When, How and Which?
IOL MASTER BASICS, APPLICATION AND FALLACIES
Background
IOL Power calculation is an important parameter in relation to postoperative visual outcome. In 1967, Fyodorov et al first presented a theoretical formula based on geometric optics using axial length and keratometry.
Many Theoretical formulae followed thereafter.
The three types of IOL power calculation formulae are:
Theoretical Formulae1
These formulae are based on an optical model of the eye.
An optics equation is solved to determine the IOL power
needed to focus light from a distant object onto the retina.
In the different formulae, different assumptions are made about the refractive index of the cornea to the IOL, the distance of the IOL to the retina as well as other factors.
They are based on a theoretical optical model of the eye.
Binkhorst Formula Pe = [N/(L-C)] – [NK/(N-KC)]
Other Theoretical Formulae:
Colenbrander’s Pe = [1366 /L – C – 0.05 ] – Formula [1366/ (1336/ K) - C – 0.05]
Gullstrand’s Formula Pe = 1348 K + 4L Fyodorov’s Formula Pe = 1336 – LK / (L – C)
(1- CK/1336)
Van der Heijde’s Pe = [1336/(L-C)] - [1/(1/K) –
Formula (C/1336) ]
Pe = Emmetropic IOL power (diopters) L = Axial length of eye (mm)
K = Corneal dioptric power (diopters)
C = Pseudophakic depth of the anterior chamber r = Average corneal radius (mm) = 337.5/K;
A = Constant derived for each type of lens and manufacturer
SE = Spherical equivalent N = Aqueous and Vitreous R.I Binkhorst Formula
Binkhorst has made a correction in his formula:
The Modified Binkhorst Formula, for surgically flattening of cornea, using a corneal index of refraction of 1.33. He also corrects for the thickness of the lens implant by subtracting approx. 0.05 mm from the measured axial length. Thus with the Binkhorst formula, 0.25 mm is added to the measured axial length to account for the distance between the vitreo-retinal interface and the photoreceptor layer, and 0.05 mm is subtracted for lens thickness, resulting in a net addition of 0.2 mm to the measured axial length.
Modified Binkhorst formula:
Pe = 1366 (4r – L) / (L – C)(4r – C) Other Modified Theoretical Formulae:
Hoffer’s Formula:
Pe = [1336/L-C-0.05] – [1336/ (1336/K+E) – C – 0.05]
Shammas’s Fudged Formula:
Pe = [1336/L-0.1(L-23) – C -0.05 ] – [1/ ( 1.0125/K) –( C+
0.05/1336)]
Disadvantages: The problem in these formulae is in the axial length measurement. Because of the variation of the acoustic density of a cataract these velocities cannot be known exactly. When cataracts are much more acoustically dense than the average lens, the sound wave will move more rapidly through the lens and return to the transducer much more quickly than would have been expected for a given axial length. As a result of the velocity error, the eyes appear to be shorter. The formula thus, calculates an IOL power for an AL which is too short. The patient then becomes too myopic.
Theoretical formulae help the surgeon to anticipate what should result, not what will result from implantation.
Regression (Empirical) Formulae 1
These formulae are derived from empirical data and are based on retrospective analysis of postoperative refraction after IOL implantation. The results of a large number of IOL implantations are plotted with respect to the corneal power, axial length of the eye, and emmetropic IOL power.
The best-fit equation is then determined by the statistical procedure of regression analysis of the data. Unlike the theoretical formulae, no assumptions are made about the optics of the eye. These regression equations are only as good as the accuracy of the data used to derive them.
Factors important for regression formulae are:
Axial Length Measurement
An error of 1 mm affects the postoperative refraction by 2.5 D approx.(L)
Corneal power: the keratometric reading. (K) Postoperative Anterior Chamber Depth: (pACD)
An error of 1 mm affects the post-op refraction by approx. by 1.0 D in myopic eye, 1.5 D in emmetropic eye and up to 2.5 D in hyperopic eye.(pACD)
The most popular regression formula is the SRK formula which was developed by Sanders, Retzlaff and Kraff popularized this in 1980.
SRK Formula Pe = A – 2.5 L – 0.9 K SRK II Formula7 Pe = A1-0.9 K-2.5 L A1 = new constant
A1 = A+ 3 if axial length L < 20 mm This is a new formula which is used to produce a desired postoperative refraction R
I = IOL power for desired Ametropia P = Emmetropia Power calculated by SRK II cr = another empirical constant defined as cr = 1 for P < 14
cr = 1.25 for P>14
Other Regression formulas:
Axt Formula7 Pe = 120.6 – 2.49 L – 0.97 K Donzis Kastle Gordon Formula7
Pe = A – 0.9 K – 58.75 + 58.75 [(23.5 – L)/L]
Pe = Emmetropic IOL power (diopters) L = axial length of eye (mm)
K = corneal dioptric power (diopters)
A = constant derived for each type of lens and manufacturer
Advantages: Implant power calculations can be made much more accurately through the use of regression formulae that are based on the analysis of the actual results of many uncomplicated IOL implantations in previous cataract surgeries.
