**INTRAOCULAR LENS POWER CALCULATION **

**IN PATIENTS WITH PRIOR REFRACTIVE SURGERY**

**By**

**H. JOHN SHAMMAS, M.D.**

**Clinical Professor of Ophthalmology**

**The Keck School of Medicine of USC**

**Los Angeles, CA**

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__CONTENTS__

Introduction

Corneal changes after myopic LASIK / PRK

Theoretical calculation of the correct IOL power after refractive surgery

Most accurate algorithms and formulas

Additional algorithms and formulas

IOL power calculation for eyes with prior hyperopic LASIK / PRK

IOL power calculation for eyes with prior RK

Consensus calculations

Computer programs

Conclusion

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__INTRODUCTION__

LASIK and PRK for the correction of near-sightedness represent the majority of refractive surgeries. A number of these patients will develop cataracts, and they will likely expect excellent uncorrected post-operative visual acuity, just like after their refractive surgery. Early experience with eyes that had undergone myopic LASIK or PRK has shown that the refractive predictability after cataract surgery is relatively poor. Two errors are introduced when IOL power calculation is performed on post-LASIK/PRK eyes:

*The first error* is in the calculation of the corneal power, where the K readings, measured after refractive surgery, do not represent the true corneal power. This is why the corneal power needs to be corrected after LASIK / PRK, no matter what formula is being used.

*The second error* is in Estimated Lens Position (ELP) prediction by the commonly used third generation IOL power formulas, notably the SRK/T, Holladay 1 and Hoffer Q formulas, where ELP is a function of the K readings. However, the Haigis formula uses a different algorithm to calculate ELP; it is based on the axial length and the anterior chamber depth, and not on the corneal curvature. In other words, this second error can be avoided if the Haigis formula is used for IOL power calculation in post-refractive surgery eyes, instead of the SRK/T, Holladay 1 or the Hoffer Q formulas.

These two errors are additive, and with standard IOL power calculations using the post-LASIK K readings, the power of the implant used during cataract surgery is usually underestimated resulting in a post-operative hypermetropic surprise.

We will concentrate on the changes that occur after myopic LASIK and how to correct them. PRK causes similar changes to the cornea, and requires identical correction. A much smaller number of patients present for cataract surgery after a hyperopic LASIK, or after an old radial keratotomy (RK). These cases will be discussed separately.

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__CORNEAL CHANGES AFTER MYOPIC LASIK / PRK__

The power of the cornea is conventionally measured by keratometry. Different investigators have shown that after refractive surgery for myopia, the true value of the corneal power is actually lower than the K readings measured by keratometry or by videokeratography.

To understand why the corneal power is over-estimated after a myopic LASIK / PRK, we should first re-visit the optical physics used by all keratometers. The keratometers measure the anterior radius of corneal surface, expressed in millimeters, which is translated into diopters by considering the entire corneal power to be at the anterior corneal surface. An arbitrary index of refraction of 1.3375 has been previously established where an anterior corneal radius of 7.5 mm would yield a corneal vertex power of 45.00 D. The relationship between the keratometric readings (K in diopters) and the value of the anterior corneal radius (r in millimeters) is

K = 1,000 (1.3375 - 1) ÷ r

In a virgin eye, the corneal index of refraction is based on the fact that the anterior to posterior corneal radius ratio is fixed at around 1.21. After LASIK, the anterior corneal surface is flattened and the ratio of the anterior to posterior radius of curvature increases proportional to the amount of corneal flattening. This in turn decreases the effective corneal index of refraction in the post-LASIK cornea compared to a virgin one.

After LASIK, the keratometer is using the conventional index of refraction (as in a virgin cornea) instead of the correct lower value (secondary to the anterior corneal flattening by the LASIK treatment). This will result in a higher measured post-LASIK Ks than it actually is. A classical example would be the cornea with a pre-LASIK Ks of 45.00 D. After a 5.00 D myopic correction at the corneal level, one would expect the post-LASIK Ks to be 40.00 D. Instead, the measured Ks are 41.25 D, an overestimation of 1.25 D.

Studies have shown that the K readings need to be decreased by a factor of 0.23 D for each diopter of myopic correction obtained by the refractive surgery. This error is due not only to changes in the net index of refraction after LASIK, but also to sampling in the periphery of an aspherical corneal surface. Variation in the keratometry measurements depends on the steepness of the cornea and is not fixed for all eyes, and the readings obtained by corneal topography depend on the number of rings evaluated.

Scheimpflug photography can now accurately measure not only the anterior corneal radius but also the posterior one to obtain an exact measurement of the total corneal power. However, most available formulas do not use the total corneal power, and they base their calculations instead on the SimK value.

