A Direct Method to Measure the Power of the Central Cornea After MyopicLaser In Situ Keratomileusis

Objective  To measure the corneal power after myopic laser in situ keratomileusis(LASIK).

Methods  Six central areas in 6 corneal power maps were studied using the OrbscanII statistical analysis device in 26 eyes that underwent myopic LASIK. Refractiveand corneal power changes were compared. Factors related to wrong cornealpower measurement were evaluated.

Main Outcome Measures  Cycloplegic refraction, refractive change at the corneal plane, andOrbscan II corneal power maps.

Results  Preoperatively, only posterior-mean power (P<<.001)and anterior-posterior power ratio (P<<.001)varied according to the size of the analyzed area. Postoperatively, total-optical(P = .03), keratometric-mean (P = .04), total-mean (P<.001), anterior-mean(P = .03), and posterior-mean (P<<.001) powers; and anterior-posterior power ratio (P<<.001) varied according to the area. Postoperatively, the differencebetween keratometric-mean and total-mean powers became larger (P<.001), and the anterior-posterior power ratio was reduced (P<<.001). A posterior-mean power change occurred(P = .04). Refractive change after myopic LASIK wasbest estimated by 2-mm total-mean power (mean ± SD difference, 0.07± 0.62 diopters [D]; P = .55) and 4-mm total-opticalpower (mean ± SD difference, −0.08 ± 0.53 D; P = .37).

Conclusions  Total corneal power is more positive and refractive change is underestimatedwhen deduced from the anterior surface radius and keratometric refractiveindex. The anterior-posterior power ratio is not a fixed value. The best areato estimate the refractive change depends on the method used to obtain thepower in diopters. Refractive change tended to be underestimated in largerareas and higher preoperative myopia. Orbscan II total-mean and total-opticalpower maps accurately assess the corneal power after myopic LASIK independentof preoperative data or correcting factors, and should improve intraocularlens calculation.

As patients who undergo refractive surgery become older, their probabilitiesof development of cataract are increased. It has been observed that residualrefractive errors can occur after cataract surgery in these cases. Thus, aresidual hyperopia was found in patients undergoing previous myopic laserin situ keratomileusis (LASIK) or photorefractive keratectomy, and the reasonfor this error is not clear. It has been suggested that formulas for intraocularlens (IOL) power calculation may not be accurate,^1-3 and/orthat the corneal power may be incorrectly measured.^4-12 MyopicLASIK produces deliberate modifications in the anterior surface of the corneaand its thickness to correct a refractive defect. The normal prolate (convexitysteeper in the center) anterior surface is converted to an oblate (convexityflatter in the center) surface. Therefore, it may not be correct to applyconventional variables assumed for normal corneas to surgically modified corneas.

Most IOL calculation formulas^1,13,14 assumethat the cornea is spherical and commonly use a corneal power determined bymeans of manual or computerized keratometry or by means of corneal videokeratography(CVK) using Placido disks. These methods deduce the total power of the corneaby measuring the radius of the corneal anterior surface curvature from a centralarea with a diameter of approximately 3 mm. Conversion of millimeters of radiusto diopters (D) is performed using a theoretical effective (keratometric)refractive index of 1.3375.^7,15,16 Toimprove accuracy, attempts to correct this index have been made,¹⁷ resultingin other adapted theoretical indexes that have been applied in automatic keratometersor IOL formulas.^7,18

On the other hand, combined slit-scanning and Placido-disk CVK (OrbscanII; Bausch & Lomb–Orbtek Inc, Salt Lake City, Utah) is a relativelynew technology able to localize 9000 points of the cornea and anterior chamberand transform them to topographic maps. This equipment calculates the powerof the cornea by diverse mathematical methods, using the keratometric refractiveindex (keratometric power maps) or the physiologic refractive indexes (anterior,posterior, or total power maps). Ray tracing (optical power maps), sphericalequivalent (mean power maps), astigmatism (astigmatic power maps), differentialwith best-fit sphere (elevation maps), and thickness (power and pachymetrymaps) may be represented.^19,20 Inaddition, this system may statistically analyze areas as small as a centralpoint with a 40-µm diameter,^21,22 andas large as the peripheral limit of data achievement around a 9-mm diameter.The definition and explanation of Orbscan II principles and maps may be obtainedelsewhere.^19-24 Manufacturernomenclature has been criticized.²⁴ In scientificreports, the terms total and mean, used to designate the type of some Orbscan II power maps, may be confusedwith terms representing values achieved from data analysis. Thus, unless otherwiseindicated, this article hyphenates compound words that identify Orbscan IImaps.

