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Correlation between refractive and measured corneal power changes after myopic excimer laser photorefractive surgery

Chen, Shuan MDa; Hu, Fung-Rong MD*,a

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Journal of Cataract & Refractive Surgery: April 2002 - Volume 28 - Issue 4 - p 603-610
doi: 10.1016/S0886-3350(01)01323-2
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Abstract

Excimer laser photorefractive surgery has been successfully used to correct myopia, hyperopia, and regular astigmatism by changing the anterior curvature of the central cornea.1–5 As the procedure has become increasingly popular, more cataract surgery in post-photorefractive surgery eyes is anticipated. These patients will expect excellent uncorrected visual acuity after cataract surgery, as it was after photorefractive surgery, with a postoperative refraction as close as possible to emmetropia. However, the accuracy of intraocular lens (IOL) power prediction after photorefractive surgery remains a challenging issue.

The corneal power changes measured by automated keratometry and corneal topography analysis are reported to underestimate corneal flattening after photorefractive keratectomy (PRK) by an average of 24%.6 The greatest source of the underestimation is the corneal power changes measured by keratometry and videokeratography.7,8 A 1.0 diopter (D) error in the keratometric reading results in nearly a 1.0 D error in the postoperative refractive power.9 To avoid underestimating the IOL power and hyperopia after cataract surgery in post-photorefractive surgery eyes, the measured corneal power values must be corrected.6

The purposes of this study were to determine the correlation between the refractive and the measured corneal power changes after myopic photorefractive surgery; to compare the magnitude of error among different methods of measuring the actual corneal power changes after photorefractive surgery; and to develop a formula to adjust the measured corneal power to improve the prediction of actual corneal power after photorefractive surgery.

Patients and Methods

Photorefractive Surgery Procedure

The medical records of all patients who had PRK or laser in situ keratomileusis (LASIK) by a single surgeon (F-R.H.) at National Taiwan University Hospital from January 1997 to December 1998 were reviewed. The criteria for inclusion in the study were regular follow-up for at least 1 year, postoperative best corrected visual acuity of 20/20 or better, and absence of topographic inhomogeneity such as a central island or keyhole.

Eighty-six eyes of 38 women and 19 men were included; 56 had PRK and 30, LASIK. The mean age at the time of photorefractive surgery was 32.6 years ± 7.1 (SD) (range 21 to 48 years). The preoperative mean spherical equivalent (SE) was −6.01 ± 1.35 D (range −2.31 to −9.13 D) in the PRK group and −8.67 ± 1.61 D (range −6.01 to −11.99 D) in the LASIK group.

The LASIK procedure was based on the technique described by Pallikaris et al.10 and Pallikaris and coauthors.11 After a 160 μm flap was created using the Automated Corneal Shaper® (Chiron Vision, Inc.), the flap was nasally reflected and the stromal bed ablated. The corneal ablation in PRK and LASIK was performed with the Summit Apex Plus laser using the aspheric program for myopia and the toric program for myopic astigmatism. The optic zone ranged from 6.0 to 6.5 mm. An anti-central-island pretreatment was performed in all patients.

After surgery, artificial tears, fluorometholone 0.1%, and gentamicin 0.3% solution were used in all eyes and a plano contact lens (Acuvue®, Johnson and Johnson Vision Products Inc.) was worn by the PRK patients. Follow-up examinations including a comprehensive ophthalmic examination, subjective refraction, automated keratometry, and computerized videokeratography were at 1, 3, 6, and 12 months.

Assessment of Subjective Refraction

The subjective refraction was obtained by correction with spectacles using the red-green and sunburst balanced tests. The subjective refraction was measured in diopters and calculated as the SE at the spectacle plane without correction for vertex distance (SEQsp) and at the corneal plane with correction for vertex distance (SEQco) using the following equation: SEQco = SEQsp ÷ [1 − (0.012 × SEQsp)].

The change in the subjective refraction at the corneal plane before and after photorefractive surgery was calculated as ΔSEQco = postop SEQco − preop SEQco.

