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 Table of Contents    
Year : 2022  |  Volume : 15  |  Issue : 3  |  Page : 290-294  

Accuracy of Barrett versus third-generation intraocular lens formula across all axial lengths

Cataract and Refractive Services, The Eye Foundation Hospital, Coimbatore, Tamil Nadu, India

Date of Submission17-Jun-2021
Date of Decision28-Jul-2021
Date of Acceptance18-Dec-2021
Date of Web Publication02-Nov-2022

Correspondence Address:
Raline Solomon
The Eye Foundation, 582, Diwan Bahadur Rd, R S Puram West, Coimbatore - 641 002, Tamil Nadu
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/ojo.ojo_188_21

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PURPOSE: The purpose of this study is to evaluate and compare the accuracy of Barrett Universal II versus third-generation formula for different intraocular lens (IOL) powers for Indian eyes with different axial lengths (ALs).
DESIGN: This is a retrospective, nonrandomized consecutive case series.
METHODS: This study reviewed 981 eyes from 825 patients who had uneventful cataract surgery and IOL implantation. The eyes were separated into subgroups based on AL as follows: short (<22.0 mm), medium (22.01–23.99 mm), and long (>24.0 mm). The predicted refractive outcome using formulas was calculated and compared with the actual refractive outcome to give the prediction error. The percentage of every refractive error absolute value for each formula was calculated at <±0.50D, 0.50D-0.75D, and >±0.75D.
RESULTS: In all, 981 eyes were analyzed. There were no significant differences in the median absolute error predicted by Barrett and the third-generation formulae. The Barrett Universal II formula resulted in significantly lowest mean spherical equivalent in short eyes (P = 0.0047) as well as a higher percentage of eyes with prediction errors within <±0.50D, 0.50D-0.75D, and >±0.75D. We found that the Barrett Universal II formula had the lowest predictive refraction error and mean absolute error across all ALs.
CONCLUSION: The Barrett Universal II formula rendered the lowest predictive error compared with SRK/T, Holladay, and Hoffer Q formulas. Thus, the Barrett Universal II formula may be regarded as a more reliable formula for achieving emmetropia and reducing postoperative refractive surprises across all ALs.

Keywords: Barrett, intraocular lens formulae, third-generation formulae

How to cite this article:
Solomon R, Tamilarasi S, Sachdev G, Dandapani R. Accuracy of Barrett versus third-generation intraocular lens formula across all axial lengths. Oman J Ophthalmol 2022;15:290-4

How to cite this URL:
Solomon R, Tamilarasi S, Sachdev G, Dandapani R. Accuracy of Barrett versus third-generation intraocular lens formula across all axial lengths. Oman J Ophthalmol [serial online] 2022 [cited 2023 Jan 27];15:290-4. Available from: https://www.ojoonline.org/text.asp?2022/15/3/290/360399

   Introduction Top

The prediction of refractive outcomes after cataract surgery has steadily improved, with more recent intraocular lens (IOL) power formulas generally outperforming those of prior generations.[1],[2] Yet, there is still considerable debate about which formula provides the most accurate refractive prediction. Because no single formula has been shown to be highly accurate across a range of eye characteristics, some authors have suggested that cataract surgeons should use different formulas for eyes of varied ocular dimensions.[3],[4] Popular third-generation formulas (Hoffer Q, SRK/T, and Holladay 1) calculate effective lens position using the anterior chamber depth (ACD), axial length (AL), and keratometry (K). The Barrett Universal II formula uses a theoretical model eye in which ACD is related to AL and K. A relationship between the A-constant and a “lens factor” is also used to determine ACD.[5] The important difference between the Barrett formula and other formulas is that the location of the principal plane of refraction of the IOL is retained as a relevant variable in the formula. To our knowledge, there is no current published data on head-on comparison of outcomes of the Barrett Universal II versus the third-generation formulae across three different ALs. However, there are studies which have compared the refractive outcomes of each of these formulae separately or as a part of the analysis of outcomes of other formulae. There is now a trend for many surgeons in our institute and others moving toward the Barrett Universal II from the third-generation formulae. This changing trend kindled our curiosity toward sketching this study.

The aim of this study was to investigate and compare the accuracy of the Barrett Universal II formula for all ALs versus the third-generation formula: SRK/T for long eyes (AXL >24 mm), Holladay 1 for medium eyes (AXL = 22.00–23.99 mm), and Hoffer Q for short eyes (AXL ≤21.99 mm) in predicting refractive outcome for standard cataract surgery.

