Vergence Formula Research Articles

Intraoperative Aberrometry versus Preoperative Biometry for Intraocular Lens Power Calculations: A Report by the American Academy of Ophthalmology

To evaluate the published literature to compare intraoperative aberrometry (IA) with preoperative biometry-based formulas with respect to intraocular lens (IOL) power calculation accuracy for various clinical scenarios. Literature searches in the PubMed database conducted in August 2022, July 2023, and February 2024 identified 157, 18, and 6 citations, respectively. These were reviewed in abstract form, and 61 articles were selected for full-text review. Of these, 29 met the criteria for inclusion in this assessment. The panel methodologists assigned a level of evidence rating to each of the articles; 4 were rated level I, 19 were rated level II, and 6 were rated level III. Intraoperative aberrometry performed better than traditional vergence formulas, including the Haigis, HofferQ, Holladay, and SRK/T, and similarly to the Barrett Universal II and Hill-RBF with respect to minimization of spherical equivalent (SE) refractive error. For toric IOLs, IA outperformed formulas that only considered anterior corneal astigmatism and was similar to formulas like the Barrett Toric Calculator (BTC), which empirically account for the contribution from the posterior cornea. In eyes with a history of corneal refractive surgery, IA performed similarly to the Barrett True-K and slightly better than other tested methods, including the Haigis-L, Shammas, and Wang-Koch-Maloney formulas. Intraoperative aberrometry corresponds well with modern vergence formulas, including the Barrett Universal II, Hill-RBF, BTC, and Barrett True-K. It has greater accuracy than traditional vergence-based IOL power calculation formulas in eyes with and without a history of corneal refractive surgery. Proprietary or commercial disclosure may be found after the references.

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.

Influencing factors of effective lens position in patients with Marfan syndrome and ectopia lentis

AimsThe aim of this study was to analyse the effective lens position (ELP) in patients with Marfan syndrome (MFS) and ectopia lentis (EL).MethodsPatients with MFS undergoing lens removal and primary...

Effect of vault on predicting postoperative refractive error for posterior chamber phakic intraocular lens based on a machine learning model

Purpose: To investigate how vault and other biometric variations affect postoperative refractive error of implantable collamer lenses (ICLs) by integrating artificial intelligence and modified vergence formula. Setting: Eye and ENT Hospital of Fudan University, Shanghai, China. Design: Artificial intelligence and big data-based prediction model. Methods: 2845 eyes that underwent uneventful spherical ICL or toric ICL implantation and with manifest refraction results 1 month postoperatively were included. 1 eye of each patient was randomly included. Random forest was used to calculate the postoperative sphere, cylinder, and spherical equivalent by inputting variable ocular parameters. The influence of predicted vault and modified Holladay formula on predicting postoperative refractive error was analyzed. Subgroup analysis of ideal vault (0.25 to 0.75 mm) and extreme vault (&lt;0.25 mm or &gt;0.75 mm) was performed. Results: In the test set of both ICLs, all the random forest-based models significantly improved the accuracy of predicting postoperative sphere compared with the Online Calculation &amp; Ordering System calculator (P &lt; .001). For ideal vault, the combination of modified Holladay formula in spherical ICL exhibited highest accuracy (R = 0.606). For extreme vault, the combination of predicted vault in spherical ICL enhanced R values (R = 0.864). The combination of predicted vault and modified Holladay formula was most optimal for toric ICL in all ranges of vault (ideal vault: R = 0.516, extreme vault: R = 0.334). Conclusions: The random forest-based calculator, considering vault and variable ocular parameters, illustrated superiority over the existing calculator on the study datasets. Choosing an appropriate lens size to control the vault within the ideal range was helpful to avoid refractive surprises.

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.

The accuracy of using vergence formula to screen myopia in children: a cross-sectional study.

