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Purpose:
To develop a new method that makes it easy to detect accuracy deficiencies of any intraocular lens power calculation formulae and to test it on 9 different formulae.
Setting:
IOA, Madrid, Spain DESIGN:: Retrospective observational case series.
Methods:
This study's first stage included 3519 eyes from 3519 candidates to cataract surgery for which frequency distributions for the following biometric eye parameters were computed: axial length (AXL), anterior-chamber depth (ACD), lens thickness (LT), white-to-white (WTW) and mean corneal radius (Rm). The resulting data for each parameter were 5, 25, 75 and 95 percentile, which allowed us to define the corresponding normality range. In a second stage, the new graphic-representation method was tested for 9 different formulae in a sample of 70 eyes undergoing cataract surgery with multifocal intraocular lens (MIOL) implantation.
Results:
Normality ranges (defined as the 25-to-75-percentile interval) were 22.84 to 24.42 mm for AXL, 2.86 to 3.39 mm for ACD, 4.36 to 4.88 mm for LT, 11.64 to 12.19 mm for WTW and 7.52 to 7.87 mm for Rm, with lower sizes in women. No significant differences were found along the 9 formulae for percentage of eyes in ±0.50D (p=0.82) or ±1.00D (p=0.97). The new graphical method showed less accuracy in ±0.50 D for ACDs from 2.46 to 2.85 mm (5 to 25 percentile) for several formulae (p<0.05).
Conclusions:
9 formulae showed non-significant differences in the general predictability for a sample of eyes candidates to MIOL implantation. Predictability in this sample decreased for short ACDs.

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... The assessment of confounding factors as corneal power changes between 1 and 12 months was evaluated with the paired t-test. The influence of biometric parameters and PE was descriptively evaluated with plots previously described in the literature [15]. The association between PCO or Nd:YAG and PE changes was evaluated with the Fisher's exact test. ...

... The relationships between the AXL and IOL power with the hyperopic shift suggest that this effect should be particularly investigated in future studies, putting special emphasis on short eyes implanted with a high IOL power for which the ALP variation can produce a higher change in SE than IOLs with a lower power. Although conclusions could not be made through the descriptive analysis of PE for several biometric parameters, our results also suggest that eyes with longer LT and bigger WTW should be further explored in future studies, having not previously been described for the Barrett formula [15]. On the other hand, in our study, the percentages of eyes in ± 0.50 D and ± 1.00 D after refraction stabilization were 67% and 90%, respectively. ...

The aim of this study was to assess the stability and differences between objective (O-Rx) and subjective (S-Rx) refraction for the assessment of the prediction error (PE). A secondary aim was to report the results of a monofocal intraocular lens (IOL). 100 subjects were included for whom S-Rx and O-Rx were obtained for all visits, and for visual performance, posterior capsular opacification incidence and Nd:YAG rates at 12 months. Either S-Rx and O-Rx showed a hyperopic shift from 1 to 6 months (p < 0.05) and stabilization after 6 months. S-Rx was related with the axial length (rho = −0.29, p = 0.007), obtaining a major tendency towards hyperopia in short eyes implanted with high-power IOLs. O-Rx showed a myopic shift in comparison to S-Rx (p < 0.05). This resulted in a decrease of the number of eyes in ±0.50 D and ±1.00 D from 79 to 67% and from 94 to 90%, respectively. The median (interquartile range) uncorrected and corrected visual acuities were 0.1 (0.29) and 0 (0.12) logMAR, respectively, and seven eyes required Nd:YAG capsulotomy at 12 months. Some caution should be taken in PE studies in which O-Rx is used or S-Rx is measured in a 1-month follow-up. Constant optimization should be conducted for this IOL after S-Rx stabilization.

... This also allows the simple calculation of area using the trapezoidal rule. 15 Curvilinear regression (fitting a curve) finds a mathematical expression that produces a curved line to be the closest or exact fit to the measured data points, when the relationship between the variables is non-linear. 14 The validity of this curvilinear regression must be assessed statistically, and there are five main models that can be used to assess GOF. ...

Introduction:
To establish the most appropriate curve fitting method to allow accurate comparison of defocus curves derived from intraocular lenses (IOLs).
Methods:
Defocus curves were plotted in five IOL groups (monofocal, extended depth of focus, refractive bifocal, diffractive bifocal and trifocal). Polynomial curves from 2nd to 11th order and cubic splines were fitted. Goodness of fit (GOF) was assessed using five methods: least squares, coefficient of determination (R2 adj ), Akaike information criteria (AIC), visual inspection and Snedecor and Cochran. Additional defocus steps at -2.25 D and -2.75 D were measured and compared to the calculated visual acuity (VA) values. Area under the defocus curve and range of focus were also compared.
Results:
Goodness of fit demonstrated variable results, with more lenient methods such as R2 adj leading to overfitting and conservative methods such as AIC resulting in underfitting. Furthermore, conservative methods diminished the inflection points resulting in an underestimation of VA. Polynomial of at least 8th order was required for comparison of area methods, but overfitted the EDoF and monofocal groups; the spline curve was consistent for all IOLs and methods.
Conclusions:
This study demonstrates the inherent difficulty of selecting a single polynomial function. The R2 method can be used cautiously along with visual inspection to guard against overfitting. Spline curves are suitable for all IOLs, guarding against the issues of overfitting. Therefore, for analysis of the defocus profile of IOLs, the fitting of a spline curves is advocated and should be used wherever possible.

... Previous studies have revealed that in eyes with average biometric values, such as axial length (AL) and keratometry (K), there is not much difference in the accuracy of the postoperative refractive error prediction between IOL power calculation formulas (Melles et al. 2018;Fern andez et al. 2020). Conversely, for eyes with biometric values that deviate from the average, accuracy can vary depending on the formulas (Gavin & Hammond 2008;Eom et al. 2013a;Eom et al. 2014;Melles et al. 2018;Kane & Melles 2020). ...

