## Dr. Sonal Dua, D16060, Dr.Vasavada Abhaykumar Raghukant, Dr. Viraj

Abhayakumar Vasavada, Dr. Shail

**Abstract:**

**Aim: **To evaluate the predictive accuracy of newer IOL formulae Barrett Universal II (BU), Hill RBF calculator (HRBF) to SRK/T, HolladayII, (Hol) Hoffer Q (HoQ) in adult eyes

**Settings and Design:** Prospective, observational study

** ****Methods and Material:** 143 eyes of 133 patients undergoing cataract surgery with monofocal IOL were studied. Prediction Error (PE) & Absolute Prediction Error (APE) was calculated as predicted refraction-actual postoperative refraction at 1 & 3 months post-op

**Statistical analysis used: **Paired ‘t’ test

**Results:**

The mean PE was 0.05__+__0.26, -0.48__+__0.31, -0.19__+__0.30, 0.10__+__0.20 & -0.06__+__0.14 diopters & APE was 0.05__+__0.26, 0.48__+__0.31, 0.19__+__0.30, 0.10__+__0.20 &0.06__+__0.14 diopters with SRK/T, Hol, HoQ, BU & HRBF. Mean PE & APE was statistically significant (P<0.0001) for myopic & emmetropic eyes, not for hypermetropic eyes (P>0.0001). SRK/T & BU had least PE & APE in Myopic & Emmetropic eyes. For Hypermetropic eyes, SRK/T & HRBF had least PE & APE

**Conclusion: **In Myopic & Emmetropic eyes, SRK/T & BU; in Hypemetropic eyes, SRK/T & HRBF gave best PE and APE results

**Keywords: **intra-ocular lens, IOL power formula, prediction error, absolute prediction error

**Key Messages:****Barret’s universal II IOL power calculation formula has the best predicatability and accuracy in calculating IOL power.**

Over the past decade, the term refractive cataract surgery has become more commonly used to describe cataract surgery. This terminology, in large part, is due to the accuracy of refractive outcomes that we can provide to the patients after cataract surgery. However, the inability to accurately predict pseudophakic anterior chamber depth (ACD) and effective lens position (ELP)remains the major source of error in IOL power calculation.

**Introduction:**

Obtaining accurate formula has been relatively easier for eyes measuring axial length (AL) between 22mm to 25mm and can be calculated using different theoretical & regression formulas available. Problem of predicting the accuracy usually arises for short eyes <22mm (AL) or long eyes >25mm(AL).

In shorter eye (Axial length:<22mm) because of higher optical power there is more chances of prediction error due to IOL position. Also there is higher possibility of having steep cornea and shallow anterior chamber depth (distance from endothelium to anterior lens capsule) in short eyes which can be the sources of error.

In long eyes (Axial length:>25mm),flat cornea, deep anterior chamber and difficulty in obtaining axial length due to staphyloma are the major sources of error. However, low IOL power makes the effect of IOL position less significant on final refraction.^{[1]}

IOL power is predicted preoperatively by means of several formulas.^{[2-10]} Third generation formulas; such as Holladay 1, Hoffer Q, and SRK/T; attempt to predict the estimated lens power using AL, corneal curvature (K), and a constant, as the only variables. Fourth generation formulas, like Haigis, take into account the preoperative anterior chamber depth (ACD) and use three constants (a0, a1, and a2), which are analogous to surgeon factor (SF), ACD and AL respectively.^{[3]}Holladay 2 and fifth generation formulas like Barrett Universal II and Olsen include ACD and corneal white-to-white(WTW). The Hill-Radial Basis Function (Hill-RBF) is a mathematical algorithm recently developed to select power of an IOL independent of a distinct ELP calculation

Of note, inaccuracy in measurement of ACD, AL, and K can contribute to 42, 36, and 22% of errors, respectively.^{[4]}It has been considered that IOL calculation formulas were more accurate for eyes with normal AL, but do not have the same level of postoperative refraction outcome for eyes with short AL or long eyes.^{[2]}

In light of the above, the purpose of our study was to evaluate and compare the predictive capacity of newer IOL power calculation formulas (Barrett universal & Hill RBF) with other conventional formulas (SRK/T, Holladay II & Hoffer Q) in emmetropes, myopes and hypermetropes.

**Subjects and Methods:**

Prospective, observational study which included the patients undergoing uneventful sutureless phacoemulsification surgery with Acrysof IQ SN60WF IOL implantation over the last 1 year. Best corrected visual acuity (BCVA) and manifest refraction assessed at 1 & 3months postoperatively. Prediction Error (PE) was calculated as predicted refraction minus actual postoperative refraction and absolute PE (APE) was calculated as predicted refraction-actual postoperative refraction independent of the sign, for all five formulae, at 1 & 3 months post operatively.

