J EMMETROPIA VOLUME 1 NUMBER 1<< BACK

UPDATE/REVIEW

Intraocular Lens Calculation after Prior Refractive Surgery
Kenneth J. Hoffer, MD, FACS

ABSTRACT
One of the most important assessments for the success of cataract surgery or clear lens surgery is that residual refractive error after intraocular lens (IOL) implantation should be near to emmetropia. In order to do so, calculation of the IOL power should be as accurate as possible. A special dilemma arises in eyes that have previously had refractive surgery; either by corneal surgery or by a phakic IOL. The present manuscript offers a review of recently published studies that analyze and try to solve the problems to calculate IOL power in eyes with prior refractive surgery. The results reviewed in this manuscript show how IOL power calculation is a real problem in eyes that have had refractive surgery. Because it has yet to be proven which proposed method works best in all eyes, it behoves the surgeon to use as many methods as data are available and carefully evaluate the results.
(J Emmetropia 2010; 1: 46-52 ©2010 SECOIR - Sociedad Espa�ola de Cirug�a Ocular Implanto-Refractiva)

Submitted: January 18, 2010

Accepted: March 26, 2010

INTRODUCTION

What could possibly be more important for patients choosing a refractive or multifocal intraocular lens (IOL) than the accurate calculation of the IOL power? This subject is considered a routine affair in most practices and the results are usually acceptable in the standard cataract patient. That may not be true in patients who are expecting (perhaps demanding) perfection and possibly paying extra for the IOL. It behooves every surgeon entering this area of surgical treatment to become completely familiar with every method to improve the accuracy of IOL power calculation in their practice.

A special dilemma arises in eyes that have previously had refractive surgery; either by corneal surgery or by a phakic IOL. Let’s solve the biphakic eye problem first.

BIPHAKIC EYES (PHAKIC EYE WITH A PHAKIC INTRAOCULAR LENS)

The problem here is eliminating the effect of the sound velocity through the phakic lens when measuring the axial length (AL) using ultrasound. I published a method1 to correct for this potential error by using the following formula:

ALCORRECTED = AL1555 + C × T

where AL1555 = the measured AL of the eye at sound velocity of 1555 m/sec, T = the central axial thickness of the phakic IOL and C = the material-specific correction factor of +0.42 for PMMA, –0.59 for silicone, +0.11 for collamer, and +0.23 for acrylic.

My publications1,2 on this subject contain tables showing the central thickness based on the dioptric power for each phakic IOL on the market today. The least error is caused by a very thin myopic collamer lens (eg, ICL) and the greatest error is seen with a thick hyperopic silicone lens (eg, PRL).

CORNEAL REFRACTIVE EYES
 Instrument error

The problem of IOL power calculation errors in corneal refractive surgery eyes was first described by Koch et al3 in 1989. The first problem that arises is that the instruments we use cannot accurately measure the corneal power needed in the IOL power formula in eyes that have had radial keratotomy (RK), photorefractive keratectomy (PRK), laser-assisted intrastromal keratomileusis (LASIK) and laser-assisted epithelial keratomileusis (LASEK). This major cause of error is due to the fact that most manual keratometers measure at the 3.2 mm zone of the central cornea, which often misses the central flatter zone of effective corneal power; the flatter the cornea, the larger the zone of measurement and the greater the error. The instruments usually overestimate the corneal power, leading to a hyperopic refractive error postoperatively.

Index of refraction error

The second problem is that the assumed index of refraction of the normal cornea is based on the relationship between the anterior and posterior corneal curvatures. This relationship is changed in PRK, LASIK, and LASEK but not in RK eyes. RK causes a relatively proportional equal flattening of both the front and back surface of the cornea, leaving the index of refraction relationship relatively the same. The other refractive procedures flatten the anterior surface but not the posterior surface thus changing the refractive index calculation, which creates an overestimation of the corneal power by approximately 1 diopter for every 7 diopters of refractive surgery correction obtained. A manual keratometer measures only the front surface curvature of the cornea and converts the radius (r) of curvature obtained to diopters (D) using an index of refraction (IR) of usually 1.3375. The formula to change from diopters to radius is [r = 337.5/D] and from radius to diopters is [D = 337.5/r].