Purpose:
To compare the prediction accuracy of algorithmic intraocular lens (IOL) power calculation formula selection method using conventional formulas (Haigis, Hoffer Q, Holladay 1, SRK/T and/or Barrett Universal II) based on keratometry (K), anterior chamber depth (ACD) and axial length (AL).
Methods:
A total of 1653 patients (1653 eyes) implanted with Tecnis ZCB00 IOL during cataract surgery were enrolled in this study. Intraocular lens (IOL) power calculation formulas with a small absolute value in the sum of the area under the curve measured by K, ACD and AL subgroup were selected to calculate IOL power in the relevant biometry subgroup. The median absolute error (MedAE) calculated by the Haigis, Hoffer Q, Holladay 1, SRK/T and Barrett Universal II formulas individually was compared to that calculated by the algorithmic selection method using four formulas, Haigis, Hoffer Q, Holladay 1 and SRK/T, or five formulas when Barrett is included.
Results:
The MedAE was 0.27 D in the Haigis, 0.30 D in the Hoffer Q, 0.27 D in the Holladay 1, 0.29 D in the SRK/T and 0.26 D in the Barrett Universal II formulas. The MedAEs determined by the algorithmic selection method using four (019 D) and five (0.21 D) formulas were significantly lower than those by the conventional IOL power calculation formulas.
Conclusions:
The IOL power calculation formula selection method by biometry subgroup combined with biometric parameters K, ACD and AL may offer a more superior postoperative refractive error prediction in cataract surgery.

Purpose:
To evaluate role of a new parameter, iris root depth (IRD), in intraocular lens power calculation using ultrasound biomicroscopy (UBM) in primary angle-closure diseases (PACDs). And to compare the accuracy of six formulas Barrett Universal II (BUII), Haigis, Hill-Radial Basis Function (RBF) Version 3.0, Hoffer Q, Kane and Sanders Retzlaff Kraff/Theoretical (SRK)/T in PACDs.
Setting:
Zhongshan Ophthalmic Center, Guangzhou, China.
Design:
Retrospective consecutive case series.
Methods:
Patients diagnosed with PACDs and undergone cataract surgery were reviewed to evaluate performance of six formulas firstly. Then preoperative UBM examinations of 58 eyes were used to measure IRD and predict effective lens position (ELP) to generate the HaigisIRD formula. The accuracy of HaigisIRD was compared with BUII, Haigis and Kane formulas. The standard deviation (SD) of predicted error was the main indicator evaluating formula performance, according to heteroscedastic analysis.
Results:
A total of 103 eyes (103 patients) were included. The SDs of Kane (0.59, P = 0.01), RBF 3.0 (0.61, P = 0.02) and SRK/T formula (0.62, P = 0.04) were significantly lower than Hoffer Q. Modified with IRD, HaigisIRD generated the lowest SD (0.41), which was significantly lower than Haigis formula (0.54, P = 0.03) and was equal to Kane formula (0.45, P = 0.37).
Conclusions:
Kane, RBF 3.0 and SRK/T were more accurate in PACD eyes. Optimized with IRD, HaigisIRD formula achieved the lowest SD and had comparable accuracy with Kane formula. IRD could be a promising parameter to improve accuracy of IOL power calculation for PACDs.

Purpose
To assess the influence in paired design studies of formulae comparison for intraocular lens (IOL) power calculation of using a single formula for deciding the implanted power with monofocal (mIOL) and multifocal (MIOL) lenses.
Design
Retrospective observational.
Methods
Ninety-six right eyes were retrospectively analyzed. Eyes were assigned in two independent groups, SG and HG, depending on the formula used for deciding the implanted power, SRK-T (n = 54) and Haigis (n = 42), respectively. Median absolute prediction error (MedAE) was evaluated between independent samples (SRK-T in SG vs Haigis in HG) and between paired samples (SRK-T vs Haigis in both SG and HG). Percentages of eyes within a specific range of prediction error (PE) were also calculated for both, the standard steps and the clinically relevant steps.
Results
MedAE difference was lower than 0.09 D between both formulas for the comparison of independent samples in the mIOL (p = 0.62) and MIOL (p = 0.83) groups. However, paired samples resulted in better MedAE for SRK-T in the SG (0.14 D lower, p = 0.003) and for Haigis in the HG (0.07 D lower, p = 0.015), but only in the mIOL group. These small differences were also manifested, but not reaching statistical significance (p > 0.05), in the percentage of eyes achieving a specific range of PE, especially in the mIOL group.
Conclusions
A small superiority for the formula used for selecting the final implanted IOL power can appear in studies following current standards. These studies should clearly specify which formula was used for selecting the implanted power.

The refractive outcome of cataract surgery is influenced by the choice of IOL power formula and the accuracy of the various devices used to measure the eye (including intraoperative aberrometry). This review aimed to cover the breadth of literature over the previous 10 years focusing on 3 main questions: 1) What IOL power formulas are currently available and which is the most accurate?, 2) What biometry devices are available, do the measurements they obtain differ from one another and will this cause a clinically significant change in IOL power selection? and 3) Does intraoperative aberrometry improve refractive outcomes?
A literature review was performed by searching the PubMed database for articles on each of these topics that identified 1,313 papers of which 166 were included in the review.
For IOL power formulas, the Kane formula was the most accurate formula over the entire axial length spectrum and in both the short (axial length ≤22.0 mm) and long eye (axial length ≥26.0 mm) subgroups. Other formulas that performed well in the short eye subgroup were the Olsen (4 factor), Haigis and Hill-RBF 1.0. In the long eye group, the other formulas that performed well included the Barrett Universal II (BUII), Olsen (4-factor) or Holladay 1 with Wang-Koch adjustment.
All biometry devices delivered highly reproducible measurements and the majority of comparative studies showed little difference in the average measures for all the biometric variables between devices. The differences seen resulted in minimal clinically significant effects on IOL power selection. The main difference found between devices was the ability to successful measure through dense cataracts with SS-OCT based machines performing better than PCI and OLCR devices.
Intraoperative aberrometry generally improved outcomes for spherical and toric IOLs in eyes both with and without prior refractive surgery when the BUII and Hill-RBF, Barrett toric calculator, or Barrett True-K formulas were not used. When they were used, intraoperative aberrometry did not result in better outcomes.