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__THEORETICAL CALCULATION OF THE IOL POWER AFTER MYOPIC LASIK: __THE CLINICAL HISTORY METHOD

In an ideal case, the pre-refractive K readings and the exact amount of refractive correction are known and presumed accurate. The two errors caused by the LASIK surgery (see the Introduction) need to be corrected, i.e. the corneal power and the Estimated Lens Position (ELP): The correct post-refractive corneal power is best calculated by the Clinical History Method. ELP is corrected with Aramberri’s double-K method if the SRK/T, Holladay 1 or Hoffer Q formulas are used; however, ELP needs no correction if the Haigis formula is used.

**STEP 1: CORRECTING THE MEASURED Ks**

After a myopic LASIK / PRK, the measured Ks are over-estimated, and need to be corrected. An accurate way to calculate the true corneal power after refractive surgery is the *Clinical History Method*; the corrected corneal power (Kc) is obtained by algebraically adding the correction at the corneal plane (-CRc in case of myopic correction) to the preoperative corneal power (Kpre), where: Kc = Kpre – CRc

The correction at the corneal plane (CRc) is determined by subtracting the pre-LASIK refractive error at the corneal plane (Rc.pre) from the post-LASIK refractive error at the corneal plane (Rc.post), where: CRc = Rc.post – Rc.pre

The refractive error at the corneal plane (Rc) is derived from the refraction at the spectacle plane (Rs) assuming a vertex distance of 12mm, where:

Rc = Rs ./. (1-0.012Rs)

This method requires access to the refractive surgery data (pre-LASIK K readings and amount of myopia corrected). When a patient is seen for cataract evaluation years after the LASIK procedure, this method often becomes less accurate because of additional refractive changes that happen with time. These can be due to corneal changes, multiple refractive surgeries or cataract progression.

**STEP 2: DOUBLE-K CALCULATIONS**

After a myopic LASIK / PRK, the Estimated Lens Position (ELP) within the SRK/T, Holladay 1 and Hoffer Q formulas is under-estimated and need to be corrected using the double-K method.

The SRK/T, Holladay 1 and Hoffer Q formulas use different algorithms based on the K values and the axial length to estimate the ELP value. In other words, a steeper cornea implies a deeper ACD and anticipates a higher ELP value, while a flatter cornea implies a shallower ACD and a smaller ELP value. After refractive surgery, the anterior corneal surface is flattened but ELP is not affected. If the flatter post-LASIK K values are used instead of the pre-LASIK Ks to calculate the ELP value; it will be under-estimated. In these cases, it is best to use Aramberri’s double-K method, where the corrected post-LASIK Ks are only used as a measure of the corneal power, while the pre-LASIK Ks are used to calculate the correct ELP value.

__MOST ACCURATE ALGORITHMS AND FORMULAS __

Besides the Clinical History Method (described in the previous paragraph), multiple algorithms and formulas have been written to calculate the IOL power after refractive surgery. Recent review articles have established some of these formulas to be consistently the most accurate.

*Masket and modified Masket formulas*

This method requires knowledge of the surgically induced change in manifest refraction by the LASIK / PRK (ΔMR). IOL power calculations are performed using the axial length as measured by optical biometry, and the post-LASIK / PRK K readings (IOLpost). Masket recommends the SRK/T for cases that had a myopic LASIK / PRK and the Hoffer Q formula for cases that had a hyperopic LASIK / PRK, although one review article recommends the Masket equation to be used with the Hoffer Q formula in all cases. This power is then adjusted according to the equation:

Adjusted IOL = IOL post + (0.326 x ΔMR) + 0.101

This formula was modified by Hill to increase the accuracy of IOL prediction in his cases, where:

Adjusted IOL = IOL post + (0.4385 x ΔMR) + 0.029

*Shammas-PL formula*

The advantage of this method is that it does not require any LASIK / PRK data (neither the pre-LASIK Ks nor the amount of corrected refraction. It uses the Shammas IOL power formula with an adjusted corneal values (Kc) derived from the post-LASIK / PRK K readings (Kpost) according to the equation:

Kc = 1.14 Kpost – 6.8

*Haigis-L formula*

The advantage of this method is that it also does not require any LASIK / PRK data (neither the pre-LASIK Ks nor the amount of corrected refraction. It uses the Haigis formula with an adjusted corneal radius (r corr) derived from the measured post-LASIK / PRK corneal radius (r meas) taken from the IOLMaster, according to the equation:

r corr = 331.5 / (-5.1625 x r meas + 82.2603 -0.35)

*Barrett True K and Barrett True K No History*

Both of these formulas use Barrett formulas to calculate the IOL power after LASIK

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__ADDITIONAL ALGORITHMS AND FORMULAS __

The following algorithms and formulas are listed as relatively accurate by at least one of the review articles. Some also are mentioned in courses given at the AAO, ASCRS and ESCRS.