   Methods Top

  • Study design: Retrospective, nonrandomized case series
  • Setting: Tertiary Eye Care Hospital, South India
  • Duration of data collection: January 2017 and December 2018 (18 months).

The study adhered to the tenets of the Declaration of Helsinki and approved by the institutions ethics committee. Informed consent was obtained from all the participants included in the study. Patients with age-related cataracts undergoing uneventful cataract surgery were included in the study. Intraoperative complications, the presence of any corneal pathology, glaucoma, retinal pathology, postoperative corrected distance visual acuity (CDVA) worse than 20/40, patients with preoperative corneal astigmatism of >0.75D, eyes requiring additional surgical procedures at the time of cataract surgery (including peripheral corneal relaxing incisions), and previous intraocular surgery (including previous refractive corneal surgery) were excluded from the final cohort.

Ocular biometry was performed in all eyes using the IOLMaster 700 (Carl Zeiss Meditec AG, Jena, Germany) based on swept-source optical coherence tomography technology. Patients were grouped into two groups, Group 1 – patients who had their IOL power calculated using the Barrett Universal II formula (Across all AL) and Group 2 – patients who had their IOL power calculated using the third-generation IOL formulae (SRK/T for AXL ≥24 mm, what about, Holladay 1 for AXL = 22–23.99 mm and Hoffer Q for AXL ≤21.99 mm). IOL power with the first myopic target refraction was selected for implantation. All surgeries were performed by a single experienced surgeon using a 2.4 mm clear corneal incision and a standard phacoemulsification technique. All patients had implantation of an AcrySof SN60WF IOL (Alcon, Ft Worth, TX, USA). Preoperative examinations, operative details, postoperative findings, and refractive data were collected.

Statistical methods

Refractive prediction error (RPE) was considered primary outcome variable. Groups (Group 1 vs. Group 2) were considered as primary explanatory variable. All quantitative variables were checked for normal distribution within each category of explanatory variable using visual inspection of histograms and normality Q-Q plots. Shapiro–Wilk test was also conducted to assess normal distribution. Shapiro–Wilk test P > 0.05 was considered normal distribution. For normally distributed quantitative parameters, the mean values were compared between study groups using independent sample t-test (two groups). P < 0.05 was considered statistically significant. IBM Corp. Released 2013. IBM SPSS Statistics for Windows, Version 22.0. Armonk, NY was used for statistical analysis.[6]

Statistical analysis

RPE was calculated as the difference between the postoperative refractive outcome expressed as spherical equivalent and the refraction predicted by each formula. A negative value indicates a myopic prediction error that shows a more myopic result than the predicted refraction. The mean numerical RPE for each formula, the mean absolute error (MAE) and median absolute error for each formula were calculated. The percentages of eyes within <±0.50 D, 0.50D-0.75D, and >±0.75 D of the predicted refraction were calculated and analyzed.

   Results Top

The study composed of 981 eyes of 825 patients. The demographics of the patients are listed in [Table 1]. Keratometry, AXL, and ACD across all the study groups were comparable. There was almost no statistical difference on comparing postoperative uncorrected distance visual acuity, RPE, MAE, and CDVA across all the groups except a significant difference in mean refractive spherical equivalent in the group with short AL, as shown in [Table 2].
Table 1: Preoperative patient demographics

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Table 2: Postoperative refractive parameters

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However, there was a good difference between the percentage prediction between the two groups, with the prediction error of the Barrett Universal II IOL formula to be far superior and much closer to emmetropia than the other third-generation IOL formulae, as shown in [Table 3] and [Table 4]. There was no documented myopic or hyperopic surprise in any of the IOL formulae.
Table 3: Percentage prediction error using Barrett universal formula

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Table 4: Percentage prediction error using third-generation formula