Using this equipment, our group recently reported that the power ofnormal corneas deduced from the measurement of only the anterior surface usingthe keratometric refractive index is approximately 1.5 D more positive thanthe power calculated from all of its optical components and using the physiologicrefractive indexes. It has been shown that the size of an analyzed area ofless than a 5-mm diameter has no effect in the total power of normal corneasor in the power of their anterior surface. It also has been shown that thepower of their posterior surface becomes less negative and that their thicknessincreases when larger areas are analyzed. Furthermore, the 10:1 ratio traditionallyaccepted for anterior and posterior corneal powers was not confirmed.²²

This study evaluates the variability of corneal power measurements obtainedby means of the Orbscan II topography system before and after myopic LASIK.Changes in the spherical equivalent (calculated using the keratometric orthe physiologic refractive indexes) and ray tracing (calculated using thephysiologic refractive indexes) corneal powers are compared with the refractivechange at the corneal plane. Among factors that have been related to wrongcorneal power measurement after refractive surgery,^4-12 thisstudy analyzes the influence of keratometric and physiologic refractive indexes,the anterior-posterior corneal power ratio, the corneal power change accordingto the size of the analyzed area, and the contribution of thickness and posteriorsurface on total power change, with the goal to determine the best variablesthat should be applied for an accurate and direct assessment of corneal powerafter myopic LASIK.

This study was designed as an observational case series. A retrospectivereview of preoperative and postoperative combined slit-scanning and Placido-diskCVK with the Orbscan II corneal topography system was made in 26 eyes of 18patients at the Department of Ophthalmology, Paulista School of Medicine,Federal University of São Paulo (UNIFESP/EPM), São Paulo, Brazil.Postoperative examination was made at least 1 month after eyes underwent myopicLASIK using the Ladar Vision excimer laser system (Alcon-Summit Autonomous,Orlando, Fla). Written informed consent and cycloplegic refraction were usedroutinely. Patients had no other abnormality except myopia (mean ±SD sphere, −3.39 ± 1.83 D) or myopic astigmatism (mean ±SD cylinder, −1.41 ± 1.17 D), and no postoperative complicationother than some residual ametropia (mean ± SD spherical equivalent,−0.50 ± 0.56 D). Cases were consecutively selected from the OrbscanII hard disk (Table 1). Averagevalues of all points of total-optical (representing the ray tracing of anteriorand posterior surfaces using physiologic refractive indexes), keratometric-mean(representing the spherical equivalent of anterior surface using the keratometricrefractive index), total-mean (representing the spherical equivalent of bothcorneal surfaces plus thickness-mean power using physiologic refractive indexes),anterior-mean and posterior-mean (representing the spherical equivalent ofeach corneal surface using physiologic refractive indexes), and thickness-mean(representing the contribution of thickness to the total power of the cornea)power maps were assessed using the Orbscan II statistical analysis device(software version 3.00D) for 6 central areas with 0.04-, 1.0-, 2.0-, 3.0-,4.0-, and 5.0-mm diameters (±0.02 mm) as described elsewhere.^21,22,24 Spherical-cylindricalspectacle refraction was converted to a spherical equivalent corneal planevalue using a vertex distance of 12 mm. The refractive change (spherical equivalentat the corneal plane) induced by LASIK was calculated by subtracting the postoperativeresidual refractive defect from the preoperative ametropia, and it was comparedwith the corneal power change determined by each Orbscan II power map in everyanalyzed area. The influence of keratometric and physiologic refractive indexeson total corneal power calculation was studied by determining the differencebetween keratometric-mean and total-mean powers for each eye and then theaverage for each area. The anterior-posterior corneal power ratio was studiedby analyzing the relationship between anterior-mean and posterior-mean powers.A posterior surface change was studied by comparison of the posterior-meanpower before and after surgery.

The 2-tailed paired t test, analysis of variancewith 1 factor, and linear correlation (R²)were calculated using Excel 2000 7.0 (Microsoft Corporation, Redmond, Wash).Nonparametric Wilcoxon signed rank test and Pearson correlation factor (multiple R) were performed using SPSS 7.5.2S (SPSS Inc, Chicago,Ill). An α risk of .05 was established. Unless otherwise indicated,data are expressed as mean ± SD. This study was reviewed and approvedby the UNIFESP/EPM Ethics Committee in Research.

Mean preoperative spherical equivalent was −4.09 ± 1.59D. Mean refractive change at the corneal plane (gold standard) was –3.59± 1.46 D. Mean follow-up for postoperative refraction and topographywas 2.54 ± 1.66 months. Information about cases and LASIK variablesare summarized in Table 1.