To evaluate the accuracy of using the vergence formula to screen myopia in children and adolescents. This was a cross-sectional study conducted between December 2022 and May 2023 at the ophthalmology clinic of Beijing Tongren Hospital. A total of 336 children aged 6 to 12 years with refractive errors were selected according to the inclusion criteria. Biometric measurements, including axial length, corneal thickness, anterior chamber depth, corneal curvature, and lens thickness, were obtained using a biometer. The Calculated spherical equivalent (SE) was then calculated using the vergence formula. Cycloplegic refraction was performed after paralysis of the ciliary muscle, and the subjective SE was recorded. A diagnosis of myopia was made if the subjective SE was ≤ -0.50 diopters. The AL/CR, subjective SE, and calculated SE were not normally distributed (p < 0.05). The AL/CR value was 3.08 (2.81, 3.27), the SE was -1.60 D (-6.00 D, 3.75 D), and the calculated SE was -1.42 D (-6.64 D, 5.73 D). There was no significant difference between the calculated SE and the SE (Z = -2.899, p = 0.004). The AL/CR value was negatively correlated with SE (r = -0.687, p < 0.01), and the calculated SE was positively correlated with SE (r = 0.827, p < 0.01). The area under the ROC curve for predicting myopia using AL/CR and calculated SE was 0.876 and 0.962, respectively, and the difference between the two was significant (p < 0.001). The sensitivity of AL/CR was 84.2%, the specificity was 70.6%, the accuracy was 82.1%, and the Youden index was 0.548. The sensitivity of calculated SE was 83.1%, the specificity was 100%, the accuracy was 85.7%, and the Youden index was 0.831. The vergence formula can be used to evaluate myopia in children and adolescents with relatively high accuracy without cycloplegic refraction.

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.

Artificial intelligence-based refractive error prediction and EVO-implantable collamer lens power calculation for myopia correction

BackgroundImplantable collamer lens (ICL) has been widely accepted for its excellent visual outcomes for myopia correction. It is a new challenge in phakic IOL power calculation, especially for those with low and moderate myopia. This study aimed to establish a novel stacking machine learning (ML) model for predicting postoperative refraction errors and calculating EVO-ICL lens power.MethodsWe enrolled 2767 eyes of 1678 patients (age: 27.5 ± 6.33 years, 18–54 years) who underwent non-toric (NT)-ICL or toric-ICL (TICL) implantation during 2014 to 2021. The postoperative spherical equivalent (SE) and sphere were predicted using stacking ML models [support vector regression (SVR), LASSO, random forest, and XGBoost] and training based on ocular dimensional parameters from NT-ICL and TICL cases, respectively. The accuracy of the stacking ML models was compared with that of the modified vergence formula (MVF) based on the mean absolute error (MAE), median absolute error (MedAE), and percentages of eyes within ± 0.25, ± 0.50, and ± 0.75 diopters (D) and Bland-Altman analyses. In addition, the recommended spheric lens power was calculated with 0.25 D intervals and targeting emmetropia.ResultsAfter NT-ICL implantation, the random forest model demonstrated the lowest MAE (0.339 D) for predicting SE. Contrarily, the SVR model showed the lowest MAE (0.386 D) for predicting the sphere. After TICL implantation, the XGBoost model showed the lowest MAE for predicting both SE (0.325 D) and sphere (0.308 D). Compared with MVF, ML models had numerically lower values of standard deviation, MAE, and MedAE and comparable percentages of eyes within ± 0.25 D, ± 0.50 D, and ± 0.75 D prediction errors. The difference between MVF and ML models was larger in eyes with low-to-moderate myopia (preoperative SE > − 6.00 D). Our final optimal stacking ML models showed strong agreement between the predictive values of MVF by Bland-Altman plots.ConclusionWith various ocular dimensional parameters, ML models demonstrate comparable accuracy than existing MVF models and potential advantages in low-to-moderate myopia, and thus provide a novel nomogram for postoperative refractive error prediction and lens power calculation.

Astigmatism analysis and reporting of surgically induced astigmatism and prediction error.