*Feiz/Mannis *

IOL power calculation is performed using the pre-LASIK Ks, to which you add the LASIK induced refractive change divided by 0.7

*Corneal bypass*

IOL power calculation is performed using the pre-LASIK Ks, and the surgically-induced change in refraction is used as the target refraction for IOL power.

*Adjusted effective refractive power *

The effective refractive power (EffRP) obtained by the EyeSys Corneal Analysis System is adjusted according to the following equation:

Adjusted EffRP = EffRP – (0.15 x ΔMR) -0.05

*Adjusted Atlas 0-3*

The mean corneal power, obtained by averaging 0.0 mm, 1.0 mm, 2.0 mm, and 3.0 mm annular powers from the Atlas corneal topographer, is adjusted according to the equation:

Adjusted Atlas = Atlas – 0.2 x ΔMR

*Latkany flat K*

The IOL power is first calculated using the flattest K readings with the SRK/T formula. The IOL power is then adjusted according to the equation:

Adjusted IOL = Calculated IOL – (0.47 x ΔMR) +0.85

*Rosa R-factor*

The post-operative corneal radius, as measured by videokeratography, is multiplied by the R factor. This correction factor varies between 1.01 and 1.22 according to the axial length of the eye.

*Geggel pachymetric technique*

A Geggel ratio is established by comparing the central corneal thickness and the estimated ablation depth to the superior corneal pachymetry. A diopter treatment at the corneal plane is estimated, and an adjustment factor is calculated. This adjustment factor is added to the IOL power as calculated by the SRK/T formula.

*Savini *

The exact power of the pre-LASIK anterior corneal surface (Pa) is calculated from the pre-LASIK SimK, which allows the calculation of the posterior corneal surface power (Pp):

Pre-LASIK Pa = SimK x (376 / 337.5) = 1.114 x SimK

Pre-LASIK Pp = (1.114x SimK) –SimK

Since the posterior corneal power does not change after LASIK / PRK, the post-LASIK corneal power is then calculated:

Post-LASIK Pa = Post-LASIK SimK x (376 / 337.5) = 1.114 x Post-LASIK SimK

Post-LASIK corrected K = (1.114 x Post-LASIK SimK) + Pre-LASIK Pp

If the pre-LASIK K readings are not available, the posterior corneal power (Pp) is set at -4.98 D

This calculated corneal power is used with the SRK/T if AL>24.9 mm and the Holladay 1 formula if AL ranges between 22.0 and 24.49 mm.

*BESSt formula*

The BESSt formula is based on the Gaussian optics formula. It estimates the true corneal power after keratorefractive surgery by taking into account the anterior and posterior corneal radii and pachymetry taken from the Pentacam unit. The BESSt formula uses a variable rather than a static index of refraction for each cornea. Calculations require a proprietary special software program, the BESSt Corneal Power Calculator.

*Mackool aphakic refraction technique*

Cataract removal is performed without IOL implantation. Manifest aphakic refraction is performed 30 minutes later, and the IOL power is obtained by a special algorithm derived from previous experience with secondary IOL implantation.

*Ianchulev intra-operative optical refractive biometry*

After cataract removal, intra-operative autorefractive retinoscopy is used to obtain the aphakic refraction. The IOL power is then determined by using an algorithm described by the author. Ianchulev’s method is at the basis of the Orange system that is being used by some surgeons intra-operatively to determine the exact IOL power to be used.

*SToP formula*

The SToP formula is a no-history method used to calculate the IOL power, preferably with the SRK/T formula. The IOL power is then adjusted according to the posterior / anterior corneal radius ratio taken from the Pentacam unit. The following adjustment is used:

IOL adjustment = (9.11 – 10.81 x rpost/ant) x1.5

__COMPUTER PROGRAMS__

The three most popular computer programs that will aid in IOL power calculation following refractive surgery are:

**1. The IOL power calculator on the ASCRS web site ****www.ascrs.org**

The ASCRS IOL power calculator runs three different programs depending if the patient had prior myopic LASIK / PRK, prior hyperopic LASIK / PRK or prior RK. All available data is entered into the appropriate program, and the IOL powers are calculated.

The results are divided into 2 categories, whether only ΔMR is being used (Masket, Modified Masket and Barrett True K), or whether no prior data is being used (Shammas-PL, Haigis-L and Barrett True K No History formulas).

The program will then give an average IOL power along with the minimal and maximal calculated powers.

