IOL Calculation

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Intraocular Lens CalculationsAfter Corneal Refractive SurgeryKenneth J. Mandell, MD, PhDUla V. Jurkunas, MD

Roberto Pineda, II, MD

IntroductionAs of 2007, more than 8 million people in the United States ofAmerica had undergone corneal refractive surgery (Market Scope, LLC,St. Louis, MO). As this population ages, many of these patients willrequire cataract surgery. Refractive surprises after cataract surgeryhave historically been a problem in postrefractive patients.1 The mainreason for this problem is that refractive surgery modifies the shape ofthe cornea, and these changes alter the accuracy of keratometrymeasurements used to perform intraocular lens (IOL) calculations forcataract surgery. This review will discuss the limitations of conventional

keratometry techniques and potential benefit to newer corneal topographytechnology for improving IOL calculations in postrefractivepatients.

Keratometry in Postrefractive PatientsThe cornea contributes approximately 45D of refractive power tothe optical system of the eye. The majority of the corneal refractivepower comes from the air-tear-cornea interface on the anterior surface.The second component of refractive power is cornea-aqueous interfaceon the posterior surface. The corneal power can therefore be estimatedusing the following formula2:www.internat-ophthalmology.com | 181INTERNATIONAL OPHTHALMOLOGY CLINICSVolume 50, Number 1, 181189r 2010, Lippincott Williams & Wilkins

1 P n2_ n1=r1 n3_ n2=r2where n1=refractive index of air=1.000; n2=refractive index ofthe cornea=1.376; n3=refractive index of aqueous humor=1.336;r1=anterior radius of curvature; and r2=posterior radius of curvature.So this formula can be used to calculate the true corneal power providedthat the anterior and posterior curvatures of the cornea are known. Untilrecently, technology to measure the posterior curvature was not readilyavailable, and historically keratometry techniques have relied solely onanterior curvature measurements. This single refracting surface formulawas developed by Javal more than 100 years ago and continues to beused today for routine keratometry measurements3:2 P n _ 1=r

where n=standard keratometric index=1.3375 and r=anterior radiusof curvature. This formula can then be simplified to the form:3 P 0:3375=rThis formula assumes a uniform relationship between the anteriorand posterior corneal surfaces with respect to the radii of curvature andtotal corneal thickness. For patients who have not undergone cornealrefractive surgery, this relationship holds true and the formula allows forconsistent estimation of corneal power based on the anterior surfacealone. In patients who have had corneal refractive surgery, however, thecurvature and/or thickness of the cornea is dramatically altered by therefractive procedure. For example, correction of myopia by laser assistedin situ keratomileusis (LASIK) results in thinning of the central cornea

and flattening of the anterior surface relative to the surroundingperiphery. In such cases, the ratio between central corneal anteriorand posterior curvature is altered, and calculations based on a standard


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keratometric index are no longer valid resulting in steeper keratometricmeasurements (actual keratometry is flatter). In addition, keratometricmeasurements obtained from points outside of the zone of ablationresult in overestimation of the true corneal power in patients who havehad myopic LASIK as well as radial keratotomy and photorefractivekeratectomy. Conversely, hyperopic refractive procedures result in

underestimation of true corneal power due to the steepening withinthe central optical zone relative to the peripheral cornea.The above examples demonstrate that the surgical changes inducedby corneal refractive surgery adversely affect the accuracy of keratometrymeasurements. These keratometric errors in turn affect IOLcalculations required for cataract surgery. Various computational methodshave been developed to compensate for the limitations of conventionalkeratometry, and the advent of newer corneal topography systemsoffers promise for more accurate assessment of true corneal power. Thebenefits and drawbacks to of each of these methods are discussed inmore detail below.182 Mandell et alwww.internat-ophthalmology.com