To provide a method for determining the vector that, when added to the preoperative astigmatism, results in no prediction error (PE) and to specify statistical methods for evaluating astigmatism and determining the 95% confidence convex polygon. Baylor College of Medicine, Houston, Texas, and University of Southern California, Los Angeles, California. Retrospective consecutive case series. An analysis of 3 clinical trials involving toric intraocular lenses was performed. 3 formulas were evaluated (generic vergence formula with zero surgically induced astigmatism, the Barrett toric formula, and the Holladay toric formula). Scalar and vector analyses were performed on each dataset with each formula and the results compared. Since the PE was not a Gaussian distribution, a 95% convex polygon was used to determine the spread of the data. The mean values for the vector absolute astigmatism PEs were not different for the 3 formulas and 3 datasets. The Barrett and Holladay toric calculators were statistically superior to the zero formula for 3 intervals (0.75, 1.0, and 1.25) in the high astigmatism dataset. Residual astigmatism and vector absolute astigmatism PE mean values and SDs are useful but require extremely large datasets to demonstrate a statistical difference, whereas examining percentages in 0.25 diopters (D) steps from 0.25 to 2.0 D reveals differences with far fewer cases using the McNemar test for a P value. Double-angle plots are especially useful to visualize astigmatic vector PEs, and a 95% confidence convex polygon should be used when distributions are not Gaussian.

Vergence Formula for Estimating the Refractive Status of Aphakic Eyes in Pediatric Patients.

Clinical RelevanceA vergence formula may provide a simple and reliable calculation of the refractive status of aphakic eyes.BackgroundMeasuring the refractive error of pediatric eyes with aphakia is difficult. This study investigated the accuracy and applicability of a vergence formula for estimating the refractive status of such eyes.MethodsA retrospective review of the medical records, created between January 2016 and December 2018, of pediatric patients with aphakia was conducted. A vergence formula, based on axial length, was used to calculate the refractive status of the aphakic eyes. The refractive values determined using retinoscopy, an automatic refractometer, and the vergence formula were compared.ResultsA total of 72 eyes (47 patients) were analyzed. The spherical equivalents of the refractive errors (mean ± standard deviation) of the eyes were determined using retinoscopy (13.01 ± 3.27 D), automatic refractometry (12.90 ± 3.23 D), and the vergence formula (12.70 ± 3.4 D). The correlation coefficient between retinoscopy values determined using retinoscopy and the vergence formula, automatic refractometry and the vergence formula, and retinoscopy and automatic refractometry were 0.968, 0.987, and 0.979, respectively. The Bland-Altman consistency analysis revealed that the mean differences in the spherical equivalent values between retinoscopy and automatic refractometry, retinoscopy and the vergence formula, and automatic refractometry and the vergence formula were 0.11 D, 0.31 D, and 0.21 D, respectively, with 95% limits of agreement of−1.20 to 1.41 D,−1.37 to 2.00 D, and−0.90 to 1.31 D, respectively.ConclusionThe vergence formula was effective for evaluating the refractive status of aphakic eyes in pediatric patients.

Трехлетний опыт имплантации заднекамерной акриловой факичной интраокулярной линзы в коррекции миопии высокой степени

Aim: to evaluate the efficacy and safety of posterior chamber phakic intraocular lens (pIOL) implantation for the high myopia correction. Patients and Methods: 37 patients (55 eyes) aged 20 to 43 years were included in the study. All patients underwent the following ophthalmic examinations before surgery: visometry, autorefractometry, biometry, tonometry, optical coherence tomography, evaluation of corneal endothelial cell density, peripheral retinal exam using a Goldmann lens. pIOL power calculation was conducted using a modified vergence formula. All surgeries were performed by one surgeon according to the standard procedure. Patients were examined after surgery after 1 day, 1 month, 3 months, then every 6 months for 3 years. Visometry was performed 1 day and 1 month after the surgery. During subsequent visits, all of the listed examinations were performed, except for peripheral retinal exam using a Goldmann lens. Results: all patients completed the study. There were no intraoperative complications. No cases of cataracts or other postoperative complications were observed during 3-year follow-up. Uncorrected visual acuity 3 years after surgery was 18.4% higher than the maximum corrected visual acuity before surgery, and target refraction was observed in 86% of the eyes. Intraocular pressure during 3-year follow-up was within the normal range and averaged 17.04 mmHg. Fluctuations in the lens vault from the pIOL posterior surface to the anterior surface of the lens (VAULT) were within the normal range. Corneal endothelial cell density decreased by an average of 0.09% 3 years after surger During 3-year follow-up, there were no clinically significant changes in the anterior chamber depth of the eye. The average change in the axis orientation was also &lt;6° for all visit intervals. At the same time, the patients did not notice a change in the pIOL orientation up to 10°. Conclusion: pIOL implantation is a safe and effective method for high myopia surgical correction. Keywords: myopia, myopia correction, implantation, phakic intraocular lens, VAULT, endothelial cell density, anterior chamber of the eye. For citation: Saliev I.F., Yusupov A.F., Mukhamedova N.I. Three-year experience of posterior chamber phakic intraocular lens implantation in the high myopia correction. Russian Journal of Clinical Ophthalmology. 2022;22(3):156–160 (in Russ.). DOI: 10.32364/2311-7729- 2022-22-3-156-160.