Purpose:
To identify the sources of error in predictability beyond the effective lens position and to develop two new thick lens equations.
Methods:
Retrospective observational case series with 43 eyes. Information related to the actual lens position, corneal radii measured with specular reflection and Scheimpflug-based technologies, and the characteristics of the implanted lenses (radii and thickness) were used for obtaining the fictitious indexes that better predicted the postoperative spherical equivalent (SE) when the real effective lens position (ELP) was known. These fictitious indexes were used to develop two thick lens equations that were compared with the predictability of SRK/T and Barrett Universal II.
Results:
The SE relative to the intended target was correlated to the difference between real ELP and the value estimated by SRK/T (ΔELP) (r = -0.47, p=0.002), but this only predicted 22% of variability in a linear regression model. The fictitious index for the specular reflection (nk) and Scheimpflug-based devices (nc) were significantly correlated with axial length. Including both indexes fitted to axial length in the prediction model with the ΔELP increased the r-square of the model up to 83% and 39%, respectively. Equations derived from these fictitious indexes reduced the mean SE in comparison to SRK/T and Barrett Universal II.
Conclusions:
The predictability with the trifocal IOL evaluated is not explained by an error in the ELP. An adjustment fitting the fictitious index with the axial length improves the predictability without false estimations of the ELP.

Background:
We aimed to measure ocular biometric characteristics in older cataract patients from western China.
Methods:
Ocular biometry records were retrospectively analyzed for 6933 patients with cataracts (6933 eyes) at least 50 years old who were treated at West China Hospital of Sichuan University.
Results:
Partial coherence laser interferometry gave the following population averages: axial length (AL), 24.32 ± 2.42 mm; anterior chamber depth (ACD), 3.08 ± 0.47 mm; keratometric power (K), 44.23 ± 1.66 diopters; and corneal astigmatism (CA), 1.00 ± 0.92 diopters. The percentage of individuals with AL > 26.5 mm was 13.66%, while the percentage with CA > 1.0 diopters was 35.54%. Mean AL and ACD showed a trend of decrease with increasing age (P < 0.001). AL correlated positively with ACD (Spearman coefficient, 0.542) and CA (0.111), but negatively with K (- 0.411) (all P < 0.01). K also correlated negatively with ACD (- 0.078, P < 0.01).
Conclusions:
These results show, for the first time, that older cataract patients from western China have similar ocular biometric characteristics as other populations. The high prevalence of severe axial myopia warrants further investigation.

Purpose
To investigate the effect of anterior chamber depth (ACD) on the refractive outcomes of the SRK/T, Holladay 1, Hoffer Q and Haigis formulae in short, normal, long and extremely long eyes.
Methods
This retrospective study involved patients who had uncomplicated cataract surgery. Preoperative axial length (AL) was divided into four subgroups: short (< 22.00 mm), normal (22.00–24.49 mm), long (24.50–25.99 mm), extremely long (≥ 26.00 mm). Preoperative ACD was divided into three subgroups: < 2.5, 2.50–3.49, and ≥ 3.5 mm. Median absolute errors (MedAEs) predicted by the SRK/T, Holladay 1, Hoffer Q and Haigis formulae were compared with the Friedman test. Post-hoc analysis involved the Wilcoxon signed rank test with a Bonferroni adjustment. Correlations between ACD and the predictive refractive errors of the four formulas were analyzed.
Results
In short eyes with an ACD < 2.5 mm, the Haigis formula revealed the highest MedAE. The difference in MedAE with the Hoffer Q formula (which had the lowest MedAE) was statistically significant (P = 0.002). In normal eyes, the Haigis formula significantly differed from the Holladay 1 (P = 0.002) and Hoffer Q (P = 0.005) formulae in the ACD < 2.5 mm group. In long eyes and extremely long eyes with an ACD ≥ 3.5 mm, the differences in MedAEs were statistically significant (P = 0.018, P = 0.001, respectively) and the Haigis formula had the lowest MedAEs in both subgroups (0.29 D, 0.30 D, respectively). In the total of 1,123 eyes, refractive errors predicted by the Haigis formula showed a significant negative correlation with the ACD (R² = 0.002, P = 0.047).
Conclusions
The Hoffer Q formula is preferred over other formulae in short eyes with an ACD shallower than 2.5 mm. In short and normal eyes with an ACD < 2.5 mm the Haigis formula might underestimate ELP. The Haigis formula is the preferred choice in eyes with an AL ≥ 24.5 mm and an ACD ≥ 3.5 mm.

Background
To evaluate how differences in ocular biometry affects the Hoffer Q, Holladay 1, SRK/T, and Haigis intraocular lens power calculation formulae predictions. Methods
This study was performed on 91 eyes of 91 patients who underwent uneventful cataract surgery. Ocular biometry values were measured using the IOL Master 500, and intraocular lens (IOL) power was calculated using the Haigis, Hoffer Q, Holladay 1, and SRK/T formulas. We calculated the expected difference (ED) of each 3rd generation formula from the Haigis formula by subtracting the predicted refraction of the Haigis formula from the predicted refraction of each 3rd generation formula. Post-operative anterior chamber depth (ACD) was measured at 1 month after surgery using the IOL master. We calculated errors of each formula by subtracting predicted from manifest refraction at post-operative 1 month. Correlation analysis was performed between ocular biometry values, formula expectation values, formula errors and absolute formula errors. ResultsMultiple regression analysis revealed that preoperative ACD was the only significant factor for ED prediction in all of the 3rd generation formulas. For mean errors, axial length and post-operative 1-month change of ACD (delta ACD) correlated significantly with the errors in all 3rd generation formulas, but not with errors of the Haigis formula. Median absolute error (MedAE) of the formulas were 0.40 D for the Hoffer Q formula, 0.37 D for the Holladay formula, 0.34 D for the SRK/T formula, and 0.41 D for the Haigis formula. The MAE of the formulas were 0.50 ± 0.47 D for the Hoffer Q formula, 0.50 ± 0.50 D for the Holladay formula, 0.47 ± 0.51 D for the SRK/T formula, and 0.50 ± 0.47 D for the Haigis formula. Conclusion
Regarding ED between the third generation and Haigis formulas, preoperative ACD demonstrated the greatest influence. Calculating mean absolute errors of the formulas, all IOL formulas showed excellent and comparable accuracy. Post-operative change (delta) of ACD correlated significantly with errors of third generation formulas according to simulated ACD.