Based on the axial length, eyes were classified as: Emmetropic (21-24mm), Myopic (>24mm), Hypermetropic (<21mm).PE and APE was calculated for each formula in each group. Statistical analysis was done using paired t-test (p-value <0.05).

**Results:**

We included total 179eyes (167 patients) with mean age 63.5± 8.3years.Subgroups were formed depending upon the axial length into emmetropes (106eyes), Hypermetropes ( 15 eyes) and myopes (31 eyes). Mean axial length emmetropes-23.42mm (22.08-24.93), myopes-26.74mm (25.23-30.35) and Hypermetropes- 21.47mm (20.9- 21.96). Mean anterior chamber depth – 3.47mm.

Mean prediction error ,PE (__+__standard deviation, SD) in Hypermetropes ( axial length: <22mm) , emmetropes (axial length:22-25mm) and myopes (axial length: >25mm) has been shown in following tables.

In hypermetropes, compared with the predicted values all formulas produced myopic refractive prediction errors with least PE seen with Holladay 2, SRK/T, Barrett Universal II and Hill-RBF followed by Hoffer Q. Absolute prediction error was least with Barrett Universal II and Hill-RBF in hypermetropic eyes.Higher percentage of eyes with prediction error less than ±0.50D seen with Barrett Universal II and Hill-RBF.

**Table 1.****PREDICTION ERROR FOR EACH FORMULA (HYPERMETROPES:< 22mm AL)**

MEAN PE ± SD |
MEAN APE ± SD |
PREDICTION ERROR % |
||

±0.50D |
±1.0D |
|||

SRK/T | -0.05 ± 0.46 | 0.36 ± 0.27 | 67% | 100% |

BARRETT | -0.08 ± 0.35 | 0.28 ± 0.21 | 87% | 100% |

HILL-RBF | -0.09 ± 0.39 | 0.33 ± 0.23 | 87% | 100% |

HOLLADAY II | -0.03 ± 0.43 | 0.35 ± 0.23 | 80% | 100% |

HOFFER-Q | -0.12± 0.42 | 0.45 ± 0.34 | 54% | 93% |

P VALUE |
0.47 |
0.78 |

In emmetropes least mean PE and Absolute PE was observed with Barrett Universal II formula which was statistically significant (p-value <0.05).Higher percentage of eyes with prediction error less than ±0.50D seen with Barrett Universal II and Holladay II.

**TABLE 2.****PREDICTION ERROR FOR EACH FORMULA (EMMETROPES: 22mm-25mm AL)**

MEAN PE ± SD |
MEAN APE ± SD |
PREDICTION ERROR % |
||

±0.50 D |
±1.00 D |
|||

SRK/T | -0.16 ± 0.41 | 0.34 ± 0.28 | 76% | 97% |

BARRETT | -0.06 ± 0.36 | 0.26 ± 0.24 | 90% | 97% |

HILL-RBF | -0.22 ± 0.40 | 0.36 ± 0.29 | 73% | 96% |

HOLLADAY II | -0.12 ± 0.44 | 0.34 ± 0.30 | 81% | 96% |

HOFFER-Q | -0.23 ± 0.41 | 0.37 ± 0.29 | 73% | 95% |

P VALUE |
0.0045 |
0.64 |

In myopes, least PE and Absolute PE was observed with Barrett Universal II formula in myopic eyes followed by SRK/T formula which is statistically not significant (p-value >0.05).Higher percentage of eyes with prediction error less than ±0.50D seen with Barrett Universal II and Holladay 2 followed by SRT/T and Hill-RBF. Hoffer-Q showed the maximum prediction error towards myopia and hence least accuracy.** **

**TABLE 3. ****PREDICTION ERROR FOR EACH FORMULA **

**(MYOPIA: >25mm AL)**

MEAN PE ± SD |
MEAN APE ± SD |
PREDICTION ERROR % |
||

±0.50 D |
±1.00 D |
|||

SRK/T | 0.05 ± 0.31 | 0.25 ± 0.18 | 93% | 7% |

BARRETT | 0.02 ± 0.26 | 0.21 ± 0.13 | 100% | 0% |

HILL-RBF | 0.11 ± 0.33 | 0.21 ± 0.27 | 93% | 7% |

HOLLADAY II | -0.08 ± 0.25 | 0.21 ± 0.14 | 100% | 0% |

HOFFER-Q | -0.31 ± 0.41 | 0.37 ± 0.29 | 87% | 13% |

P VALUE |
0.53 |
0.90 |

** ****Discussion:**

With current technology, accuracy of IOL calculation formulas has been comparatively high for emmetropes in comparison with Hypermetropes ( Axial length:<22mm) and myopes (>25mm).The goal of our study was to determine whether newer IOL power prediction formulas might improve outcomes in these challenging eyes. Overall we found only modest differences between all 5 formulas. Over the entire AL range, the Barrett Universal II

was the most accurate formula, having a lower MAE and a higher percentage of eyes with prediction errors between ±0.50 D and ±1.00 D than the other 4 formulas assessed.