Formula error

The third problem is that most of the modern IOL power formulas [Hoffer Q3, Holladay 14, and SRK/T5 but not the Haigis6] use the AL and corneal power (K) reading to predict the position of the IOL postoperatively. The flatter than normal K in RK, PRK, LASIK, and LASEK eyes causes an error in this prediction because the anterior chamber dimensions do not really change in these eyes.

HISTORY OF SOLUTIONS

In 1989, Holladay8 was the first to publish and popularize two methods to attempt to predict the true corneal power in refractive surgery eyes. I referred to them as the Clinical History Method and the Contact Lens Method9,10. The latter was first described by Frederick Ridley11 in the United Kingdom in 1948 and introduced in the United States by Soper and Goffman12 in 1974. Over the years many researchers and authors have proposed multiple methods to solve this problem. No one procedure has yet to be proven to be the most accurate in all cases.

In this regard Giacomo Savini of Bologna, Italy and I collaborated, over a 2-year period to create an Excel spreadsheet tool that would automatically calculate most all the proposed methods and also provide a place to store all the data collected and entered. All the information could be stored in one place and it could be printed out on one sheet and stored in the patient’s chart. The Hoffer/Savini LASIK IOL Power Tool was finished on July 4, 2007 and can be downloaded at no cost from www.EyeLab.com by clicking on the IOL Power button and then the Hoffer/Savini button.

In the creation of the tool, we divided all the published methods into those that attempt to predict the true power of the cornea and those that fudge the target IOL power calculated with the standard data. We then divided each group into those methods that need historical data regarding the status of the patient’s eye prior to refractive surgery and those that do not need any historical data.

Before finishing the Tool, we asked each formula author to beta test it to make sure they agreed with our calculations and assumptions. We have converted formula abbreviations to maintain consistency. The legend for these abbreviations is listed on Sheet #3 in the Tool and at the end of this discussion.

Methods to estimate true postoperative corneal power
 Those Needing Clinical History

Clinical History Method1,9
K = KPRE + RPRE - RPO or [K = KPRE + RCC]

This method is based on the fact that the final change in refractive error the eye obtains from surgery was due only to a change in the effective corneal power. If this refractive change the patient experienced is algebraically added to the presurgical corneal power, we will obtain the effective corneal power the eye has now. Obviously this requires knowledge of the K reading and refractive error prior to refractive surgery.

Originally it was recommended to vertex-correct the refractive errors to the corneal plane. Odenthal et al13 showed that clinical results were better if they were not corrected. We have decided to use vertex correction in the Hoffer/Savini Tool because this is more scientifically accurate. Several IOL power calculation computer programs calculate the Clinical History method automatically when needed [Hoffer� Programs and Holladay� IOL Consultant].

Hamed-Wang-Koch Method14
K = TKPO - (0.15 * RC) - 0.05

This method requires knowledge of the refractive change from the surgery and the postoperative Sim-K from the topography unit.

Speicher15 [Seitz16,17] Method
K = 1.114 * TKPO - 0.114 * TKPRE

This method requires obtaining the pre- and postoperative topographic Sim-Ks.

Jarade Formula18
K = TKPRE-(0.376*(TKPOr-TKPREr)/(TKPOr * TKPREr)

This method requires obtaining the pre- and postoperative topographic Sim-Ks in radius of curvature, not diopters.

Ronje Method19
K = KPOFLAT + 0.25 * RC

This method requires knowledge of the refractive change from the surgery and the postoperative flattest K reading measured now.

Adjusted Refractive Index Methods

These methods attempt to �correct� the index of refraction to better predict the corneal power. The first two methods require knowing the surgically induced refractive change at the spectacle plane and the average radius of curvature of the cornea now. The third method requires knowing the surgically induced refractive change at the corneal plane and the average radius of curvature of the cornea now.

a) Savini20 Method:
K = ((1.338 + 0.0009856*RCS) - 1)/(KPOr/1000)

b) Camellin21 Method:
K = ((1.3319 + 0.00113*RCS) - 1)/(KPOr/1000)

c) Jarade22 Method:
K = ((1.3375 + 0.0014*RCC) - 1)/(KPOr/1000)

Those Not Needing Clinical History

Contact Lens Method11,12
K = BCL + PCL + RCL - RNoCL

The Contact Lens Method was first described by Frederick Ridley11 of England (the inventor of NaOH IOL sterilization) in 1948 and taught by Jospeh Soper12 in 1974. This method is based on the principle that if a hard PMMA (not rigid gas permeable) contact lens (CL) of plano power (PCL) and a base curve (BCL) equal to the effective power of the cornea is placed on the eye it will not change the refractive error of the eye. Therefore, the difference between the manifest refraction with the contact lens (RCL) and without it (RNoCL) is zero. The formula above computes the effective corneal power if there is a difference in any of these parameters.