To describe the distribution and determinants of ocular biometric parameters and to ascertain the relative importance of these determinants in a large population of adults in rural central China.
A population-based, cross-sectional study performed in rural central China included 1721 participants aged 40 or more years. Ocular biometrical parameters including axial length (AL), anterior chamber depth (ACD), radius of corneal curvature (K) and horizontal corneal diameter [white-to-white (WTW) distance] were measured using non-contact partial coherence interferometry [intraocular lens (IOL)-Master].
Ocular biometric data on 1721 participants with a average age of 57.0±8.7y were analyzed at last. The general mean AL, ACD, mean corneal curvature radius (MCR), WTW were 22.80±1.12, 2.96±0.36, 7.56±0.26 and 11.75±0.40 mm, respectively. The mean values of each parameter in 40 to 49, 50 to 59, 60 to 69, and 70 to 91 years age groups were as follows: AL, 22.77±0.87, 22.76±1.06, 22.89±1.41, 22.92±0.80 mm; ACD, 3.10±0.32, 2.98±0.34, 2.86±0.36, 2.77±0.35 mm; MCR, 7.58±0.25, 7.54±0.26, 7.55±0.26, 7.49±0.28 mm; WTW, 11.79±0.38, 11.75±0.40, 11.72±0.41, 11.67±0.41 mm. The AL, ACD, MCR and WTW were correlated with age and the AL was correlated with height and weight.
Our findings can serve as an important normative reference for multiple purposes and may help to improve the quality of rural eye care.

Abstract Background Ocular biometric parameters can be influenced by race, ethnicity, and genetics; their differences across different populations can probably explain differences in refractive errors in these populations. The aim of this study is to determine the normal range of axial length, anterior chamber depth, lens thickness, and vitreous chamber depth in the population of Shahroud in the north of Iran. Methods In the first phase of Shahroud Eye Cohort Study, the 40–64 year old population were sampled cross-sectionally; 6311 were invited and 5190 (82.2%) participated in the study. Biometric examinations were done using the LENSTAR/BioGraph (WaveLight AG, Erlangen, Germany) after vision tests and before cycloplegic refraction tests. Any type of eye surgery, extensive pterygium, and lack of cooperation were used as exclusion criteria, and analyses were done with data from 4869 eyes. Results We found a mean axial length of 23.14 mm (95% confidence interval [CI], 23.11-23.17), mean anterior chamber depth of 2.62 mm (95% CI, 2.60-2.63), mean lens thickness of 4.28 mm (95% CI, 4.27-4.29), and the mean vitreous chamber depth was 15.72 mm (95% CI, 15.70-15.75). Kolmogorov-Smirnov tests showed that the distribution of axial length, anterior chamber depth, lens thickness, and vitreous chamber depth significantly differed from normal; axial length and vitreous chamber depth demonstrated a leptokurtic distribution as well. Axial length, anterior chamber depth, and vitreous chamber depth significantly decreased with age, and lens thickness significantly increased with age (p

Calculation of intraocular lens (IOL) power for implantation during cataract surgery depends on ocular biometric measurements. The aim of this study was to characterise the normal range of intra- and interindividual variation in axial length (AL) and corneal power (K) when IOLMaster measurements were possible and to derive recommendations as to which outlying measurements merit verification before acceptance.
The Medisoft electronic patient database contains prospectively collected data conforming to the United Kingdom (UK) Cataract National Dataset on 55,567 cataract operations. From this AL and K information on the 32,556 eyes (14,016 paired) of patients older than 25 years, without corneal pathology, history of intraocular surgery and who had all biometric measurements taken with the Zeiss IOLMaster (Carl Zeiss Meditec) were extracted. R 2.8.1 (R Foundation for Statistical Computing) was used for statistical analysis.
Mean age was 76.4 years and 62.0% were female. Mean (95% confidence interval) values for AL, mean K and corneal astigmatism were 23.40 (21.27-26.59) mm, 43.90 (40.94-47.01) D and 1.04 (<2.50) D. Nearly all astigmatism was either with or against the rule. Differences between paired eyes were not statistically significant. 95% individuals had asymmetry of AL and mean K<0.70 mm and 0.92 D, respectively.
On the basis of approximation of the 95% CI above, it is suggested that AL, mean K and keratometric astigmatism measurements outside the ranges 21.30-26.60 mm, 41.00-47.00 D and >2.50 D, respectively, and intraindividual asymmetry of AL >0.70 mm or mean K>0.90 D should be verified before acceptance.

To report relationship of age group and axial length (AL) category to lens thickness values in eyes with a clear lens or different types of isolated cataract (nuclear, cortical, and posterior subcapsular (PSC)). Further, we evaluated lens thickness values on anterior chamber depth (ACD) in these eyes.
Observational clinic-based study.Methods
An observational study of 1442 eyes of 1442 individuals (816 eyes with isolated cataract and 626 eyes with clear lens) of those above 25 years of age was evaluated. AL and lens thickness were performed with an A-scan ultrasound after dilatation of the pupil, and manual optical pachymetry was used to measure ACD after dilatation of the pupil.
Lens thickness.
Multiple regression analysis revealed that with each decade of advancement in age, the lens thickness increased by 0.155 mm (P<0.001). The difference in lens thickness after adjusting for age group and AL category was less in cortical cataract by -0.25 mm (P<0.001) and PSC by -0.29 mm (P<0.001); With advancement in AL category, lens thickness decreased by 0.004 mm (P<0.001). After adjusting for all the parameters/variables, regression analysis revealed that as lens thickness increased, there was a significant decrease in ACD (mean -0.44 mm; P<0.001).
Lens thickness was significantly greater in clear lenses when compared with isolated cataracts-greatest with nuclear cataract and least with PSC. Age group and AL category had a significant impact on the lens thickness of both cataract and clear lens. A significant decrease in ACD was found with the increase in lens thickness.