Intraocular lens power calculation in eyes with previous corneal refractive surgery.

Intraocular lens (IOL) power calculation after corneal refractive surgery (CRS) becomes an expanding challenge for ophthalmologists as more and more cataract surgeries after CRS are required. These patients typically also have high expectations as to visual performance. Conventional IOL power calculation schemes frequently provide inaccurate results in these cases. This review aims to summarize and recommend currently available IOL power calculation methods for eyes with the most common CRS methods: radial keratotomy (RK), photorefractive keratectomy (PRK), laser in situ keratomileusis (LASIK), and small incision lenticule extraction (SMILE). To this end, biometry measuring methods and IOL formulas will be explained and combinations of both are proposed. In synopsis, it is evident that the latest generation of vergence formulas exhibit favorable IOL power prediction accuracy in post-CRS eyes, even though the predictive precision of methods in eyes without CRS is not attained. Ray tracing computation, intraoperative aberrometry, and machine learning–based formulas hold potential to further improve refractive outcomes in post-CRS eyes.

The Castrop formula for calculation of toric intraocular lenses

PurposeTo explain the concept behind the Castrop toric lens (tIOL) power calculation formula and demonstrate its application in clinical examples.MethodsThe Castrop vergence formula is based on a pseudophakic model eye with four refractive surfaces and three formula constants. All four surfaces (spectacle correction, corneal front and back surface, and toric lens implant) are expressed as spherocylindrical vergences. With tomographic data for the corneal front and back surface, these data are considered to define the thick lens model for the cornea exactly. With front surface data only, the back surface is defined from the front surface and a fixed ratio of radii and corneal thickness as preset. Spectacle correction can be predicted with an inverse calculation.ResultsThree clinical examples are presented to show the applicability of this calculation concept. In the 1st example, we derived the tIOL power for a spherocylindrical target refraction and corneal tomography data of corneal front and back surface. In the 2nd example, we calculated the tIOL power with keratometric data from corneal front surface measurements, and considered a surgically induced astigmatism and a correction for the corneal back surface astigmatism. In the 3rd example, we predicted the spherocylindrical power of spectacle refraction after implantation of any toric lens with an inverse calculation.ConclusionsThe Castrop formula for toric lenses is a generalization of the Castrop formula based on spherocylindrical vergences. The application in clinical studies is needed to prove the potential of this new concept.

Considerations on the Castrop formula for calculation of intraocular lens power

BackgroundTo explain the concept of the Castrop lens power calculation formula and show the application and results from a large dataset compared to classical formulae.MethodsThe Castrop vergence formula is based on a pseudophakic model eye with 4 refractive surfaces. This was compared against the SRKT, Hoffer-Q, Holladay1, simplified Haigis with 1 optimized constant and Haigis formula with 3 optimized constants. A large dataset of preoperative biometric values, lens power data and postoperative refraction data was split into training and test sets. The training data were used for formula constant optimization, and the test data for cross-validation. Constant optimization was performed for all formulae using nonlinear optimization, minimising root mean squared prediction error.ResultsThe constants for all formulae were derived with the Levenberg-Marquardt algorithm. Applying these constants to the test data, the Castrop formula showed a slightly better performance compared to the classical formulae in terms of prediction error and absolute prediction error. Using the Castrop formula, the standard deviation of the prediction error was lowest at 0.45 dpt, and 95% of all eyes in the test data were within the limit of 0.9 dpt of prediction error.ConclusionThe calculation concept of the Castrop formula and one potential option for optimization of the 3 Castrop formula constants (C, H, and R) are presented. In a large dataset of 1452 data points the performance of the Castrop formula was slightly superior to the respective results of the classical formulae such as SRKT, Hoffer-Q, Holladay1 or Haigis.