Preoperative (Table 2) total-optical,keratometric-mean, total-mean, anterior-mean, and thickness-mean powers werenot statistically different in all analyzed areas. The average of the posterior-meanpower varied from –6.74 D when measured in the smallest central areato –6.39 D when assessed from an area with a 5-mm diameter. The standarddeviation of posterior-mean power in all areas was proportionally similar(3%-5% of average values) to the standard deviation found in all other maps,except thickness-mean power maps (around 10%).

Postoperative (Table 3)total-optical, keratometric-mean, total-mean, and anterior-mean powers becamelarger (more positive), and posterior-mean power became smaller (less negative)when larger areas were analyzed. Thickness-mean power was not statisticallydifferent in all analyzed areas.

Preoperative (Table 2) andpostoperative (Table 3) betterPearson correlations between anterior-mean and posterior-mean powers werefound when larger analyzed areas were measured. Before LASIK, the averageof the anterior-posterior corneal power ratio varied from 7.27 in the smallestanalyzed area to 7.63 in the 5-mm-diameter area. After the myopic LASIK, thisratio was smaller (2-tailed paired t test, P<<.001) and varied from 6.25 to 7.28, respectively.Preoperatively and postoperatively, this variability was extremely significant,meaning that the anterior-posterior power ratio was not a fixed value.

Preoperative keratometric-mean power was more positive than total-meanpower by 1.61 D in the smaller analyzed area, and by 1.31 D in the 5-mm-diameterarea (Table 4). Postoperatively,this difference was larger and ranged from 2.50 to 1.61 D, respectively.

Changes in keratometric-mean and total-mean powers after myopic LASIKwere smaller when assessed in larger areas (Table 5). Changes in total-optical power had this tendency, butthey were not statistically different in all 6 analyzed areas. The refractivechange at the corneal plane had very good Pearson correlation (P<<.001) with the total-optical (R≥0.80),total-mean (R≥0.87), and keratometric-mean (R≥0.89) power changes. Linear correlation showed thatmeasurement of power on larger areas with total-optical (Figure 1) and total-mean (Figure2) power maps tended to underestimate the LASIK outcome, especiallyfor higher ametropias.

Total-optical power changes in a 3-mm-(Wilcoxon, P = .07) and a 4-mm-(Wilcoxon, P = .37) diameterarea were not different from the refractive change. Total-optical power changesmeasured in other area sizes were different. Keratometric-mean power changeswere best assessed in the smallest analyzed area (Wilcoxon, P = .009), but they were different from the refractive change in all6 areas. Total-mean power changes were best assessed in a 2-mm-diameter area(Wilcoxon, P = .60). Total-mean power changes inother area sizes were different from the refractive change.

Symmetry of values above and below confirmed the more representativeareas. A difference of larger than 1 D was found in only 2 eyes (1.15 and−1.02 D) with the 4-mm total-optical power, and in 1 case (1.40 D) withthe 2-mm total-mean power.

Changes in anterior-mean power after myopic LASIK were smaller whenassessed in larger areas (Table 6).The refractive change at the corneal plane correlated (R≥0.89; P<<.001) with the anterior-meanpower change in all 6 analyzed areas. Anterior-mean power changes in the centralsmallest area (Wilcoxon, P = .85) and in the 1-mm-diameterarea (Wilcoxon, P = .27) were not different fromthe refractive change. Anterior-mean power changes in other area sizes weredifferent from the refractive change.

The posterior-mean power increased (steepening) almost −0.50 Din the central point and the 1-mm-diameter area (12%-13% of total-mean powerchange), and some more than −0.25 D in the 2-mm- and 3-mm-diameter areas(8%-10%). The larger the analyzed area, the smaller its contribution to thetotal-mean power change. Although it had statistical significance, posterior-meanpower change was without clinical importance and hardly noticeable when a5-mm-diameter area was analyzed. The refractive change had no correlationwith the change found in the posterior-mean power (R≤−0.28; P≥.17).

Preoperative thickness-mean power ranged from 0.11 to 0.17 D (mean,0.14 D [Table 2]). Changes ofthickness-mean power were too small (mean, −0.01 D; never larger than–0.03 D) to have clinical importance, so we waived statistical testsfor them.

The cornea is an optic system composed of anterior and posterior surfaces,a distance between them (thickness), and basically 3 optical media (air, cornealtissue, and aqueous humor), each one with its own refractive index. Presently,it is known that all these components must be considered when calculatingthe real power of the cornea.^7,15,22 Traditionalmethods (eg, keratometry, simulated keratometry [sim-K]) assume the totalpower of the cornea from the measurement of the radius of curvature of itsanterior surface. Only recently, when slit-scanning CVK (Orbscan I) measurementof the posterior surface power of the cornea became available, such an assumptionbegan to be challenged. Accuracy questioning^12,25 andverification²⁶ of this technology have beenreported. Although its reliability may be controversial, it seems improvedafter it was combined with Placido-disk–based CVK (Orbscan II).