Clinical History MethodMany methods for IOL calculation have been developed to accountfor the changes in corneal power after refractive surgery. The clinicalhistory method, also known as the calculation method or perioperative datamethod, relies on 3 known parameters: (1) corneal power beforerefractive surgery, (2) spherical equivalent manifest refraction beforerefractive surgery, (3) and the spherical equivalent manifest refractionsoon after refractive surgery.4,5 In this case, the current corneal power iscalculated by subtracting the change in refractive error from the cornealpower measured before refractive surgery. The formula for the clinicalhistory method is: K=Kpre+RxpreRxpo. For example, if a myopicpatient with corneal power of 44.00D undergoes LASIK, the refractive

error may change from 5.00D to emmetropia. The post-LASIKcorneal power is calculated as 44.00 5.00=39.0 D. This makes sense,because myopic LASIK flattens the anterior cornea, so the net change inrefractive error should be equivalent to the decrease in corneal power bystromal ablation.A simplified version of the clinical history method uses the sphericalequivalent refractive change at the spectacle plane to assess the change inrefractive power. In reality, the change at the spectacle plane is slightlydifferent from the change at the corneal plane. Consequently, a secondcalculation is required to convert from the power at the spectacle planeto the power at the corneal plane using a formula that accounts for thevertex distance. This is but a minor detail which, in all likelihood, does

not affect patients with low degrees of myopia or hyperopia. For patientswith high amounts of myopia or hyperopia, the change in refractionmeasured at the spectacle plane may differ substantially from that at thecorneal plane. In such cases, the conversion to the corneal plane shouldbe applied as demonstrated by Speicher.6The most apparent limitation to the clinical history method is that itrequires historical information from medical records obtained before therefractive surgery. It is common for patients to have cataract surgerymany years after their refractive surgery, and often at a different facilityfrom their original refractive procedure. Consequently, prerefractivedata are not usually available to the cataract surgeon, and thus theclinical history method is not a practical option. Alternative methods forestimating corneal power in postrefractive patients must therefore beconsidered.

Contact Lens Overrefraction


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The contact lens overrefraction (CLO) method does not require anyhistorical data. For this method, manifest refraction is performed bothIOL Calculations After Refractive Surgery 183www.internat-ophthalmology.com

with a plano hard contact lens of known base curve and without thecontact lens.4,5 The difference between these refractive measurements is

equivalent to the difference between the base curve of the plano hardcontact lens and actual curvature of the cornea. In this way, cornealpower can be determined by adding the difference in refractiveerror with and without the hard contact lens to the known basecurve of the contact lens. The equation for the CLO method is:K=BCL+PCL+RxCLRxnoCL. For example, if a patients refraction is 4.0D with a plano contact lens of base curve 40.0 D. Without thecontact lens, the refraction is 1.0 D. The contact lens seems to be moresteeply curved than the actual cornea, thus it is inducing a myopic shiftof 3.0 D. The actual corneal power is therefore 3.0D less than the basecurve of the hard contact lens: 40.0 3.0=37.0 D.One limitation of the CLO method is that it requires patients to haveadequate visual acuity and cognitive ability to perform reliable manifestsrefraction.6A study by Zeh and Koch7 suggests this method to be reliablefor patients with visual acuity of 20/20 to 20/40, but the accuracy of CLOdecreases with increasing amounts of media opacification. The authorsclaim, however, that it is acceptable for visual acuity up to 20/70.7 Inany case the ability of the patient to reliably cooperate with manifestrefraction should be taken into consideration when performing the CLOmethod.

Calculations Based on Anterior Surface KeratometryVideokeratography systems provide detailed topographic informationabout the anterior corneal surface. In postrefractive patients forwhom preoperative and postoperative corneal power is available, it ispossible to estimate the true corneal power based on the net difference in

anterior surface power measured by videokeratography. This change inanterior surface power can be applied to the estimated corneal powerobtained from the standard keratometric index formula (Equation 2).The resulting number is an estimate of the corneal power after refractivesurgery. The calculations for this method are relatively complex, andmore detailed examples are provided by Speicher.6 Like the clinicalhistory method, such calculation-based methods require prerefractivecorneal measurements, and such information may not be routinelyavailable at the facility where cataract surgery is performed.

No-History MethodIn contrast to the above method that requires prerefractive clinicaldata,8 Shammas and Shammas9 developed a no-history method based

only on post-LASIK keratometry measurements. This method is based184 Mandell et alwww.internat-ophthalmology.com

largely on a prior study involving a linear regression model obtainedfrom 200 patients who had undergone LASIK.9 It seems to be amathematically sound approach that yields consistent, reproducibleresults within the patient population studied. The only drawback tosuch regression-based models is that the results may not be readilyapplied to other populations in which the patient demographics orsurgical technique employed differ from the group that was studied.

