For almost a half a century obtaining accuracy in intraocular lens (IOL) power calculation has been relatively easy in eyes with an axial length (AL) between 22 and 26 mm with normal range (unoperated) corneas. That even includes the early methods of adjusting an 18-diopter (D) IOL based on the patient's previous refractive error through the development of many formulas based on theoretical optics and even regression formulas developed in the 1980s. However, the vexing problems that have arisen over the years have been in eyes that are very short (<22 mm) or very long (>26 mm). Thus, let us look at these 2 particular situations separately.
The major problem with short eyes is due to the higher optical power of the required IOL that gives more weight to any error in the predicted IOL position. Other sources of error in short eyes are related to the higher probability of having a steep corneal and a shallow anterior chamber depth (ACD, distance between the corneal epithelium and the anterior lens surface).1 Another cause is the fact that IOLs over 30 D are only required to be within ±1.00 D of the labeled power compared with ±0.50 D for IOLs less than 30 D.
The first evaluation of the accuracy of formulas for IOL power calculation in eyes of various AL ranges was 24 years ago.2 In that study, one of us (K.J.H.) showed a greater accuracy in prediction with the Hoffer Q formula in eyes shorter than 22 mm (using immersion ultrasound biometry). Later on, this difference was confirmed statistically in a series of 984 eyes shorter than 22 mm (provided by James Gills, MD), which unfortunately was never published. The greater accuracy of the Hoffer Q formula in short eyes was conclusively and statistically proven by Aristidemou et al3 in 2011, using optical biometry in 8108 eyes. However, the comparison was only with the other 2 third-generation formulas (ie, the Holladay 1 and the SRK/T formulas).4,5 The difference among these formulas lies in the use of the tangent of the corneal power to predict the IOL position with Hoffer Q, rather than the corneal height formula of Fyodorov.6
Over the past several decades there have been many publications showing different results with different formulas. In 1996, Holladay debuted the unpublished Holladay 2 formula, which uses 7 biometric variables and was designed to get the best accuracy in all ranges of AL. There are few published studies reporting the results with the Holladay 2; however, Hoffer7 showed in 2000 that the Holladay 2 was equally as accurate as the Hoffer Q in eyes shorter than 22 mm, and that it was less accurate than the Holladay 1 in eyes between 22 and 26 mm.
In 2000, Haigis originated his formula using AL and the preoperatively measured ACD to predict the IOL position based on 3 constants.8 Many studies have shown excellent accuracy of the Haigis formula in all ranges of eyes, including short eyes. Eom et al9 showed that the Haigis formula becomes more accurate than the Hoffer Q in short eyes as the ACD gets shallower than 2.40 mm. Olsen10 has consistently shown the Hoffer Q and Haigis formulas to be the least accurate formulas in short eyes versus his formula.
In the past several years the Barrett Universal II formula has received much attention, without any major published study showing it to be more accurate in any specific AL range than the basic 3 third-generation formulas. However, in 2016, Kane et al11 published a series of 3241 eyes and showed statistically—when comparing the Barrett Universal II with the Haigis, Hoffer Q, Holladay 1 and 2, SRK/T, and T2 formulas—no superiority of any of these 7 formulas in short eyes.11
The radial basis function (RBF), which uses pattern recognition and data interpolation to predict postoperative refraction, has more recently become available and the only published study so far on its accuracy is by Kane,12 who did not find any statistical improvement of this method over the other formulas.
Our conclusion, from looking at these 50 years of analysis, is that one can reliably depend on the Haigis, Hoffer Q, and Holladay 2 formulas for IOL prediction in short eyes.
In the same regard, long eyes have created problems. We are dealing with eyes that have long ALs, flatter corneas, thinner crystalline lenses, and deeper ACDs.1 Obtaining correct AL measurements had been difficult until the introduction of optical biometry in 1999, due to the common presence of staphyloma. On the other hand, the low power of the IOL makes the effect of IOL position less significant on the final refraction of the eye. However, importantly, Haigis13 has shown that constant optimization in these eyes leads to bizarre constants for theoretical formulas, with negative and positive IOLs between −5 and +5 D, mandating that personalization of constants be used in such unusual cases. With these constants, the Haigis formula has produced accurate results. We support this method for long eyes, as described by Haigis, over the Koch and Wang14 adjustment of AL.