A great variability on corneal power may be achieved with the OrbscanII by measuring different area sizes using different mathematical processes.²² Essentially, the basis of calculation of all mapsis the measurement of the distance between each point localized by the systemand the sphere that best fits these points. This distance is called elevation and may be negative (down to the best-fit sphereand represented by cold colors) or positive (up to the best-fit sphere andrepresented by warm colors).^19-22 Optical,mean, keratometric, total, and other power maps may be obtained.^21,22 However,a few values automatically shown are a potential source of confusion if appliedin IOL calculation. The power of the posterior best-fit sphere shown on topof default quad maps, for example, is calculated using the keratometric refractiveindex of the cornea (1.3375), despite the fact that components of this opticalinterface are the cornea (refractive index of 1.376) and the aqueous humor(refractive index of 1.336). On the other hand, diopters automatically repeatedat right of several individual maps, for standard or default statistical zones,also seem to be obtained using the keratometric refractive index, are notthe same values found by the Orbscan II statistical analysis device,²² and should be interpreted only as keratometric data.The Orbscan II statistical analysis device is able to give the average measurementof all identified points in a selected area of any of multiple available maps,its lowest and highest value, and its standard deviation. It is a simple (usingthe control-a keyboard shortcut) but time-consuming process, and it seemsto be the best way to obtain information from this equipment. A suggestionhas been made to the manufacturer to simplify the achievement of data withit.Variability of this method is on the third decimal in power maps.²²

Several methods were suggested to measure the power of corneas subjectedto refractive surgery. Keratometry has been replaced by Placido-disk–basedCVK, by sim-K,^7,27-29 orby mean central corneal power.⁴ However, thesemethods evaluate areas of approximately 3 mm in diameter that might not beappropriate to calculate the power of corneas that have undergone refractivesurgery when the keratometric refractive index is used. The tendency thesekeratometric powers have to indicate a more positive total corneal power andto underestimate the refractive change after myopic LASIK^7,15,30 orphotorefractive keratectomy^7,29,31,32 seemsto be compatible with the undercorrection usually found after cataract surgeryin patients with myopic refractive surgery.^7,15,29-34

Presently, the criterion standard and the more accurate method for cornealpower estimation after refractive surgery is the clinical history method,also called refraction-derived keratometry. The refractive change is subtractedfrom the power of the cornea before the refractive surgery to determine thefinal corneal power to be applied in IOL calculation.^{5,7,11,12,15,32-37} Sincethis information is not always available, it was suggested that an overrefractionwith a rigid contact lens with a known base curve should be made,^{7,12,15,35,38} ahigher fictitious refractive index for the cornea should be adopted,^10,12,17 regression formulasto adjust the smallest ring on CVK should be applied,³⁰ cornealradius correcting factors should be calculated,³⁹ orcomputer programs should be used.⁴⁰ Althoughthese empirical methods may be effective, they assume an expected value anddo not assess a realistic corneal power. A more pragmatic approach would beto understand why traditional methods result in errors and then, instead ofadapting these errors, look for how to avoid them. The capability of the OrbscanII corneal topography system to evaluate the central portion of the corneaseems to give us such an opportunity.

The keratometric refractive index of 1.3375 assumes that the power ofthe anterior surface of the cornea is almost 10 times the power of the posteriorsurface. However, our results show a smaller anterior-posterior corneal powerratio, confirming our earlier report.²² Thisseems to be because the Gullstrand model eye from which the keratometric refractiveindex is deduced assumes a lower theoretical posterior surface power thanwhat was actually assessed by the Orbscan I^7,41 andII.²² Furthermore, this ratio is not fixedin all of the extension of both corneal surfaces, but it changes accordingto the size of the measured area. That correlation between powers of bothsurfaces improves when larger areas are assessed. This study also confirmsthat the total corneal power is more positive when deduced from the anteriorsurface radius using such a keratometric refractive index. As a consequenceof changes on corneal surfaces, these findings are more remarkable after myopicLASIK, suggesting that traditional methods to calculate the corneal powermay be inappropriate in these cases.