Originally it was recommended to vertex-correct the refractive errors to the corneal plane. Odenthal et al13 showed that clinical results were better if they were not corrected. We have decided to use vertex correction in the Hoffer/Savini Tool because this is more scientifically accurate. Several IOL power calculation computer programs calculate this method and the Clinical History Method automatically when needed [Hoffer� Programs and Holladay� IOL Consultant]. Plano contact lens sets for performing this procedure are commercially available.

Obviously, this method is impossible if the cataract precludes performing an accurate refraction whereby the visual acuity is worse than 20/80.

Maloney Central Topography Method23
K = 1.1141 * TKPO-CTRl -5.5

Based on his analysis of post-LASIK corneal topography central Ks (TK) on LASIK eyes, Maloney developed a formulation to predict true corneal power using only the single central postoperative reading TK.

Koch/Wang Method24
K = 1.1141 * TKPO - 6.1

Koch and Wang analyzed several of these methods and obtained the best results using the Maloney method (discussed earlier) but only after increasing the constant from 5.5 to 6.1. They also offered a second method to calculate true corneal power if the change in the patient's refractive error (RC) is known. The formula is:

K = KtPO - (0.19 × RC)

Savini-Barboni-Zanini Method25
K = 1.114 * KtPO - 4.98

This method only requires the postoperative Sim-K from topography.

Shammas No History Method26
K = 1.14 * KPO - 6.8

Shammas studied a series of eyes that had had LASIK. His analysis led him to propose a formula to predict the effective power of the cornea without needing any of the patient's clinical history, only the postoperative K reading obtained with manual keratometry.

Adjusted Refractive Index Methods

a) Ferrara27 Method: K = ((-0.0006*AL2 + 0.0213*AL + 1.1572) - 1)/(KPOr/1000)

This method requires the AL measurement and the postoperative K reading in radius of curvature.

Table 1Rosa28 Method
K = (1.3375 - 1)/(( KPOr * RCF)/1000)

This method requires the postoperative K reading in radius of curvature and the use of a table (Table 1) to obtain a factor (RCF) based on AL. Unfortunately, they used the SRK II regression formula in their computation, which I disagree with.

Haigis Method29
K = -5.1625 * Kr + 82.2603 - 0.35

This method requires only the postoperative K reading form the Zeiss IOLMaster in radius of curvature (or converted to diopters using the index of refraction setting in the IOLMaster).

Pentacam

A new comprehensive Eye Scanner, the Oculus Pentacam (Oculus, Inc, Wetzlar, Gemany) (www.oculususa. com) images the anterior segment of the eye by a rotating Scheimpflug camera measurement. This rotating process supplies pictures in three dimensions, provides a topographic analysis of the corneal front and back surfaces as well as central corneal thickness and generates a TrueNetPower map of the cornea.

The TrueNetPower map of the postoperative cornea produced has been proposed as an accurate measure of the true corneal power. Initial results were disappointing and the software was reconfigured in early 2007. Several studies on the new software have also not lived up to expectations as of September 2007 and newer changes are being proposed.

The BESSt� Formula30

Published by Borasio, it uses the anterior and posterior corneal curvatures as well as the central pachymetry from the Pentacam unit to produce a predicted central corneal power. The formula is quite complicated but it is incorporated into the Hoffer/Savini LASIK Tool.

Methods to adjust/calculate the target intraocular lens power
 Those Needing Clinical History

Aramberri31 Double-K Method

Use KPRE to calculate ELP & KPO to calculate IOL power.