As an aside, it is interesting that Hoffer2 showed in 1993 that the Holladay 1 formula gave the very best results in medium-long eyes (24.5-26 mm) and the best results one can obtain performing IOL power calculation. In 2000, Hoffer7 then showed that the Holladay 1 was superior to the Holladay 2 in this medium AL range.
Historically, as noted above with short eyes, Hoffer showed in 1993 that the SRK/T formula would provide more accurate IOL power prediction in eyes over 26 mm compared with the Hoffer Q and the Holladay 1 formulas.2 In 2000 he showed that the Holladay 2 was comparable to the SRK/T in these eyes.7 The accuracy of the SRK/T has since been confirmed statistically by Aristodemou et al.3 More recently, Olsen reported that his C-constant formula provided the best outcomes in long eyes.10 In a small sample of 54 eyes, Cooke et al15 reported that the Olsen, Haigis, and Barrett formulas (in this order) gave the most accurate results in these long eyes. The good outcomes of the Barrett Universal II formula have also been reported by Kane et al.11 Additionally, regarding the RBF method, they reported that no statistically significant difference was detected with respect to the Barrett and SRK/T formulas.12
Because, as of July 2017, the RBF method will not allow calculations for eyes 30 mm or longer, our conclusion at this time is that one can reliably depend on the Barrett Universal II, Haigis (with optimized constants), Olsen, and the old stand-by SRK/T formulas for IOL prediction in very long eyes.
1. Hoffer KJ. Biometry of 7,500 eyes. Am J Ophthalmol.
2. Hoffer KJ. The Hoffer Q formula: a comparison of theoretic and regression formulas [published errata in J Cataract Refract Surg
. 1994;20:677; 2007; 33:2-3]. J Cataract Refract Surg
3. Aristodemou P, Cartwright NEK, Sparrow JM, et al. 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.
4. Holladay JT, Prager TC, Chandler TY, et al. A three-part system for refining intraocular lens power calculations. J Cataract Refract Surg.
5. Retzlaff JA, Sanders DR, Kraff MC. Development of the SRK/T intraocular lens power calculation formula. J Cataract Refract Surg.
1990;16:333-340; erratum, 528.
6. Fyodorov SN, Galin MA, Linksz A. Calculation of the optical power of intraocular lenses. Invest Ophthalmol.
7. Hoffer KJ. Clinical results using the Holladay 2 intraocular lens power formula. J Cataract Refract Surg.
8. Haigis W, Lege B, Miller N, et al. Comparison of immersion ultrasound biometry and partial coherence interferometry for intraocular lens calculation according to Haigis. Graefes Arch ClinExp Ophthalmol.
9. Eom Y, Kang SY, Song JS, et al. Comparison of the Hoffer Q and Haigis formulae for intraocular lens power calculation according to the anterior chamber depth in short eyes. Am J Ophthalmol.
10. Olsen T, Hoffmann PC. C constant: new concept for ray tracing-assisted intraocular lens power calculation. J Cataract Refract Surg.
11. Kane JX, Van Herdeen A, Atik A, et al. Intraocular lens power formula accuracy: comparison of 7 formulas. J Cataract Refract Surg.
12. Kane JX, Van Herdeen A, Atik A, et al. Accuracy of 3 new methods for intraocular lens power selection. J Cataract Refract Surg.
13. Haigis W. Intraocular lens calculation in extreme myopia. J Cataract Refract Surg.
14. Wang L, Shirayama M, Ma XJ, et al. Optimizing intraocular lens power calculations in eyes with axial lengths above 25.0 mm. J Cataract Refract Surg.
15. Cooke DL, Cooke TL. Comparison of 9 intraocular lens power calculations formulas. J Cataract Refract Surg.