**2. The Hoffer / Savini Tool**

The Hoffer / Savini Tool can be downloaded from the Eye Lab – Hoffer Programs. This tool allows the user to enter, calculate and analyze data. It uses all the published and proposed methods to aid in IOL power calculation in LASIK and PRK eyes.

All available data is entered into the Excel file and the program will calculate all the results for the corrected K readings and for the IOL power.

**3. The Holladay IOL Consultant Software**

The Holladay IOL Consultant Software is a proprietary program that calculates the IOL power with the Holladay 2 formula with its enhanced algorithm, and compares the results to the Holladay 1, Hoffer Q and the SRK/T formulas.

For the post-refractive surgery cases, the program calculates alternate K-values from refractive data and topography and corrects the formulas within the program to calculate the required IOL power.

__CONSENSUS CALCULATIONS__

All the methods described in this Clinical Module have shortcomings. The difficulties in determining the correct corneal power and in calculating ELP after LASIK /PRK have been described along with the different methods to correct them.

Consensus calculations are strongly advised. Some computer programs, like the ASCRS calculator, average the different calculated IOL power values. All formulas based on the Clinical History have been removed. These methods depend on both the pre-LASIK / PRK K readings and the amount of correction obtained by the refractive surgery. An error of 1 D in the estimated amount of LASIK /PRK correction will cause almost 1 D error in the IOL power calculation. The same 1 D error in the estimated LASIK / PRK correction will only cause 0.33 D error in the Masket formula, and does not affect at all the Haigis-L and the Shammas-PL formulas.

When a patient presents for cataract surgery, and the prior LASIK corrected a mild myopia with a post-LASIK Ks of 40 D or above, all formulas will give almost similar results. The calculations will be quite accurate. See the Clinical Application.

When a patient presents for cataract surgery, and the prior LASIK corrected a high myopia with a post-LASIK Ks lower than 40 D, the formulas will differ in their calculations. The Masket formula tends to yield the lowest IOL power while the Haigis-L and the Shammas formulas tend to yield the highest IOL power. Consensus will be strongly advised. It might be wise to aim towards a slight myopia in the calculations to avoid any potential hyperopic result. An addendum to the Informed Consent explaining the shortcomings of the IOL calculations in these cases and the possibility of residual refraction should be part of the pre-surgical routine.

__IOL POWER CALCULATION AFTER HYPEROPIC LASIK__

Hyperopic LASIK steepens the central cornea to correct the refractive error. The corneal power and ELP need to be re-calculated, as in post-myopic LASIK cases. However, in the post-hyperopic LASIK cases, the corneal power is under-estimated and the ELP value is over-estimated. These changes are less marked than the post-myopic LASIK cases because the amount of hyperopia corrected is usually only between 1 and 3 diopters.

The best formulas are: Masket, Modified Masket, Shammas-PHL, Haigis-L, Barrett True K and Barrett True K No History.

__IOL POWER CALCULATION AFTER RADIAL KERATOTOMY__

IOL power calculation after RK presents different challenges than the post-LASIK / PRK cases. Manual and auto-keratometry are relatively difficult, especially if the RK cuts are impinging on the central 3mm. A corneal topography is always helpful to determine the corneal changes. For IOL power calculation, the steepest central corneal power needs to be used. It is also advisable to study these corneas with Scheimpflug photography to determine the anterior and posterior corneal curvatures.

The main problem with RK cases is that the Estimated Lens Position (ELP) is miscalculated with the SRK/T, Holladay 1 and Hoffer Q formulas. If any of these formulas are used, a double-K correction, as described for the LASIK cases, is needed to recalculate ELP.

It is easier to use the Haigis formula that does not depend on the corneal curvature to calculate ELP, or the Barrett True K Formula. The steepest corneal power, taken from the keratometer, is entered into the formula, and the IOL power is calculated without any further adjustment.

__CONCLUSION__

Different methods have been designed to calculate IOL power after refractive surgery. The Clinical history method has been hailed as the gold standard, and this is true if calculations are performed immediately after the LASIK / PRK procedure or if the refractive changes produced by the LASIK / PRK have been stable. Unfortunately, this is not always the case. When a patient is seen for cataract evaluation years after the LASIK procedure, this method often becomes less accurate because of additional refractive changes that happen with time due to corneal changes, multiple refractive surgeries or cataract progression. The Masket and Barrett True K formulas have been reported to be quite accurate if the ΔMR is known and has remained stable. The Haigis-L, the Shammas-PL and the Barrett True K No History formulas can be used in every case, especially if the refractive changes produced by the LASIK / PRK are not known. However, if accurate data from the refractive surgery is not available, consensus calculations are recommended.