Assessment of Corneal Power

The corneal power was measured by automated keratometry (CR 3000, Topcon) and computerized videokeratography (TMS-1, software version 1.51, Computed Anatomy, Inc.). Four corneal power readings were measured at the same time: Auto K, Sim K, Central K, and Pupil K. The Auto-K value was obtained by automated keratometry and calculated with the mean vertical and horizontal powers. The topographic simulated keratometric power, Sim K, was derived from the power points on photokeratoscopic rings 7, 8, and 9. It provides the power and axis of the steepest meridian and the meridian 90 degrees away. The mean value of the power of the steepest meridian and the meridian 90 degrees away was calculated and recorded. Because the real central corneal power could not be read on topography, the Central K was recorded as the power of the first photokeratoscopic ring on topography. The corneal power values at 3, 6, 9, and 12 o'clock of the pupil margin were obtained by moving the cursor on topography. The mean value was calculated and recorded as the Pupil K.

The changes in measured corneal power were calculated according to the preoperative-to-postoperative change in Auto-K, Sim-K, Central-K, and Pupil-K values, and recorded as ΔAuto K, ΔSim K, ΔCentral K, and ΔPupil K, respectively.

Statistical Analysis

The differences between the refractive changes (ΔSEQco) and each of the measured corneal power changes were calculated and compared by paired t test. The values of the 4 measured corneal power changes (ΔAuto K, ΔSim K, ΔCentral K, and ΔPupil K) were also compared by paired t test. The correlation between ΔSEQco and the measured corneal power changes were assessed by multiple linear regression analysis (SAS program) and were compared by an F test. A P value of 0.01 or less was considered statistically significant.

Results

Differences Between Refractive and Measured Corneal Power Changes

Table 1 shows the refractive and measured corneal power changes 1 year after photorefractive surgery. The changes in Auto K, Sim K, Central K, and Pupil K significantly underestimated the ΔSEQco. The mean change in Central K correlated best with the ΔSEQco at 1 year (Table 2). The mean difference between ΔSEQco and ΔAuto K was the largest among the corneal power readings. Based on the mean differences between the changes in measured corneal power and the ΔSEQco, the relationship of these parameters can be described as follows: ΔSEQco > ΔCentral K > ΔSim K > ΔPupil K > ΔAuto K.

Table 1
Table 1:
The refractive and the measured corneal power changes 1 year postoperatively.
Table 2
Table 2:
Differences between the refractive and measured corneal power changes 1 year postoperatively.

The differences between each measured corneal power change are summarized in Table 3. At 1 year, the differences among ΔSim K, ΔPupil K, and ΔAuto K were not statistically significant; the value of ΔCentral K was significantly greater than that of the other 3 parameters (P < .01).

Table 3
Table 3:
Correlation between each measured corneal power change (N = 86).

Linear Regression Formulas

The linear regression formulas for the refractive changes and the measured corneal power changes at 1 year are shown in Table 4. All the changes in measured corneal power (including ΔCentral K, ΔSim K, ΔPupil K, and ΔAuto K) predicted the refractive changes well; the correlation coefficients were around 0.9 (P < .01). However, the regression coefficient of all 4 measurements had a value less than 1.0. The regression coefficient of ΔAutoK to ΔSEQco was 0.7397 (Figure 1) and of ΔCentral K to ΔSEQco, 0.9183 (Figure 2). These data suggest that all the changes in measured corneal power underestimated the refractive change. The ΔAuto K was farthest from ΔSEQco; the ΔCentral K was closer to it than the other 3 parameters.

Table 4
Table 4:
Regression formulas of the refractive and the measured corneal power changes 1 year postoperatively (N = 86).
Figure 1.
Figure 1.:
(Chen) Correlation between the difference in ΔAuto K and in ΔSEQco at 1 year.
Figure 2.
Figure 2.:
(Chen) Correlation between the difference in ΔCentral K and in ΔSEQco at 1 year.

Discussion

In normal corneas, the central area has a relatively uniform curvature and the measured corneal power is almost the same at the center and 3.0 mm from the center. However, after excimer laser photorefractive surgery, the central cornea is flatter than the adjacent cornea and the change is more marked with high correction.12 This change may result in an underestimation of corneal power measured by keratometry or videokeratography. Thus, a keratometric reading or corneal topography analysis will not accurately reflect the refractive changes.13–21

Three methods to better estimate corneal power after keratorefractive surgery have been proposed: the calculation method, subtracting the ΔSEQco induced by the refractive surgery from the mean corneal power measured before surgery15–17; the contact lens method, subtracting the difference between the manifest refraction with and without a plano hard contact lens of known base curve from the base curve16,18,19; and the videokeratographic method, measuring the central corneal power inside the 3.0 mm zone.6,19,20 The calculation method is reported to be the most reliable22,23 except in patients with nuclear sclerosis that might limit the accuracy.18,19,22 Because no cataract was found in any patient enrolled in this study, we applied the calculation method by calculating the ΔSEQco to represent the actual corneal power change after refractive surgery.