Previous studies have shown that the Hoffer Q is the most popular formula for use in eyes with an AL of 22.0 mm or lessand has been reported as the most accurate formula for short eyes in studies by Hoffer(although the study included only 10 eyes with a short AL), Gavin and Hammond (although it was tested only against the SRK/T), and Aristodemou et al(although only in eyes with an AL <21.0 mm).^{[11,12,13]}In our study, 15 eyes had an AL of 22.0mm or less, with Holladay 2 & SRK/T having the least prediction error whereas least Absolute prediction error with Barrett’s universal II &Hill-RBF, which is statistically not significant.

Most eyes (106) in our study had a medium AL (between 22.0mmand 25mm). The Barrett Universal II was the most accurate formula in this AL range, with the lowest MAE (statistically significant over all other formulas) and highest percentage of eyes with

±0.50 D and±1.00 D prediction errors. Our results are consistent with those reported in Barrett’s initial publication for medium length eyes.^{[14]}

In our study, 33 eyes had an AL of 25.00 mm or above and we found that the most accurate formula was the Barrett Universal II followed by the SRK/T, Holladay 2 and Hill-RBF. A similar conclusion was reported by the only recent study to report on the Barrett Universal II formula in eyes with a long AL.^{[15]}

**CONCLUSION**

All 5 Formulae performed very well in Emmetropes Hypermetropes & Myopic Eyes except the Hoffer-Q. In emmetropes, least prediction error with Barrett’s universal II formula followed by Holladay II & SRK/T (Statistically significant).In hypermetropes, least Prediction error with Holladay II & SRK/T whereas least Absolute prediction error with Barrett’s universal II &Hill-RBF (not significant).

And in myopes, least prediction error with Barrett’s Universal II & SRK/T, however not statistically significant. Highest % of eyes within __+__ 0.50 D with Barrett Universal II formula.

Hence, Barrett Universal II formula has worked best for all axial lengths in our case series.** **

**REFERENCES**** **

1.Hoffer KJ. Biometry of 7,500 eyes. *Am J Ophthalmol. *1980;90:360‒368.

2.Roh YR, Lee SM, Han YK, Kim MK, Wee WR, Lee JH. Intraocular lens power calculation usingIOLMaster and various formulas in short eyes. Korean J Ophthalmol. 2011;25:151–5.

3.Olsen T, Thim K, Corydon L. Accuracy of the newer generation intraocular lens power calculationformulas in long and short eyes. J Cataract Refract Surg. 1991;17:187–93.

4.Wang L, Shirayama M, Ma XJ, Kohnen T, Koch DD. Optimizing intraocular lens power calculations ineyes with axial lengths above 25.0 mm. J Cataract Refract Surg. 2011;37:2018–27.

5.Lee AC, Qazi MA, Pepose JS. Biometry and intraocular lens power calculation. Curr Opin Ophthalmol.2008;19:13–7.

6.Narváez J, Zimmerman G, Stulting RD, Chang DH. Accuracy of intraocular lens power prediction usingthe Hoffer Q, Holladay 1, Holladay 2, and SRK/T formulas. J Cataract Refract Surg. 2006;32:2050–3.

7.Gavin EA, Hammond CJ. Intraocular lens power calculation in short eyes. Eye. 2008;22:935–8.

8.MacLaren RE, Natkunarajah M, Riaz Y, Bourne RR, Restori M, Allan BD. Biometry and formulaaccuracy with intraocular lenses used for cataract surgery in extreme hyperopia. Am J Ophthalmol.2007;143:920–31.

9.Fenzl RE, Gills JP, Cherchio M. Refractive and visual outcome of hyperopic cataract cases operated onbefore and after implementation of the Holladay II formula. Ophthalmology. 1998;105:1759–64.

10.Preussner PR, Olsen T, Hoffmann P, Findl O. Intraocular lens calculation accuracy limits in normal eyes. J Cataract Refract Surg. 2008;34:802–8.

11.Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg 2000; 26:1233–1237.

12.Gavin EA, Hammond CJ. Intraocular lens power calculation in short eyes. Eye 2008; 22:935–938.

12.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.

13.Barrett GD. An improved universal theoretical formula for intraocular lens power prediction. J Cataract Refract Surg 1993;19:713–720.

14.Abulafia A, Barrett GD, Rotenberg M, Kleinmann G, Levy A, Reitblat O, Koch DD, Wang L, Assia EI. Intraocular lens power calculation for eyes with an axial length greater than 26.0 mm: comparison of formulas and methods. J Cataract Refract Surg 2015; 41:548–556.

## Leave a comment or raise a query to the author