Since regression analysis is based on the results of actual operations, it includes the vagaries of the eye and measuring devices, vagaries that theoretical formulae attempt to address with correction factors.
Newer/3rd Generation Theoretical Formulae SRK/T: It is a non-linear modified theoretical optical formula empirically optimized for post-op ACD, Retinal thickness, and Corneal RI.
This formula is for long eyes >28 mm.
Haigis Formula
In 1991, Wolfgang Haigis, the head of the biometry Department of the University of Würzburg Eye Hospital in Germany, published the Haigis formula.
Using the same mathematical backbone as other theoretic formulas, the Haigis formula approaches the problem of IOL power accuracy with three constants (a0, a1, and a2) and adds a measured anterior chamber depth for a third required variable.
With the a0 constant optimized in a manner similarly to SRK/T, and the a1 and a2 constants based on schematic eye parameters, the formula performs similar to most third-generation two-variable formulas.
When all three constants are optimized by regression analysis based on surgeon-specific IOL data, however,
IOL Calculations: When, How and Which?
39
the range of the Haigis formula can be extended greatly to cover both high-axial hyperopia and high-axial myopia.3,4 This formula uses three constants to set both the position and shape of a power prediction curve. The IOL calculation according to Haigis is based on the elementary IOL formula for thin lenses.
D = a0+ (a1x ACD) + (a2 x AL) Uses three constants: a0, a1, a2 D = Effective Lens Position ( ELP )
a0 = same as lens constants for the different formulas given before
a1 = tied to anterior chamber depth a2 = measured axial length
The constants interact with ACD AND AL. These constant are derived by tracking post-op results specific to the surgeon.2
Hoffer Q Formula
The Hoffer Q Formula was published in 1993, based on the earlier work of Kenneth J Hoffer, MD.
P = f (A, K, Rx, pACD) It is a function of A: axial length
K: average corneal refractive power
K=0.5(K1+K2) with ( K1=337.5/R1C & K2= 337.5/R2C) R1C/R2C=corneal radii
Rx: refraction = f (A, K, P, pACD)
pACD: personalized ACD =ACD –constant=0.583*A-const-63.89
Holladay Formula: I and II8
Holladay I: In 1988 when Dr Holladay created the Holladay I formula, he used the axial length and keratometry to determine the ELP using the Fyodorov formula to calculate corneal height. Likewise, the SRK/T formula used a similar method to predict the ELP while the Hoffer Q formula also used axial length and K but in a different manner (tangent of K) to predict the ACD.
These three formulas became grouped together when Dr Hoffer used all three in the first Windows computer IOL power calculation program for clinical use (Hoffer Programs) and are referred to as third-generation formulas. The Holladay IOL Consultant used a similar system and added the Holladay II formula.
Holladay II: The Holladay II formula uses seven variables to predict lens position, and is derived from the result of a study that Dr Holladay conducted in which he used data on myopic and hyperopic eyes from 35 surgeons (30,000 cases) around the world. In addition to the axial length and keratometry, Dr Holladay and his colleagues asked these surgeons to measure the horizontal? white-to-white?
corneal diameter, the ACD, the lens thickness, the refraction, and the age of the patient.
The initial formula uses “Basic Surgeon Factor”. It can be calculated from the A constant provided by lens manufacturer.
The Holladay II formula, available since 1998, is considered by many to be the most accurate of the theoretic formulas currently offered. The formula is easy to optimize and works well across a wide range of axial lengths.
Components of this are:
Data screening criteria to identify improbable axial length and keratometric measurement.
The modified theoretical formula , which predicts the effective lens position of the IOL based on axial length and average corneal curvature.
Personalized surgeon factor that adjusts for any consistent bias on surgeon from any source. It is advance method, which requires patient refractions.
Constant of IOL Formulae7
This value represents where we anticipate the IOL to sit in relationship to the cornea. Specifically how near or far from the cornea. The “constant” will decrease with an ACIOL as compared to a PCIOL. The ACL sits closer to the cornea, hence less power is needed.
Currently three constants are in use:
The SRK/T USES “A-Constant”
The Holladay I uses “Surgeon Factor”
The Holladay II and Hoffer Q use “Ant Chamber Depth”
These formulae assume that the distance from the cornea to the IOL is proportional to the axial length, i.e.
Short eyes have shallow ACD and long eyes will have deeper AC.2
Effective Lense Position3,4,7
In actual practice, the two eyes with same AL and K may have different lens power, this may be due to:
• Effective lens position (i.e. Distance of lens from the cornea)
• Individual geometry of Lens model.