We found that all the changes in measured corneal power underestimated the refractive changes, especially the Auto K, which underestimated by the largest amount. It implied that the corneal power measured by keratometry after photorefractive surgery overestimated the actual corneal power. This overestimation also correlated with the amount of myopic correction; the higher the myopic correction, the larger the overestimation. This finding supports those in previous reports of patients having radial keratotomy and PRK.1–5,22–24

The inaccuracy of automatic keratometry and videokeratography in measuring the corneal power after photorefractive surgery could be attributed to the changes in anterior and posterior corneal curvature and the reduction in corneal thickness. After PRK or LASIK, the central corneal curvature is flatter in the central cornea than in other areas. The closer to the visual axis, the flatter the cornea becomes after photorefractive surgery. As a consequence, the corneal power measurement varies by the area being measured. Since the Central K measures the first photokeratoscopic ring, which is closer to the visual axis than other parameters, it is closest to the actual corneal power. Since automatic keratometry measures the farthest area of the central cornea, it overestimates the actual corneal power the most.

Along with the corneal curvature change, the corneal thickness is decreased after photorefractive surgery. Since automatic keratometry and videokeratography measure the corneal power based on Gullstrand's model eye, the value shown is derived from the anterior corneal curvature using a paraxial formula (power [D] = (n −1)/radius) with a fixed refractive index.25 However, the refractive index is not valid when the relationship between the radii of the anterior and posterior surfaces of the cornea do not match those of the model eye. Because the corneal thickness and posterior corneal curvature are changed after photorefractive surgery, the traditional method of calculating corneal power using a fixed refractive index becomes inappropriate after photorefractive surgery.8,18,25,26 This may explain why the inaccuracy of the measurement by keratometry or videokeratography was correlated with the amount of myopic correction by photorefractive surgery.

Many studies of modifying the conversion index for corneal power calculation after refractive surgery have been reported.8,26–32 Recently, Holladay and Waring31 and Mandell26 recommended using the refractive index of the anterior stroma (n = 1.376), corresponding to a corneal power correction factor of 1.114 (1.376/1.3375), to calculate the change in anterior corneal curvature measured by keratometry or videokeratography after PRK. Hugger et al.32 suggest that a higher refractive index of 1.4083, corresponding to a correction factor of 1.21, is necessary to equalize the change in the SE of the subjective manifest refraction and anterior corneal refractive power averaged over the central 3.0 mm. These higher values for the refractive index are used to calculate the change in corneal refractive power; they cannot be used to directly calculate corneal refractive power from measured values of the radius of curvature.

In the present study, we found that the difference between curvature-style measurements and refractive changes is a constant fraction with a correlation coefficient around 0.9. Thus, the postoperative corneal power could be calculated by linear regression formulas. The regression coefficient of ΔAutoK to ΔSEQco was 0.7397 with a constant of 0.3778, which corresponds to a correction factor of 1.16, 1.24, and 1.28 for a myopic correction of 3.0 D, 6.0 D, and 9.0 D, respectively. These results suggest that the correction factor for measuring corneal power by keratometry is related to the amount of myopic correction by photorefractive surgery. However, the constants of the regression formula of ΔSim K to ΔSEQco, ΔCentral K to ΔSEQco, and ΔPupil K to ΔSEQco were close to zero, suggesting that the correction factor for measuring corneal power by videokeratography is not related to the amount of myopic correction by photorefractive surgery.

We think these results can be explained by the difference between videokeratography and standard keratometry instruments. Videokeratography measures the Sim K, Pupil K, and Central K at a rather fixed zone (eg, 0.5 mm zone for Central K and 3.0 mm zone for Sim K), while the area measured by standard keratometry is dependent on the steepness of the cornea (eg, a 4.0 mm zone for a 36.0 D cornea and a 2.8 mm zone for a 50.0 D cornea).33 Thus, the area of the cornea measured by standard keratometry is related to the amount of myopic correction by refractive surgery.