This biometric analysis of 7,500 eyes of cataract patients gave a mean axial length of 23.65 mm, a mean average keratometric value of 43.81 diopters, a mean preoperative anterior chamber depth of 3.24 mm, and a mean central endothelial cell count of 2,470 cells/mm2. There is a statistically significant but clinically insignificant 0.16-diopter flattening of the cornea after cataract surgery without an intraocular lens, but none with an intraocular lens. Pseudophakic eyes do not show a clinically significant increase in corneal flattening over aphakic eyes. Anterior chamber depth increases from 3.24 mm to 3.32 mm (±0.08) in pseudophakic eyes and to 3.67 mm (±0.43) in aphakic eyes. Astigmatism averaged 1.0 diopter in phakic eyes preoperatively, showing a mean increase of only 0.5 diopter in aphakic eyes and 0.65 diopter in pseudophakic eyes.

A new formula, the Hoffer Q, was developed to predict the pseudophakic anterior chamber depth (ACD) for theoretic intraocular lens (IOL) power formulas. It relies on a personalized ACD, axial length, and corneal curvature. In 180 eyes, the Q formula proved more accurate than those using a constant ACD (P < .0001) and equal (P = .63) to those using the actual postoperative measured ACD (which is not possible clinically). In 450 eyes of one style IOL implanted by one surgeon, the Hoffer Q formula was equal to the Holladay (P = .65) and SRK/T (P = .63) and more accurate than the SRK (P < .0001) and SRK II (P = .004) regression formulas using optimized personalization constants. The Hoffer Q formula may be clinically more accurate than the Holladay and SRK/T formulas in eyes shorter than 22.0 mm. Even the original nonpersonalized constant ACD Hoffer formula compared with SRK I (using the most valid possible optimized personal A-constant) has a better mean absolute error (0.56 versus 0.59) and a significantly better range of IOL prediction error (3.44 diopters [D] versus 7.31 D). The range of error of the Hoffer Q formula (3.59 D) was half that of SRK I (7.31 D). The highest IOL power errors in the 450 eyes were in the SRK II (3.14 D) and SRK I (6.14 D); the power error was 2.08 D using the Hoffer Q formula. The series using overall personalized ACD was more accurate than using an axial length subgroup personalized ACD in each axial length subgroup. The results strongly support replacing regression formulas with third-generation personalized theoretic formulas and carefully evaluating the Holladay, SRK/T, and Hoffer Q formulas.

Purpose:
To evaluate the standard clinical outcomes, defocus curves, and satisfaction obtained with a new diffractive low addition trifocal intraocular lens (IOL).
Methods:
Thirty patients who were implanted with the Versario Multifocal 3F IOL (Valeant Med Sp.zo.o., Warsaw, Poland) were recruited for a prospective observational study at Qvision, Vithas Virgen del Mar Hospital, Almería, Spain. Variables for reporting standard outcomes were collected at the 1-month visit for monocular vision and the 3-month visit for binocular vision, including best spectacle refraction and corrected and uncorrected visual acuities at far, intermediate (67 cm), and near (40 cm) distances. In addition, monocular and binocular visual acuity defocus curves were measured and questionnaires for grading subjective visual quality, satisfaction, and visual function were supplied at the end of the follow-up.
Results:
Monocular corrected distance visual acuity decreased progressively from far (-0.05 logMAR) to near (0.25 logMAR) and improved approximately -0.1 logMAR along the defocus curve in binocular vision. The mean residual spherical equivalent (SE) was 0.15 ± 0.47 diopters (D), with 79% of eyes within ±0.50 D and 97% within ±1.00 D with the SRK/T formula. All of the visual function tasks improved after surgery, especially driving at night, which increased from 58 to 79 (P < .05). Of 27 patients, 84.4% were satisfied or very satisfied with their general vision.
Conclusions:
This new lens was similar in terms of visual performance and satisfaction to other trifocal IOLs. It can be classified as a trifocal extended depth of focus IOL because of the performance between extended depth of focus IOLs and medium-high addition trifocal IOLs. [J Refract Surg. 2019;35(4):214-221.].

Purpose:
To determine the effect of anterior chamber depth (ACD) on the accuracy of 8 intraocular lens calculation formulas in patients with normal axial lengths (ALs).
Setting:
Baylor College of Medicine, Alkek Eye center, Houston, Texas, USA.
Design:
Retrospective case series.
Methods:
Patients having cataract surgery with ALs between 22.0 mm and 25.0 mm were divided into 3 groups based on their preoperative ACD measurement. The mean prediction errors, mean absolute errors (MAEs), and median absolute errors for each group were calculated.
Results:
For the ACD of 3.0 mm or less group and the ACD of 3.5 mm or more group, the Barrett Universal II, Holladay 2, Haigis, and Olsen ray-tracing formulas had mean prediction error values that were not significantly different from zero. For the ACD of 3.01 to 3.49 mm group, all formulas had mean prediction error values that were not significantly different from zero. For the ACD of 3.0 mm or less group, the Barrett Universal II formula had a smaller median absolute error than the Haigis, Hoffer Q, and Olsen optical low-coherence reflectometry (OLCR) (Lenstar) formulas and a smaller MAE than the Hoffer Q, Hill-RBF, and Olsen OLCR (P < .05). In the ACD of 3.5 mm or more group, the Barrett MAE was smaller than the Hoffer Q (P < .05); however, there were no significant differences between median absolute errors.
Conclusion:
In eyes with normal ALs, taking preoperative ACD values into consideration might improve refractive outcomes.