One of the most important developments to improve the prediction of corneal power in eyes that have had refractive surgery was proposed in 2001 and is termed the �Double-K� method by Aramberri of San Sebastian, Spain. His proposal makes eminent sense. The modern theoretic formulas (except the Haigis) use the input of corneal power for two purposes; the first is to predict the ultimate position of the IOL (ACD or ELP) and the second (along with AL, target refraction, and ELP) is to calculate the power of the IOL. The formulations and algorithms used to predict the ELP are based on the anatomy of the anterior segment, which is not changed by corneal refractive surgery (only the center is flattened and thinned). Therefore, if the postoperative refractive surgery K reading (which is flatter) is used to calculate the ELP it will produce an erroneous ELP value. Because the anatomy has not changed, Aramberri recommends the use of the preoperative K reading to calculate the ELP. The IOL power is then calculated using the postoperative K reading, thus the use of two K readings (�Double-K�). His analysis of a small series of eyes proved the benefit of this idea.

Feiz-Mannis32

Formula: P = PE - RCS/0.7

In this method you calculate the emmetropic IOL power using the preoperative K reading and adjust that value (PE) using the surgically induced refractive change.

Feiz-Mannis33 Method

This method utilizes the change in refractive error to offset the calculated target IOL power. There is one formula for myopic eyes and another for hyperopic:

Myopic Eye P = PTARG - 0.595*RCC + 0.231
Hyperopic Eye P = PTARG - 0.862*RCC + 0.751

Latkany34 Methods [Myopic eyes only]
P = PTARG FlatK - 0.47 * RPRE + 0.85

This method requires knowledge of the pre-LASIK refractive error and the calculation of the target IOL power using the flattest postoperative K rather than the usual average K.

Table 2Masket35 Method
P = PTARG - 0.326 * RCC + 0.101
[SRK/T: myopes; Hoffer Q: hyperopes]

This method is a play on the Latkany method, which adjusts the power of the IOL calculated using the postoperative measured data using the knowledge of the surgically induced refractive change. He recommends using the SRK/T formula for myopic ALs and the Hoffer Q for hyperopic ALs. Example calculations are shown in table 2.

In a series of 28 post-LASIK eyes, he reported 43% of the eyes obtaining a postoperative refractive error of plano, 95% within �0.50 D of prediction and a total error range from -0.75 D to +0.50 D.

Wake Forest Method36

Use RPRE as the RXTARG using measured AL and KPRE. In 2005, Gagnon, et al., from Wake Forest University, published an alternative calculation method that has been discussed by others over the past 20 years. This method simply uses the patient's preoperative refraction before LASIK as the target or �desired� PO refraction in the calculation and the measured AL and K readings without modification.

Those Not Needing Clinical History

Aramberri31 Double-K Method

Use 43.5 or 44.00 to calc ELP & KPO to calc IOL power.

The use of a standard normal K reading in the Double-K method is a great improvement over using the calculated very flat K reading.

Ianchulev37 Intraoperative Aphakic Refraction Method
P = 2.02 * AR + (A - 118.4)

In 2003, Ianchulev et al. proposed calculating IOL power by performing an aphakic refraction on the operating room table using a hand-held automated refractor immediately after the cataract has been removed and the AC is inflated to normal status. The resultant refraction is modified by the formula.

His early results are quite promising. This method would completely eliminate the need for axial length, corneal power measurements, and the problems with LASIK and silicone oil-filled eyes. However, it would require a large IOL inventory in the operating room.

Mackool38 Secondary Implant Method
P = 1.75 * AR + (A - 118.84)

This method is similar to the above except the patient is removed from the operating room without an IOL implanted, then refracted in a refraction lane and then taken back to the operating room for secondary lens implantation. It is my impression that this method would not be popular with most surgeons.

FORMULA LEGEND

A = The IOL A constant for planned IOL style.
AL = Axial Length
AR = aphakic refractive error (SE).
B = base curve, PCL = power of CL, NoCL = bare refraction.
CL = contact lens
K = predicted PO corneal power
KPO = the average PO corneal power by manual keratometry (in diopters D)
KPOFLAT = flattest measured PO manual keratometry
KPOr = the average PO corneal power by ""(in radius r [mm])
KPRE = refractive surgery preoperative corneal power (K readings)
Kt = exact singular PO topography central K
P = IOL Power
PEMM = the IOL power calculated for emmetropia
PFlatK = IOL power calculated for RxTARG using the PO flattest K
PTARG = the target IOL power to produce the PO desired refractive error
R = refractive error, PRE = preoperative, PO = postoperative
RCC = surgical change in refractive error (SE) vertexed to Corneal Plane
RCF = Rosa Correction Factor based on Axial Length
RCS = surgical change in refractive error (SE) at Spectacle Plane
RPO = refractive surgery PO refractive error (spherical equivalent)
RPRE = refractive surgery preoperative refractive error (spherical equivalent)
RxTARG = planned postoperative Target refractive error
TK = average PO topography central Sim-K or EffRP