Refractive Outcomes and Anterior Chamber Depth after Cataract Surgery in Eyes with and without Previous Pars Plana Vitrectomy

ABSTRACT Purpose: To compare the differences in refractive outcome and anterior chamber depth (ACD) after phacoemulsification between eyes with and without previous pars plana vitrectomy (PPV). Materials and Methods: Patients who had significant cataracts after PPV were included in the study group, and patients with a matched axial length (AL) who had cataracts without PPV were selected as the control group. The performance of new generation intraocular lens (IOL) power calculation formulas (Barrett Universal II, Kane, Ladas Super formulas), and the traditional formulas (SRK/T, Holladay 1, Hoffer Q, Haigis) with and without the Wang–Koch (WK) AL adjustment were compared between the two groups. The postoperative ACD was measured using the Scheimpflug imaging system with manual correction at least three months after surgery. Results: In total, there were 193 eyes from 193 patients in each group. The mean prediction errors (MEs) of the new generation formulas had no significant systemic bias in the study group; the hyperopic shift was displayed in the traditional formulas for eyes with AL > 26mm. However, the difference of MEs between the two groups among all the formulas were not significant. The absolute prediction error (MAE) and median prediction error (Med AE) in the study group were larger than those in the control group among all the formulas. The postoperative ACD of the study group was deeper but not significant than that of the control group. Conclusions: There was no refractive shift in vitrectomized eyes compared with non-vitrectomized eyes no matter in new generation formulas or traditional vergence formulas. The prediction error among all the formulas in vitrectomized eyes were significantly higher than those in non–vitrectomized eyes. The ACD after phacoemulsification in vitrectomized eyes was not significantly different from non–vitrectomized eyes.

Back-calculation of the keratometer index-Which value would have been correct in cataract surgery?

In the clinical routine the conversion of corneal radii into corneal refractive power using akeratometer index is rarely discussed. The purpose of this study was to back-calculate the keratometer index in pseudophakic eyes based on the refractive power of the lens, biometric measurements and refraction, and to compare it to clinically established values. In this retrospective case series 99eyes of 99patients without pathological alterations, previous diseases, comorbidities or history of ocular surgery apart from the uneventful cataract surgery were enrolled. In all eyes a CT Asphina 409M(P) (Carl-Zeiss Meditec, Berlin, Germany) had been implanted by twosurgeons (EF and PE). For calculation we used shape and power data of the intraocular lens and data from optical biometry (axial length, pseudophakic anterior chamber depth, lens thickness, corneal radius; IOLMaster 700, Carl-Zeiss Meditec, Jena, Germany). The refraction was derived manually with atrial frame (measurement distance 5 m) and autorefractometry (iProfiler, Carl-Zeiss, Jena, Germany). For this three model eyes were used: athin lens with the nominal refractive power positioned in the equatorial plane (modelA) or in the secondary principal plane of the thick lens (modelB) as well as amodel considering the intraocular lens as athick lens located at its measured position (modelC). Back-calculation of the keratometer index using vergence formulas resulted in akeratometer index based on subjective refraction measurements considering lane distance correction of 1.3307 ± 0.0026/1.3312 ± 0.0026/1.332 ± 0.0027 for modelA/modelB/modelC, respectively. Based on objective refraction measurements (autorefraction calibrated to infinity object distances) resulted in akeratometer index of 1.3301 ± 0.0021/1.3306 ± 0.0021/1.3315 ± 0.0021, for modelA/modelB/modelC, respectively. The keratometer index did not show any trend in linear regression for axial length or corneal radius for any of the three models or for any refraction method. The keratometer index derived from back-calculation matched with the Zeiss index (1.332) but was much lower compared to other established indexes, e.g. the Javal index (1.3375). The missing trend for axial length or corneal radius implies that simple vergence formulas for intraocular lens refractive power calculation without correction terms or fudge factors perform best with akeratometer index slightly below 1.332, if the biometrically measured position of the intraocular lens is used as the effective lens position.