Purpose:
To develop and compare the accuracy and reproducibility of the VRF IOL power calculation formula with well-known methods.
Setting:
Kiev Clinical Ophthalmology Hospital Eye Microsurgery Center, Kiev, Ukraine.
Design:
Development and validation study.
Methods:
This analysis comprised 823 eyes of 823 patients operated on by one surgeon with three hydrophobic different types of lenses (IQ SN60WF (494 eyes), ReSTOR SN6AD1 (169 eyes), Alcon Labs, Fort Worth, TX, USA and AMO Tecnis MF ZMB00 (160 eyes), J&J, Santa-Ana, CA, USA). The full data set was divided into 2 subsets, the first to develop the new formula and second to evaluate theirperformance with other most commonly used modern methods of IOL power calculation (Haigis, Hoffer Q, Holladay 1, Holladay 2, SRK/T and T2).The VRF algorithm is empirical; it uses four predictors for estimation of postoperative lens position, including axial length (AL), corneal power (K), preoperative anterior chamber depth (corneal epithelium to lens) (ACD), and horizontal corneal diameter (CD). The results are also stratified into groups of short (≤22 mm), medium (>22 to <24.5 mm), medium-long (≥24.5 to <26 mm) and long (≥26 mm) axial length.
Results:
The mean error (ME), median absolute error (MedAE), and mean absolute error (MAE) were evaluated for all seven methods with 1 IOL type. The VRF formula had the lowest median (0.305 D) absolute error over the entire axial length range, and was comparable with the formulas for T2 (0.321 D), and Holladay 1 (0.326 D).
Conclusion:
The new formula was comparable with well-known methods and was better over the entire axial length range.

Purpose:
To compare the accuracy of intraocular lens (IOL) calculation formulas (Barrett Universal II, Haigis, Hoffer Q, Holladay 1, Holladay 2, Olsen, and SRK/T) in the prediction of postoperative refraction using a single optical biometry device.
Design:
Retrospective consecutive case series.
Participants:
A total of 13 301 cataract operations with an AcrySof SN60WF implant and 5200 operations with a SA60AT implant (Alcon Laboratories, Inc., Fort Worth, TX).
Methods:
All patients undergoing cataract surgery between July 1, 2014, and December 31, 2015, with Lenstar 900 optical biometry were eligible. A single eye per patient was included in the final analysis, resulting in a total of 18 501 cases. We compared the performance of each formula with respect to the error in predicted spherical equivalent and evaluated the effect of applying the Wang-Koch (WK) adjustment for eyes with axial length >25.0 mm on 4 of the formulas.
Results:
For the SN60WF, the standard deviation of the prediction error, in order of lowest to highest, was the Barrett Universal II (0.404), Olsen (0.424), Haigis (0.437), Holladay 2 (0.450), Holladay 1 (0.453), SRK/T (0.463), and Hoffer Q (0.473), and the results for the SA60AT were similar. The Barrett formula was significantly better than the other formulas in postoperative refraction prediction (P < 0.01) for both IOL types. Application of the WK axial length modification generally resulted in a shift from hyperopic to myopic outcomes in long eyes.
Conclusions:
Overall, the Barrett Universal II formula had the lowest prediction error for the 2 IOL models studied.

Although there are inherent differences between corneal and IOL-based refractive surgery procedures, the aim of the procedure is the same in each case, so it makes sense that the 9 standard graphs be applied unaltered to corneal laser refractive surgery, phakic IOL implantation, and RLE. Cataract surgery is a different scenario that warrants a simplified version of the standard graphs. By considering these issues, we hope to standardize the quality of reporting for lens-based procedures from its current level and strive to encourage authors to go beyond these basic graphs to match the standard of studies reporting outcomes of corneal refractive surgery that now have good adherence to the standard graphs. Only by homogenizing the reporting of outcomes as a first step can we hope to glean comparative information among published studies.

Purpose:
To evaluate the accuracy of 3 new methods for intraocular lens (IOL) power selection (Hill-Radial Basis Function [Hill-RBF] method, FullMonte method, and the Ladas Super Formula) compared with that of the Holladay 1 and Barrett Universal II formulas.
Setting:
Ophthalmology Department, Alfred Hospital, Melbourne, Australia.
Design:
Retrospective case series.
Methods:
Patients who had uneventful cataract surgery with insertion of the Acrysof IQ SN60WF IOL over 5 years were included in the study. Data obtained from the electronic medical record and the IOLMaster device were entered into the respective calculators using self-designed computer programs. Using optimized lens constants, the predicted refractive outcome using each of the 5 methods/formulas was calculated and compared with the actual refractive outcome to give the prediction error. Eyes were separated into subgroups based on axial length as follows: short (≤22.0 mm), medium (>22.0 to <24.5 mm), medium-long (≥24.5 to <26.0 mm), and long (≥26.0 mm).
Results:
The study comprised 3122 eyes of 3122 patients. A statistically significant difference in the mean absolute prediction error (MAE) between the 5 methods for IOL power calculation was found (P < .001), with the Barrett Universal II formula being the most accurate. The Ladas Super Formula had the third lowest MAE, the Hill-RBF the fourth lowest MAE, and the FullMonte the highest MAE of the 5 methods assessed.
Conclusion:
New methods for predicting the postoperative refraction failed to yield more accurate results than current formulas.

