700 (Carl Zeiss Meditec AG) was used for biometric measurements. With optimized lens constants, the mean prediction error (PE) and its standard deviation (SD), the median absolute error (MedAE), the mean absolute error (MAE), and the percentage of eyes with prediction erros within ±0.25, ±0.50, ±0.75, ±1.00, and ±2.00 D were analyzed. Three hundred eyes of 300 patients were enrolled. The heteroscedastic method revealed statistically significant differences (P < .05) among formulas. Newly developed methods such as the VRF-G (standard deviation [SD] ±0.387 D), Kane (SD ±0.395 D), Hoffer QST (SD ±0.404 D), and Barrett Universal II (SD ±0.405) were more accurate than older formulas (P < .05). These formulas also yielded the highest percentage of eyes with a PE within ±0.50 D (84.33%, 82.33%, 83.33%, and 81.33%, respectively). Newer formulas (Barrett Universal II, Hoffer QST, K6, Kane, Karmona, RBF 3.0, PEARL-DGS, and VRF-G) were the most accurate predictors of postoperative refractions. [J Refract Surg. 2023;39(4):249-256.].