IOL calculation concepts

AbstractThe first intraocular lenses implanted resampled the shape of the natural lens and resulted in high postoperative myopia. First attempts to preoperatively calculate the intraocular lens (IOL) power by vergence formulas were presented by Fjodorov in 1967. Other authors soon followed presenting numerous attempts to estimate the required IOL power. While most of the calculation schemes nowadays are based on the vergence formula, there were also empirical approaches such as the SRK and SRK‐II formulas. Beside different interpretation of corneal power from the measured radii of curvature and several offset values, the main difference between formulas is in the estimation of the effective lens position (reference plane of the thin lens in the pseudophakic eye) (ELP): We will present various approaches for calculating IOL power and discuss differences between formulas as well as the pros and cons of these different concepts.

Comparison of intraocular lens power calculation formulas in Chinese eyes with axial myopia

To assess the accuracy of intraocular lens (IOL) power calculation formulas in Chinese eyes with axial lengths (ALs) longer than 26.0mm. Department of Cataract Surgery, Shanxi Eye Hospital, China. Prospective case series. This study evaluated (1) two new formulas (Barrett Universal II and Hill-RBF 2.0), (2) three vergence formulas (Haigis, Holladay 1, and SRK/T), and (3) the original and modified Wang-Koch AL adjustment formulas with Holladay 1 and SRK/T. The User Group for Laser Interference Biometry lens constants were used for IOL power calculation. The refractive prediction error was calculated by subtracting the predicted refraction from the actual refraction postoperatively. The mean numerical error (MNE), percentage of eyes with hyperopic outcomes, and mean absolute error (MAE) were determined. The study comprised 136 eyes. The Barrett and Hill-RBF formulas had MNEs close to zero (-0.09 D to 0.03 D), the Haigis, Holladay 1, and SRK/T produced hyperopic MNEs (0.25 to 0.70 D), and the original and modified Wang-Koch AL adjustment formulas induced myopic MNEs (-0.48 to -0.22 D). The original Wang-Koch formulas produced significantly lower percentages of eyes with hyperopic outcomes (15% to 18%) than all other formulas (28% to 91%). There were no significant differences in MAEs between the Barrett, Hill-RBF, Haigis, and original and modified Wang-Koch adjustment with the Holladay 1 (0.32 to 0.41 D). The performances of the Barrett and Hill-RBF were comparable in long eyes. The incidence of hyperopic outcome with the Wang-Koch AL adjustment formula was significantly lower than other formulas.

New algorithm for toric intraocular lens power calculation considering the posterior corneal astigmatism

To assess the accuracy of toric intraocular lens (IOL) power calculations of a new algorithm that incorporates the effect of posterior corneal astigmatism (PCA). Abbott Medical Optics, Inc., Groningen, the Netherlands. Retrospective case report. In eyes implanted with toric IOLs, the exact vergence formula of the Tecnis toric calculator was used to predict refractive astigmatism from preoperative biometry, surgeon-estimated surgically induced astigmatism (SIA), and implanted IOL power, with and without including the new PCA algorithm. For each calculation method, the error in predicted refractive astigmatism was calculated as the vector difference between the prediction and the actual refraction. Calculations were also made using postoperative keratometry (K) values to eliminate the potential effect of incorrect SIA estimates. The study comprised 274 eyes. The PCA algorithm significantly reduced the centroid error in predicted refractive astigmatism (P<.001). With the PCA algorithm, the centroid error reduced from 0.50 @ 1 to 0.19 @ 3 when using preoperative K values and from 0.30 @ 0 to 0.02 @ 84 when using postoperative K values. Patients who had anterior corneal against-the-rule, with-the-rule, and oblique astigmatism had improvement with the PCA algorithm. In addition, the PCA algorithm reduced the median absolute error in all groups (P<.001). The use of the new PCA algorithm decreased the error in the prediction of residual refractive astigmatism in eyes implanted with toric IOLs. Therefore, the new PCA algorithm, in combination with an exact vergence IOL power calculation formula, led to an increased predictability of toric IOL power.