Purpose:
To assess the accuracy of 7 intraocular lens (IOL) power formulas (Barrett Universal II, Haigis, Hoffer Q, Holladay 1, Holladay 2, SRK/T, and T2) using IOLMaster biometry and optimized lens constants.
Setting:
Public hospital ophthalmology department.
Design:
Retrospective case series.
Methods:
Data from patients having uneventful cataract surgery with Acrysof IQ SN60WF IOL implantation over 5 years were obtained from the biometry and patient charts. Optimized lens constants were calculated for each formula and used to determine the predicted refractive outcome for each patient. This was compared with the actual refractive outcome to give the prediction error. Eyes were separated into subgroups based on axial length (AL) as follows: short (≤22.0 mm), medium (>22.0 to <24.5 mm), medium long (≥24.5 to <26.0 mm), and long (≥26.0 mm).
Results:
The study included 3241 patients. The Barrett Universal II formula had the lowest mean absolute prediction error over the entire AL range (P < .001, all formulas) as well as in the medium (P < .001, all formulas), medium-long (P < .001, except Holladay 1 and T2), and long AL (P < .001, except T2) subgroups. No statistically significant difference was seen between formulas in the short AL subgroup. Overall, the Barrett Universal II formula resulted in the highest percentage of eyes with prediction errors between ±0.25 diopter D, ±0.50 D, and ±1.00 D.
Conclusion:
In eyes with an AL longer than 22.0 mm, the Barrett Universal II formula was a more accurate predictor of actual postoperative refraction than the other formulas.
Financial disclosure:
None of the authors has a financial or proprietary interest in any material or method mentioned.

Purpose
To evaluate the accuracy of 9 intraocular lens (IOL) calculation formulas using 2 optical biometers.
Setting
Private practice, Saint Joseph, Michigan, USA.
Design
Retrospective consecutive case series.
Methods
Nine IOL power formula predictions with observed refractions after cataract surgery were compared using 1 IOL platform. The performance of each formula was ranked for accuracy by machine and by axial length (AL). The Olsen was further divided by a preinstalled version (OlsenOLCR) and a purchased version (OlsenStandalone). The Holladay 2 was divided by whether a refraction was entered (Holladay 2PreSurgRef) or not (Holladay 2NoRef). The OLCR device used in the study was the Lenstar L5 900 and the PCI device, the IOLMaster.
Results
The formulas were ranked by the standard deviation of the prediction error (optical low-coherence reflectometry [OLCR], partial coherence interferometry [PCI]) as follows: OlsenStandalone (0.361, 0.446), Barrett Universal II (0.365, 0.387), OlsenOLCR (0.378, not applicable), Haigis (0.393, 0.401), T2 (0.397, 0.404), Super Formula (0.403, 0.410), Holladay 2NoRef (0.404, 0.417), Holladay 1 (0.408, 0.414), Holladay 2PreSurgRef (0.423, 0.432), Hoffer Q (0.428, 0.432), and SRK/T (0.433, 0.44).
Conclusions
The formulas gave different results depending on which machine measurements were used. The Olsen formula was the most accurate with OLCR measurements, significantly better than the best formula with PCI measurements. The Olsen was better, regardless of AL. If only PCI measurements (without lens thickness) were available, the Barrett Universal II performed the best and the Olsen formula performed the worst. The preinstalled version of Olsen was not as good as the standalone version. The Holladay 2 formula performed better when the preoperative refraction was excluded.
Financial Disclosure
Neither author has a financial or proprietary interest in any material or method mentioned.

Purpose:
To analyze biometry data and corneal astigmatism in cataract candidates from Southern China.
Setting:
Guangdong Eye Institute, Guangdong General Hospital, Guangzhou, China.
Design:
Cross-sectional hospital-based study.
Methods:
The axial length (AL), anterior chamber depth (ACD), horizontal corneal diameter (white to white [WTW]), and corneal power (keratometry [K], flat K, steep K) were measured using the IOLMaster system. Ocular biometric data were collected and analyzed between 2007 and 2011.
Results:
The study comprised 6750 eyes of 4561 consecutive cataract candidates with a mean age of 70.4 years ± 10.5 (SD). The mean AL, ACD, and WTW were 24.07 ± 2.14 mm, 3.01 ± 0.57 mm, and 11.68 ± 0.45 mm, respectively. All values were statistically significantly greater in men than in women (P < .001) and had a significant trend toward a decrease as age increased (P < .001). The mean K value was 44.13 ± 1.63 D. The median corneal astigmatism was 0.90 D (interquartile range, 0.54-1.43). Corneal astigmatism of 1.00 D or greater was found in 2963 eyes (43.9%), and 3590 eyes (53.2%) had against-the-rule (ATR) astigmatism. The axis of corneal astigmatism turned in the ATR direction with age.
Conclusions:
This study provides reference data for cataract patients from Southern China. The profiles of ocular biometric data and corneal astigmatism can help improve surgical procedures and intraocular lens design for the Chinese population.
Financial disclosure:
No author has a financial or proprietary interest in any material or method mentioned.

PurposeTo assess demographics and refractive outcomes in patients undergoing refractive lens exchange surgery (RLE), with a population of cataract patients as a reference.MethodsA RLE cohort from a private eye clinic (n = 675) and a cataract cohort from the outcome registration of the Swedish National Cataract Register were studied and compared from an epidemiological perspective regarding age, gender, preoperative refraction and postoperative refractive outcome.ResultsThe RLE patients were younger (52.1 ± 7.7 versus 73.84 ± 9.32 years) with a smaller percentage of women (45.28% versus 60.46%; p < 0.001) and were more often myopic than the cataract patients. Astigmatism and hyperopia did not differ between the cohorts. Uncorrected visual acuity after RLE equalled the best corrected visual acuity in best cases after cataract surgery. The absolute biometry prediction was more accurate in RLE (0.17 ± 0.27 D versus 0.40 ± 0.58 D; p < 0.001), particularly in patients given a customized toric IOL (0.12 ± 0.27 D; p < 0.05). In cataracts, the Haigis' formula showed higher accuracy than the SRK/T formula (0.39 ± 0.53 D versus 0.43 ± 0.61 D; p < 0.01). Postoperatively after RLE, Laser Epithelial Keratomileusis was performed in 9.04% and Yttrium Aluminium Garnet capsulotomy in 7.41% of the eyes. Other reoperations were performed in three cases, and five postoperative retinal detachments occurred after RLE.Conclusion
Compared with patients undergoing cataract surgery, we see many similarities, but also many interesting differences in patients undergoing RLE. Basic information about the growing population choosing to undergo RLE can help us plan future ophthalmic care.