The main part of highly accurate IOL power calculation is ability to correctly predict ‘D’ i.e. The effective lens position for any given patient and IOL.
SRK/T ‘D’= A constant Hoffer Q ‘D’= pACD
Holladay I ‘D’= Surgeon Factor Holladay II ‘D’= ACD
Haigis ‘D’= a0+(a1xACD) +(a2xAL) Lens Position Constant3,4
Dr Michael Hennessy (MSAC Supporting Committee, 2002) designed a table containing the different lens calculation formulae to teach trainees.
Commonly used lens calculation formulae (as devised and used by Dr M Hennessy)
Generation Lens Position Constant Formulae
1st Fixed LPC SRK
2nd LPC adjusted by length SRK II 3rd LPC adjusted by length SRK/T Hoffer
and K Q, Holladay
4th LPC adjusted by length, K, Holladay II other anterior segment
measurements
APPLICATIONS3,4 of various formulae
• The Holladay 1 formula which works well for eyes with normal and long axial lengths.
• The SRK/T formula, which works well for normal to moderately long axial lengths.
• The Hoffer Q formula works well for eyes with short and normal axial lengths.
Because most biometry equipment already comes with several theoretic formulas, a simple rule to follow is to use the Holladay 1 formula for normal-to-long eyes and Hoffer Q formula for normal-to-short eyes.
The following tabulation would help to pick a parti-cular formula which applies best to a given situation.
Comparison in Efficacy of Formulae
Certain comparative studies performed have shown the following:
• As can be seen, there are a number of options to choose from when using formulae. In a review of 900 eyes comparing SRK I, SRK II, SRK/T, Holladay, Hoffer and Binkhorst formulae, Sanders et al. (1990) found that the SRK/T and Holladay formulae worked best overall.9
• In a further study of 450 eyes Hoffer (1993) compared regression and theoretical formulae and found that SRK I and II were least accurate.10
• In the same study Hoffer found that there was no statistical difference between SRK/T, Hoffer Q and the Holladay formulae.10
• In conjunction with Dr Holladay, A retrospective review by R Zaldivar concludes that there was no difference in outcomes of Holladay II, Hoffer Q and SRK/T. Also they are statistically superior to SRK I and II.11
• To compare the accuracy of intraocular lens (IOL) power calculations using 4 formulas: Hoffer Q, Holladay I, Holladay II, and SRK/T5.
• Results: No formula was more accurate than the others as measured by mean absolute error. The formulas were also equally accurate when eyes were stratified by axial length.
• To compare the accuracy of the Hoffer Q and SRK-T formulae in eyes below 22 mm in axial length, using biometry measured with partial coherence inferometry (PCI), without a customised ACD constant.6
• Result: Hoffer Q was found to be more accurate than the SRK-T formula in this series of eyes
< 22 mm axial length when customised ACD constants are not used.
Axial Length Primary Secondary Category
< 20 mm Holladay II - High Axial Hyperopia Poly pseudophakia
< 20 mm Holladay II Hoffer Q Moderate to High Axial Hyperopia 20 to 21.99 mm Holladay II Hoffer Q Low to Moderate Axial Hyperopia 22 to 24.49 mm Holladay II Holladay I/SRK-T Emmetropia to low Axial Hyperopia 24.5 to 25.9 mm Holladay II Holladay I/SRK-T Emmetropia to low Axial Myopia 26 to 28 mm Holladay II Holladay I Low to moderate Axial Myopia 28 to 30 mm Holladay II Holladay I Moderate to High Axial Myopia
> 30 mm Holladay II Holladay I High Axial Myopia – Minus power IOL
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41
Fallacies of Newer Formulae3,4
• Limitations of all third-generation theoretic two-variable formulas are that they work best near schematic eye parameters, apply a number of broad assumptions to all eyes, and, apart from the lens constant, predict the final position of the optic of the IOL based solely on central corneal power and axial length. For example, some formulas assume that the anterior and posterior segments of the eye are mostly proportional, or that there is always the same relationship between central corneal power and the effective thin-lens position, which is not always true, especially in axial hyperopia.
• Regression formulas like Binkhorst II, SRK I, and SRK II soon became of historical interest only. Interestingly, SRK II is still used by many in spite of its obvious limitations.
• The main limitation to using the Haigis formula for all axial lengths is that only Dr Haigis or Dr Holladay l presently carry out the required regression analysis, and a patient database of approximately 200 cases containing a wide range of axial lengths is required.
• Limitation of Holladay formula is that it requires the manual input of seven variables and is relatively expensive to purchase. Surgical practices serious about their refractive outcomes will typically use the Holladay II formulae.
COMPARISON IMMERSION ULTRASOUND