Consensus-K TechniqueIn contrast to the no-history method described above, the Consenus-K technique reported by Randleman et al10 uses all available techniques

to calculate IOL power in postrefractive patients. This study by thegroup was a retrospective comparative series in which keratometric data


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from multiple techniques were pooled for each subject. Outliers K valueswere excluded if they were greater than 1.5D from the mean. Theresulting consensus value was used to calculate a predicted IOLimplant power that was compared with the ideal IOL power backcalculatedfrom postcataract surgery refraction. This difference betweenthe predicted IOL power and ideal IOL power was used to assess the

accuracy of the consensus-K technique. Their results suggested that theconsensus-K method was more accurate than any individual keratometrytechnique alone with the exception of the clinical history method.

Corneal Topography for Estimation of True CornealPowerTwo commercially available corneal topography systems are theOrbscan by Bausch & Lomb (Rochester, NY) and Pentacam by Oculus(Lynnwood, WA). Both systems produce detailed topographic models ofthe anterior and posterior corneal surfaces and provide estimates of totalcorneal power. The Orbscan system uses scanning slit technology thathas limitations within the central 2-mm optical zone due to the positionof its measurement camera. In general, it provides lower resolution

images than the Pentacam system, and it has been shown to be lessreliable with regard to the repeatability and reproducibility of itsmeasurements.11 The Orbscan system has specifically been criticizedfor the poor quality posterior images in which ectactic artifacts have beenobserved. In contrast, the Pentacam uses rotating Scheimpflug technologyto image the entire cornea including the central 2-mm optical zone.The results of recent tests have shown high reproducibility and reliabilitywith the Pentacam system.11A major advantage of the Pentacam system over conventionalkeratometry techniques is that it allows for imaging of the entire cornea,IOL Calculations After Refractive Surgery 185www.internat-ophthalmology.com

including the central optical zone.11 It provides detailed topographic

information about the anterior and posterior contours as well as cornealthickness estimates throughout the entire cornea. These measurementsare important in postrefractive corneas where the anterior radiusof curvature and cornea thickness may have been modified by therefractive procedure. Thus changes in stromal thickness within theoptical zone and deviation from the normal ratios of anteriorto-posterior curvature can be incorporated into corneal power calculations.Instead of calculating corneal power using the anterior curvatureand standard keratometric index (Equation 2), the Pentacam softwareuses the 2-surface formula that accounts for both anterior and posteriorcurvature (Equation 1). The result of this formula is an estimate of truecorneal power. The Pentacam software then converts true corneal power

to an equivalent K reading (EKR), which is an adjustment for IOLcalculations that are usually performed with the standardized singlesurfaceformula (Equation 2).In theory, the benefit of the Pentacam system over conventionalkeratomtery is that it incorporates topographic information about theanterior and posterior surfaces of the cornea and allows measurement ofthe central optical zone. In patients who have had refractive surgery, thisreduces the potential for keratometric errors and fewer refractivesurprises after cataract surgery. To date, however, there is a paucity ofclinical data to fully substantiate these concepts. One major question thatremains unanswered is how to use the data generated from the cornealpower map? The Pentacam system produces a table containing a series

of EKR readings derived from 8 concentric optical zones ranging from1 to 7mm in diameter (Fig. 1A). The EKR values are representedpictographically in false color on an EKR map (Fig. 1B). There is also a


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plot illustrating the relationship between the choice of optical zone sizeand EKR estimate resulting from that zone (Fig. 1C).It is clear from these data that EKR estimates are highly dependenton the region of the cornea from which they are measured, with thelowest EKR values generated from the smallest optical zones. Selectionof too large or too small optical zone can undoubtedly affect the accuracy

of IOL calculation based on these numbers. By default, the Pentacamsoftware uses an EKR zone of 4.5mm, a value recommended byHolladay12 and Hill.13 Some studies, however, suggest that a smallerEKR zone may be more accurate for estimating corneal power inpostrefractive patients. For example, Savini et al14 showed that cornealpower estimates derived from EKR zones of 1 to 3mm were similar tothose obtained from the clinically history method. One limitation of thisstudy was that it did not evaluate the predictive value of such data in IOLcalculations for cataract surgery. Surgeons should carefully consider theEKR zone selected for use in IOL calculations. More studies are requiredto determine the optimal Pentacam EKR zone for postrefractive patients.186 Mandell et alwww.internat-ophthalmology.com