We aimed to describe norms for the distribution of axial length (AL) and other ocular biometric parameters in an older Caucasian population, measured using partial coherence laser interferometry (Zeiss IOL Master; Carl Zeiss AG, Oberkochen, Germany), a technique now routinely used in measuring AL before cataract surgery. We also aimed to assess age and gender relationships with these parameters and their correlations with spherical equivalent refraction (SER).
Cross-sectional analysis of the Blue Mountains Eye Study (BMES) cohort at the examinations (10-year follow-up examination).
From 2002 to 2004, 1952 persons (76% of surviving baseline BMES participants) aged 59 years or older had ocular biometry measured at the 10-year examinations.
Spherical equivalent refraction was calculated as the sum of sphere +0.5 cylinder power, after protocol refraction. Measurements of AL, corneal curvature (K1), anterior chamber depth (ACD), and corneal diameter (WTW) were performed using the IOL Master. Only right phakic eyes (n = 1335) with biometry data were included.
Axial length distribution.
Mean AL was 23.44 mm (95% confidence interval [CI], 23.38-23.50) and was greater in men, 23.76 mm (CI, 23.68-23.84), than in women, 23.19 mm (CI, 23.11-23.27). The mean K1, ACD, and WTW were 43.42 diopters (D), 3.10 mm, and 12.06 mm, respectively. The AL and ACD distributions were both positively skewed and peaked, whereas the WTW and K1 distributions were near normal. From age 59 years or older, a mean reduction in AL with age was observed (P for trend = 0.005), 0.12 mm per decade (P = 0.0176) in women but only 0.02 mm per decade (P = 0.6319) in men. Mean SER was 0.58 D, and the distribution was peaked with a negative skew. The SER was negatively correlated with both AL (beta coefficient -0.688) and ACD (beta coefficient -0.222), but not with K1 or WTW.
These data provide normative values in the older general population for AL measured using the IOL Master. Axial length distribution was peaked and skewed, suggesting an active modulation process.

To describe the ocular biometry and determinants of refractive error in an adult population in Myanmar.
A cross-sectional, population-based survey of the inhabitants 40 years of age and over from villages in the Meiktila District was performed; 2481 eligible participants were identified, and 2076 participated in the study. Biometric components including axial length (AL), anterior chamber depth (ACD), vitreous chamber depth (VCD), lens thickness (LT) and corneal curvature (CC) were measured. Lens opalescence was measured using the Lens Opacity Grading System III. Non-cycloplegic refraction was measured with an autorefractor.
Complete biometric, refractive and lenticular data were available on 1498 participants. Men had longer ALs, ACDs, VCDs and steeper CCs than women. There was an increase in LT, nuclear opalescence (NO) and myopic shift with increasing age, with no significant change in AL with age. In the 40-59 year age group, VCD was a significant predictor of refractive error, but LT (p<0.001) and NO (p<0.001) were stronger predictors. In the 60+ age group, NO (p<0.001) was also the dominant predictor of refractive error.
This Burmese population, particularly women, has a relatively short AL and ACD. NO is the strongest predictor of refractive error across all age groups in this population.

A rather simple clinical approach has been used to derive formulas necessary to calculate the power of pupillary intracameral prosthetics and these have been applied in 150 eyes. In 136 eyes, the postoperative measurements were within one diopter of preoperative calculations.

A new implant power calculation formula (SRK/T) was developed using the nonlinear terms of the theoretical formulas as its foundation but empirical regression methodology for optimization. Postoperative anterior chamber depth prediction, retinal thickness axial length correction, and corneal refractive index were systematically and interactively optimized using an iterative process on five data sets consisting of 1,677 posterior chamber lens cases. The new SRK/T formula performed slightly better than the Holladay, SRK II, Binkhorst, and Hoffer formulas, which was the expected result as any formula performs superiorly with the data from which it was derived. Comparative accuracy of this formula upon independent data sets is addressed in a follow-up report. The formula derived provides a primarily theoretical approach under the SRK umbrella of formulas and has the added advantage of being calculable using either SRK A-constants that have been empirically derived over the last nine years or using anterior chamber depth estimates.

Several different formulas are available for preoperative calculation of the required implant power for a desired postoperative refraction. However, the application of both theoretical and statistically derived regression formulas to the new generation of soft intraocular lens implants poses several difficulties. In this paper the calculation of an A constant for a specific intraocular hydrogel lens implant, as well as the derivation of a universal theoretical formula, is described. The theoretical formula can be applied to other implant styles with various optical configurations and composed of different biomaterials. The SRK and theoretical formulas have been applied retrospectively to a series of patients receiving an intraocular hydrogel lens implant. A comparison shows that both perform satisfactorily in predicting the desired postoperative refraction.

The precision of intraocular lens (IOL) calculation is essentially determined by the accuracy of the measurement of axial length. In addition to classical ultrasound biometry, partial coherence interferometry serves as a new optical method for axial length determination. A functional prototype from Carl Zeiss Jena implementing this principle was compared with immersion ultrasound biometry in our laboratory.
In 108 patients attending the biometry laboratory for planning of cataract surgery, axial lengths were additionally measured optically. Whereas surgical decisions were based on ultrasound data, we used postoperative refraction measurements to calculate retrospectively what results would have been obtained if optical axial length data had been used for IOL calculation. For the translation of optical to geometrical lengths, five different conversion formulas were used, among them the relation which is built into the Zeiss IOL-Master. IOL calculation was carried out according to Haigis with and without optimization of constants.
On the basis of ultrasound immersion data from our Grieshaber Biometric System (GBS), postoperative refraction after implantation of a Rayner IOL type 755 U was predicted correctly within +/- 1 D in 85.7% and within +/- 2 D in 99% of all cases. An analogous result was achieved with optical axial length data after suitable transformation of optical path lengths into geometrical distances.
Partial coherence interferometry is a noncontact, user- and patient-friendly method for axial length determination and IOL planning with an accuracy comparable to that of high-precision immersion ultrasound.