IMPORTANT THINGS TO KEEP IN MIND

1. Be sure the Index of Refraction is set to 1.3375 in the Setup screen of the IOLMaster computer for the Hoffer Q formula to operate properly for Hyperopic refractive eyes.

2. If the AL is very difficult to obtain and the eye appears to have a length greater than 25 mm, suspect a STAPHYLOMA.

3. Hard contact lenses (including gas permeable) should be removed permanently for at least two weeks prior to measuring corneal power for IOL power calculation on at least one eye.

4. All patients having corneal refractive surgery should be given the following data to maintain in their personal health records: 1) Preoperative corneal power, 2) Preoperative refractive error, 3) Postoperative healed refractive error (before lens changes effected it). They should be told to give it to anyone planning to perform cataract/IOL surgery on them.

WHAT FORMULA TO USE

My study4 of 450 eyes (by one surgeon using one IOL style) showed that in the normal range (72%) of axial length (22.0 to 24.5 mm) almost all formulas function adequately, but that the SRK I formula is the leading cause of poor refractive results in eyes outside this range. Koch warned against the use of regression formulas in refractive surgery eyes way back in 1989.

It also showed that the Holladay I formula was the most accurate in medium long eyes (24.5 to 26.0 mm) (15%) and the SRK/T was more accurate in very long eyes (>26.0 mm) (5%). In short eyes (<22.0 mm) (8%) the Hoffer Q formula was most accurate and this was confirmed (p > .0001) in an additional large study of 830 short eyes as well as in a multiple-surgeon study by Holladay. Holladay has postulated that the other formulas overestimate the shallowing of the effective lens position (ELP) in these very short eyes.

We performed a later study39 on 317 eyes, which showed that the Holladay 2 formula (unpublished) equaled the Hoffer Q in short eyes but was not as accurate as the Holladay I or Hoffer Q in average and medium long eyes (Table 3). It appears that in attempting to improve the accuracy of the Holladay 1 formula, the addition of more biometric data input has improved the Holladay II formula in the extremes of axial length but deteriorated its excellent performance in the normal and medium long range of eyes (22.0 to 26.0 mm), which accounts for 82% of the population.

Therefore, because the majority of refractive surgery eyes are high myopes (>26 mm), I would recommend the use of the SRK/T formula. In those eyes between 24.5 to 26.0 mm, I recommend the Holladay 1 (not the Holladay 2). Use the Hoffer Q in hyperopic eyes less than 22 mm in length.

Table 3 HOW TO HANDLE PROBLEMS AND ERRORS

The major problem is an unacceptable postoperative refractive error. The sooner it is discovered, the sooner it can be corrected and the patient made happy. Therefore, it is wise to perform K readings and a manifest refraction on the first postoperative day in these demanding patients. Immediate surgical correction (24 to 48 hours) will allow easy access to the incision and the capsular bag, a single postoperative period, and excellent uncorrected vision40. The majority of medico-legal cases today are due to a delay in diagnosis and treatment of this iatrogenic problem.

Up to now, we could only correct this problem by lens exchange, which creates the dilemma of determining which factor created the IOL power error; axial length, corneal power, or mislabeled IOL or a combination of the above. Today, with the advent of low-powered IOLs, the best remedy may be a piggyback IOL. Using a piggyback IOL, it is not necessary to determine what caused the error or to remeasure the axial length of the freshly operated pseudophakic eye.

CONCLUSION

IOL power calculation is a real problem in eyes that have had refractive surgery. Because it has yet to be proven which proposed method works best in all eyes, it behooves the surgeon to use as many methods as data is available and carefully evaluate the results. The Hoffer/Savini Tool is an attempt to make this process easier. If surgeons using the Tool forward their results to us we may be able give an accuracy weight to each of the methods.

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