Preoperatively, the total power of the normal cornea and the power ofits anterior surface do not vary and are independent of the size of the analyzedarea if it has a diameter of less than 5 mm. Nevertheless, the power of theposterior surface becomes less negative when measured in larger areas.²² Myopic LASIK iatrogenically modifies the normal geometryof the cornea by promoting higher power changes in the central portion ofthe cornea. The expected flattening (less positive power) of the anteriorsurface, reflected by the change in anterior-mean power maps, tended to diminishprogressively when larger areas were analyzed and, consequently, the totalpower of the cornea became more positive. The changes on the anterior surfacewere responsible for most but not all of the myopic correction induced bythe LASIK. As this study shows, a change in the power of the posterior surfaceof the cornea contributes around 10% of the total power change inside a centralarea 3 mm in diameter.

Theoretically, the refractive change (gold standard) induced by theLASIK should be the same as the power change found in the cornea. However,this was not observed in all the Orbscan II maps or in all of the analyzedareas. The refractive change at the spectacle plane might be used, but wedecided to compare this change at the corneal plane because the Orbscan IIassesses corneal power changes and not spectacle power changes. Although changesin anterior and total power maps in all 6 analyzed areas had good correlation,correlation tests did not confirm which map or which area reflected betterthe refractive change after myopic LASIK. Thus, refractive and Orbscan IIcorneal power changes were also compared using the paired t and Wilcoxon tests. Both tests had equivalent results. To simplify,the P values shown in Table 5 correspond to paired t test results.Areas larger than 4 mm in diameter in most maps tended to underestimate therefractive change, particularly for eyes with higher preoperative myopia.The larger underestimation occurred with the keratometric-mean power (Table 5), suggesting that traditional keratometricmethods used to obtain the corneal power may be more sensitive to the oblateshape of the anterior surface secondary to the higher energy applied to thecentral point. Although the effective optical zone of treatment is relatedto the amount of treatment,⁴² we do not yetknow whether the size of the effective optical zone may also influence theselection of the best representative central area to compute the refractivechange. From this study, we know that the size of this area modifies the resultaccording to the method used to obtain the value in diopters. The best total-opticalpower map to reflect the refractive change was found using a 4-mm-diameterarea (Table 5 and Figure 1, bottom and center). Keratometric-mean power maps had theirbest measurement in the smallest, most central point, but always underestimatedthe refractive change. The best total-mean power map was found using a 2-mm-diameterarea (Table 5 and Figure 2, top and right). Anterior-mean power maps also accuratelyresemble the refractive change when assessed in areas smaller than 1 mm indiameter; however, they do not represent the total corneal power (Table 6). Despite some apparent differencesin our methods to obtain the data and the upgraded equipment we used, ourmore accurate results are in agreement with those of an earlier report, suggestingthe use of the 4-mm total-optical power map.⁴³ Wewere unable to find any other previous report of this in the literature.

Although we studied a limited number of patients, from our results wefind it reasonable to recommend the use of the 2-mm total-mean power and/orthe 4-mm total-optical power, assessed by the Orbscan II statistical analysisdevice, as accurate values to be applied for IOL calculation in patients whounderwent myopic LASIK. Until more information is collected, it might be prudentto use the smaller of both values when it is known that the corrected refractivedefect was higher than −5 D. Caution must be taken to extrapolate ourresults to other refractive errors. Further prospective studies with patientswho will undergo cataract surgery might demonstrate the validity of theserecommendations. More research is needed to understand all factors that mayinduce the variability observed in corneal power measurement and to find thebest variables that should be used to directly assess the most representativecorneal power after other corneal surgeries like photorefractive keratectomy,hyperopic LASIK, radial keratotomy, and penetrating keratoplasty, and evenin corneal abnormalities like keratoconus.

Corresponding author and reprints: Carlos G. Arce, MD, Ocular BioengineerLaboratory, Institute of Vision, Department of Ophthalmology, UNIFESP/EPM,Rua Borges Lagoa 368, São Paulo, SP 04038-000, Brazil (e-mail: cgarce@mpc.com.br).

Submitted for publication February 19, 2003; final revision receivedSeptember 1, 2003; accepted October 6, 2003.

This study was presented at the XXVII Annual Symposium of the ParanáAssociation of Ophthalmology; June 13, 2003; Curitiba, Brazil; at the XXXIIBrazilian Congress of Ophthalmology; September 11, 2003; Salvador, Brazil;and at the 23rd Biennial Cornea Research Conference, the Schepens Eye ResearchInstitute and Massachusetts Eye and Ear Infirmary; Harvard Medical School,October 4, 2003; Boston, Mass.

This study is the winner of the Paraná Association of Ophthalmology2003 Prize and of the 23rd Biennial Cornea Conference Research Award.

We thank Peter J. Polack, MD, for editorial assistance.