IOL Formulas and Effective Lens PositionIt would seem that more accurate assessment of corneal power withtopographic systems such as the Pentacam would be enough to improveaccuracy of IOL calculations and prevent refractive surprises. Recentstudies, however, suggest that errors in corneal power assessment do notalone account for residual refractive error in postrefractive patients whounderwent cataract surgery.13,15,16 The reason for this is that most thirdgenerationIOL formulas such as the SRK/T, Hoffer Q, and Holladay 1rely on assumptions about effective lens position (ELP) that are not validin postrefractive patients. That is, such formulas presume a relationshipbetween anterior chamber depth and corneal power such that an eyewith a relatively flat cornea would be assumed to have a proportionately

shallow anterior chamber. In a cornea that has undergone ablation formyopia, however, such equations erroneously underestimate anteriorchamber depth and assume an ELP that is more anterior. Despite properassessment of central cornea power, the IOL power predicted by thirdgenerationformulas may be artificially low in patients who haveundergone myopic LASIK. One way around this problem is to use 2separate K values for IOL calculations. For example, the SRK/T formulacan be adapted to use a prerefractive K value for ELP calculation and apostrefractive K value for the remainder of the IOL calculations. ThisB CZone Diameter (mm) 1.0 2.0 3.0 4.0 4.5 5.0 6.0 7.0Mean Zonal EKR36.4 36.9 37.7 38.7 39.3 40 41.3 42.7

A

Figure 1.An example of EKR data produced from the Oculus Pentacam system in a postrefractivepatient. A, Mean zonal EKR values as a function of zone diameter (mm). B, Topographicalrepresentation of EKR readings throughout the surface of the cornea. C, A plot of mean zonal EKRvalues versus of zone diameter (mm) illustrating that the smallest EKR value is often obtained in thecentral EKR zone, which corresponds to the blue false color in panel (B). EKR indicates equivalent Kreading.IOL Calculations After Refractive Surgery 187www.internat-ophthalmology.com

double-K method has been studied and it has shown to be effective.15In addition, there are nomograms available to estimate the residualrefractive error based solely on the axial length and amount of refractivecorrection performed.16 For patients for whom preoperative data arenot available, the Holladay Consultant software uses a default K value of44 to compute ELP.13 In practice, precise historical data are often not

available at the facility where cataract surgery is performed. Thus, onlyrough estimates of the original K value can be incorporated into the IOL


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calculations using a nomogram or a fixed value of 44D as suggested bythe Holladay software. In any case, it is important for the surgeon toconsider this additional factor involving ELP when computing IOLpower in postrefractive patients.

SummaryMany patients who have had corneal refractive surgery ultimately

require cataract surgery several years later. Estimation of corneal poweris important for IOL calculations, but conventional keratometry techniqueslead to inaccurate results in postrefractive patients. Although theknowledge of prerefractive keratometry reading may be useful inmaking adjustments to such calculations, such historical data are oftennot available. There is a need for more direct nonhistorical keratometrytechniques and the Oculus Pentacam or similar devices (Ziemer Galilei)have the potential for use in such settings. However, more studies arerequired to evaluate the optimal parameters for Pentacam-based IOLcalculations in postrefractive patients.

References1. McDonneil PJ. Can we avoid an epidemic of refractive surprises after cataract

surgery? Arch Ophthalmol. 1997;115:542543.2. Elkington AR, Frank HJ. Clinical Optics. Oxford. Boston. St. Louis, Mo.: BlackwellScientific Publications; 1991:197.3. Javal E . Memoires Dopthalmometrie Annotes Et Precedes Dune Introduction. Paris: G.Masson; 1890:627.4. Hoffer KJ. Intraocular lens power calculation for eyes after refractive keratotomy.J Refract Surg. 1995;11:490493.5. Holladay JT. IOLs in LASIK patients. How to get them right the first time. RevOphthalmol. 2000:5962.6. Speicher L. Intra-ocular lens calculation status after corneal refractive surgery. CurrOpin Ophthalmol. 2001;12:1729.7. Zeh WG, Koch DD. Comparison of contact lens overrefraction and standardkeratometry for measuring corneal curvature in eyes with lenticular opacity.J Cataract Refract Surg. 1999;25:898903.8. Odenthal MT, Eggink CA, Melles G, et al. Intraocular lens power calculationfor cataract surgery after photorefractive keratectomy. Arch O

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