IOL Calculation Formulas Explained
When planning cataract surgery, one of the most crucial stages for treatment success is choosing the correct intraocular lens (IOL) power.^{1} To reach the targeted refraction, the selection must be performed according to the anatomical and optical parameters of the eye.^{2} In most cases, the target refraction is emmetropia but in some cases, depending on the specific needs and demands of the individual patient, other targets might be required, such as leaving some level of residual myopia in one eye (monovision).^{3} One of the most important parameters in IOL calculation, particularly in nonsyndromic myopia, is axial length (AL). AL is a combination of anterior chamber depth (ACD), lens thickness and vitreous chamber depth and can change the IOL power by up to 2.5 to 3 times. [Meng 2011, Eyewiki] Corneal power is another important component of IOL power determination and keratometry (K) is the measurement of the corneal radius of curvature. The cornea is the transparent part of the eye that covers the iris, pupil and anterior chamber and it accounts for around two thirds of the eye's total optical power. Changes in corneal power can alter the IOL power in a ratio of nearly 1:1. As well as AL and K, other parameters that may be also required, depending on the type of formula used, are the preoperative ACD^{5} and the corneal whitetowhite distance (WTW; also called the horizontal corneal diameter).^{6} The anterior chamber is the fluidfilled space between the iris and the innermost surface of the cornea and the WTW distance is the horizontal distance between the borders of the corneal limbus.
What is the effective lens position?
The only parameter that cannot be measured preoperatively is the position where the IOL "settles down" after surgery, which is also known as the effective lens position (ELP). Prediction of this parameter is initially performed by the IOL manufacturer in form of the Aconstant. The Aconstant is an empirical value and is specific to the design of the IOL. This constant is later refined by statistical optimizations that reflect the variance of the patient's particular preoperative biometry, and the surgeon's personal surgical technique is also taken into account. ELP is defined as the effective distance between the anterior surface of the cornea and the lens plane if the lens was infinitely thin.^{4,5} The ELP is considered to be the main limiting factor for refractive predictability after cataract surgery, as the accuracy of AL and corneal power measurements has been widely demonstrated.^{7} Improvements in IOL power calculations over the past 30 years are the result of improved predictability of the ELP variable.
Mathematical formulas have been developed for best estimation of the ELP, most of which are based on paraxial optics (Figure 1).^{2,4} In these formulas, some ocular parameters are required and the surgeon should know the intended target refraction.^{2,4}
What are the differences between the IOL formulas?
Many published and unpublished IOL formulas are available. The most frequently used formulas are based on two measurements, AL and K, as well as a single IOL constant^{8} (Holladay 1,^{9} SRK/T^{10 }and Hoffer Q^{11}). Predictions of ACD, which increases relative to the increase of AL, are based on initial and generally large datasets from which the formulas have been derived; however individual ACD measurements were not included in the prediction model. The Haigis formula therefore uses three measurements, AL, K and preoperative ACD with the three IOL constants a0, a1 and a2.^{12} Olsen's formula is based on two additional measurements  preoperative refraction and lens thickness  and delivers one IOL constant whereas the Holladay 2 formula is based on seven measurements, including the patient's age and the horizontal WTW measurement).^{1,5 }Finally, the Barrett formula uses a theoretical model eye whereby ACD is related to AL and K, and is also determined by the relationship between the Aconstant and a ‘lens factor'. The position of the principle plane of the IOL is kept as a relevant variable.^{13}
SRKI/II, SRK/T, manufacturer  Holladay 1  Hoffer Q  Haigis 
Aconstant  sf (surgeon factor)  pACD  a0, a1, a2 
Which formula to use for which eye (length)?
For normal ALs of 22.5 to 24.5 mm most formulas work well with minimal discrepancies. In 1993^{11} and again in 2000,^{14} Hoffer performed studies to analyse which formula was the most accurate for ALs of a shorter or longer length than normal. These studies concluded that the Hoffer Q formula provided the most reliable results in short eyes (AL < 22.0 mm) while the SRK/T formula was best in long eyes (AL > 26.0 mm).^{11,14} Recently, in a database study of 8,108 eyes undergoing cataract surgery, the Hoffer Q formula was found to provide the best refractive outcomes in eyes shorter than 21.00 mm and the Holladay 1 and Hoffer Q formulas were equally reliable for eyes with an AL between 21.00 mm and 21.49 mm.^{15} This same study also concluded that the Holladay 1 formula may perform marginally better for eyes between 23.50 mm and 25.99 mm, although the Hoffer Q, Holladay I and SRKT formulas gave comparable refractive outcomes.^{14} Finally, these authors found that the SRK/T formula performed significantly better for eyes with an AL of 27.00 mm or longer.^{15} For highly myopic eyes the Barrett II formula may be a suitable choice and other studies have demonstrated the high level of accuracy of the Haigis formula in extreme hyperopia.^{16 ,17 }See Figure 1.
In conclusion, calculation of the IOL power can be performed using a great variety of formulas. According to clinical studies, the SRKT formula is recommended for rather long eyes whereas the Hoffer Q formula is recommended for rather short eyes. The Holladay 1 and Hoffer Q formulas are equally good for eyes with an AL between 21.00 mm and 21.49 mm and the Holladay 1 formula seems to perform better than the Hoffer Q formula for eyes between 23.50 mm and 25.99 mm. Fourth generation formulas, like the Barrett, Haigis or Holladay 2 formula, have the advantage of including the nonproportional relationship between the ACD and AL and therefore should provide the highest accuracy over the full range of ALs.
REFERENCES

Hoffer KJ. IOL power. Thorofare, NJ, USA: Slack Incorporated, 2011.

Shammas HJ. Intraocular lens power calculations. Thorofare, NJ, USA: Slack Incorporated, 2004.

Shammas HJ, Chan S. Precision of biometry, keratometry, and refractive measurements with a partial coherence interferometrykeratometry device. J Cataract Refract Surg 2010; 36: 14748.

MacLaren RE, Bourne RR, Restori M, Allan BD. Biometry and formula accuracy with intraocular lenses used for cataract surgery in extreme hyperopia. Am J Ophthalmol 2007; 143: 92031.

http://www.doctorhill.com/iolmain/formulas.htm Accessed 26 September 2016.
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