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   Discussion Top

CDVA has long been the principal outcome measure following cataract surgery; however, surgeons are now being judged more and more on refractive outcomes and the ability to achieve the desired refractive target and expected degree of spectacle independence.[7],[8] Published results suggest that surgeons are, by and large, meeting expectations.[9],[10] Refractive outcomes remain variable based on differences in surgeon technique and experience, preoperative diagnostic technology, and population cohort.[11],[12],[13],[14] Proposed benchmark outcomes also vary. Based on a large subset of patients undergoing surgery across the National Health Service, Gale et al. have previously suggested that 55% of patients should achieve postoperative spherical equivalent of ± 0.5D of the intended target and 85% of patients within ± 1.0D.[15] Subsequent papers, however, suggest that outcomes in excess of these figures may be feasible. Simon et al. achieved 67% of cases within ± 0.5D and 94% of cases within ± 1.0D in their own case series located at an academic teaching institution.[16] Considering the combination of modern optical biometry, informed formula choice, and IOL constant optimization, Sheard had proposed that surgeons should be able to achieve 60% and 90% within ± 0.5D and ± 1.0D, respectively.[17] To determine the effectiveness of the IOL formula in a relatively standard population, we calculated the theoretical performance of the Barrett Universal II formula in comparison with existing optimized formulas (Holladay I, SRK/T, and Hoffer Q).

In our study, the prediction error of <±0.50D using the Barrett Universal II formula across all ALs is given in [Table 3]. RPE of 96%, 92.3%, and 90.6% in patients with long, normal, and short ALs was seen. In those whose third-generation formula was used, the prediction error of <±0.50 D was seen in 93.1%, 82.5%, and 75% in patients with long, normal, and short ALs [Table 4]. However, there was no statistical significance in prediction error of patients in extreme of axial length long eyes P = 0.4360, short eyes P = 0.0525. The percentage of prediction error of < ±0.50D in normal eyes between the Barrett and third-generation formulae was statistically significant (P < 0.0001). This difference in statistical significance could also be due to large variation in the sample size across the three groups. In a study by Roberts et al., the percentage prediction of <±0.50D using SRK/T and Hoffer Q was 80%, Holladay –78%, and Barrett Universal II formula – 81%, compared to our study where the percentage prediction was SRK/T –93%, Hoffer –Q-75%, and Holladay –82.5%, and Barrett Universal II formula was 96%, 92.3%, 90% across long, normal, and short eyes, respectively, although not statistically significant is much higher than the other formulae [Table 3] and [Table 4].[18] A study by Gökce et al. comparing the prediction percentage outcomes of <±0.50D in short eyes using Hoffer Q was 64% and Barrett Universal II was 68.6% compared to our study which was 75% in short eyes using Hoffer Q and 90% using Barrett Universal II formula.[19]

The MAE derived from using the Barrett Universal II was lower than those of the third-generation formulae, across all ALs [Table 2]. The real challenge in giving the best postoperative refractive outcomes lies in selecting the IOL formulae that would give the lowest RPE, especially in eyes with extreme of ALs (AXL >24.00 mm and <22.00 mm). In our study, the Barrett Universal II formula had prediction error of 0.07 ± 0.31, 0.07 ± 0.49 versus 0.04 ± 0.35, −0.12 ± 0.13 using SRK = T, Hoffer Q in long and short eyes, respectively, the differences were not statistically significant and the results are almost comparable to those published by Zhou et al. and Gökce et al.[19],[20] In terms of overall accuracy, the Barrett Universal II formula provided the equivalent or lowest variation within the data, and thereby smallest percentage of refractive surprises compared to other formulas for all cohorts. Our results, representative of a nontoric cataract population show that excellent results can be achieved combining optical biometry with consistent technique and latest IOL power calculation formulas. The advantages of the Barrett Universal II formula are that (i) it is independently available, (ii) it requires minimal additional manipulation to achieve excellent results across all ALs, and (iii) it does not require the calculation of surgically induced astigmatism. The limitation of our study remains the relatively small numbers in the short and long AL groups. Study inclusion was limited to the SN60WF IOL as this was one of the most commonly used IOL in this part of the world. Although it would be reasonable to expect that the formulas would produce similar outcomes for additional lenses, further investigation may be useful to confirm this.

   Conclusion Top

We found that excellent results can be obtained with a variety of IOL power calculation formulas for eyes with different ALs, especially extreme of ALs. The Barrett Universal II formula may provide additional benefits for patients by reducing possible refractive surprises and a very effective tool to reaching the goal of emmetropia which is a desirable goal for every cataract surgeon in the present-day world.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

   References Top

Kane JX, Van Heerden A, Atik A, Petsoglou C. Intraocular lens power formula accuracy: Comparison of 7 formulas. J Cataract Refract Surg 2016;42:1490-500.  Back to cited text no. 1
Cooke DL, Cooke TL. Comparison of 9 intraocular lens power calculation formulas. J Cataract Refract Surg 2016;42:1157-64.  Back to cited text no. 2
Aristodemou P, Knox Cartwright NE, Sparrow JM, Johnston RL. Formula choice: Hoffer Q, Holladay 1, or SRK/T and refractive outcomes in 8108 eyes after cataract surgery with biometry by partial coherence interferometry. J Cataract Refract Surg 2011;37:63-71.  Back to cited text no. 3
Ladas JG, Siddiqui AA, Devgan U, Jun AS. A 3-D “super surface” combining modern intraocular lens formulas to generate a “super formula” and maximize accuracy. JAMA Ophthalmol 2015;133:1431-6.  Back to cited text no. 4
Barrett GD. An improved universal theoretical formula for intraocular lens power prediction. J Cataract Refract Surg 1993;19:713-20.  Back to cited text no. 5
IBM Corp. Released 2013. IBM SPSS Statistics for Windows, Version 22.0. Armonk, NY: IBM Corp.; 2013.  Back to cited text no. 6
Olsen T. Calculation of intraocular lens power: A review. Acta Ophthalmol Scand 2007;85:472-85.  Back to cited text no. 7
Lee AC, Qazi MA, Pepose JS. Biometry and intraocular lens power calculation. Curr Opin Ophthalmol 2008;19:13-7.  Back to cited text no. 8
Colin J, El Kebir S, Eydoux E, Hoang-Xuan T, Rozot P, Weiser M. Assessment of patient satisfaction with outcomes of and ophthalmic care for cataract surgery. J Cataract Refract Surg 2010;36:1373-9.  Back to cited text no. 9
Behndig A, Montan P, Stenevi U, Kugelberg M, Lundström M. One million cataract surgeries: Swedish National Cataract Register 1992-2009. J Cataract Refract Surg 2011;37:1539-45.  Back to cited text no. 10
Haigis W. Intraocular lens calculation in extreme myopia. J Cataract Refract Surg 2009;35:906-11.  Back to cited text no. 11
Lam S. Comparing optical low coherence reflectometry and immersion ultrasound in refractive outcome after cataract surgery. J Cataract Refract Surg 2013;39:297-8.  Back to cited text no. 12
Carifi G, Aiello F, Zygoura V, Kopsachilis N, Maurino V. Accuracy of the refractive prediction determined by multiple currently available intraocular lens power calculation formulas in small eyes. Am J Ophthalmol 2015;159:577-83.  Back to cited text no. 13
Reitblat O, Assia EI, Kleinmann G, Levy A, Barrett GD, Abulafia A. Accuracy of predicted refraction with multifocal intraocular lenses using two biometry measurement devices and multiple intraocular lens power calculation formulas. Clin Exp Ophthalmol 2015;43:328-34.  Back to cited text no. 14
Gale RP, Saldana M, Johnston RL, Zuberbuhler B, McKibbin M. Benchmark standards for refractive outcomes after NHS cataract surgery. Eye (Lond) 2009;23:149-52.  Back to cited text no. 15
Simon SS, Chee YE, Haddadin RI, Veldman PB, Borboli-Gerogiannis S, Brauner SC, et al. Achieving target refraction after cataract surgery. Ophthalmology 2014;121:440-4.  Back to cited text no. 16
Sheard R. Optimising biometry for best outcomes in cataract surgery. Eye (Lond) 2014;28:118-25.  Back to cited text no. 17
Roberts TV, Hodge C, Sutton G, Lawless M, Contributors to the Vision Eye Institute IOL Outcomes Registry. Comparison of Hill-radial basis function, Barrett Universal and current third generation formulas for the calculation of intraocular lens power during cataract surgery. Clin Exp Ophthalmol 2018;46:240-6.  Back to cited text no. 18
Gökce SE, Zeiter JH, Weikert MP, Koch DD, Hill W, Wang L. Intraocular lens power calculations in short eyes using 7 formulas. J Cataract Refract Surg 2017;43:892-7.  Back to cited text no. 19
Zhou D, Sun Z, Deng G. Accuracy of the refractive prediction determined by intraocular lens power calculation formulas in high myopia. Indian J Ophthalmol 2019;67:484-9.  Back to cited text no. 20
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