The region of the central cornea that contributes to the refractive power of the eye varies from patient to patient. The 2 primary determining factors are the diameter of the entrance pupil and the Stiles-Crawford effect.34,35 Since the central corneal curvature is altered from prolate to oblate after refractive surgery, standard keratometry cannot accurately measure the central corneal power. Hence, many sophisticated techniques using videokeratographic data have been developed to determine the corneal curvature in the postsurgical cornea. Maloney and coauthors36 developed a best-fit method for measuring the refractive power of the cornea based on all points on the corneal topography in the central 4.0 mm of the cornea. Their method was accurate in a normal cornea. However, the technique underestimated the corneal power after refractive surgery.

Maeda and coauthors13 developed a procedure to calculate the average central power (ACP) of the cornea within the entrance pupil from videokeratography. None of the eyes with normal corneas or regular astigmatism had a greater than 0.25 D difference between the ACP and the Sim K. But, 25% of the PRK eyes had differences greater than 0.50 D. Smith and coauthors37 compared the changes in cycloplegic refraction, keratometry, and Sim K derived from the TMS-1 system and the values calculated with a best-fit parabolic equation that incorporated the Stiles-Crawford effect and videokeratography values within the central 6.0 mm zone. They found that the best-fit method is more accurate than Sim K and standard keratometry in evaluating corneal refractive power after refractive surgery. The slope of the regression line was 0.94 in the best-fit equation compared with 0.63 for Sim K and 0.67 for standard keratometry. Hugger et al.32 compared changes in manifest refraction and corneal power in patients 1 month after PRK. They found that the correlation between the SE of the subjective manifest refraction and the axial central power provided better results than standard keratometry and Sim K. They also found that the axial central power values at the 1.0 mm zone have the smallest differences between the mean change in the SE of the subjective manifest refraction and the mean change in corneal power after PRK. The slope of the regression line in their study was 0.93 for the axial power at the 1.0 mm zone, 0.72 for the axial Sim K, and 0.88 for the standard keratometry.

In the present study, we also found that the changes in corneal power measured by the first ring on videokeratography were closest to the change in the manifest refraction. The slope of the regression line in our study was 0.92 for the first keratoscopic ring, 0.88 for Sim K, and 0.74 for standard keratometry. Our results are comparable to the results of more complicated topographic analysis.13,32,36,37 They suggest that measuring the corneal power at the first videokeratographic ring is a clinically practical and simple method for determining corneal power after photorefractive surgery.

Although Central K was closer to the actual corneal power than the other K values, it varied slightly from the refractive changes. The possible reasons for the discrepancies include the following: The subjective refraction obtained by spectacle correction has several limitations, including the inability to correct for some small irregular astigmatism; the use of red-green and sunburst balanced tests results in subjective differences among patients; the real central corneal power cannot be measured on topography directly, and the power of the first ring is measured instead; the corneal anatomic center may be different from the visual axis, especially in patients with a large kappa angle.

Clinical Application of the Regression Formulas

All the changes in measured corneal power predicted the refractive changes well, with correlation coefficients greater than 0.9. This indicates that the measured corneal power changes can be predicted from the refractive changes with more than 90% reliability. Using this formula, we can adjust the measured corneal power to better represent the actual corneal power. For example, if the ΔSEQco corrected by photorefractive surgery were 6.0 D, we could obtain the ΔCentral K and ΔAuto K values using the regression formula. The value of ΔCentral K would be 5.4894 D and the value of ΔAuto K, 4.816 D. The actual corneal power changes would be underestimated by 0.5106 D with Central K and by 1.184 D with Auto K. Thus, the actual corneal power after PRK or LASIK could be calculated by subtracting 0.5106 D from the postoperative Central K or by subtracting 1.184 D from the postoperative Auto K.

As another example, if the ΔSEQco corrected by photorefractive surgery were 10.0 D, the results of ΔCentral K and ΔAuto K would be 9.1626 D and 7.7748 D, respectively. Thus, the underestimation of the ΔCentral K and ΔAuto K would be 0.8374 D and 2.2252 D, respectively. These examples clearly demonstrate that when the ΔSEQco corrected by photorefractive surgery increased (from 6.0 to 10.0 D), the magnitude of the underestimation increased as well, especially the Auto K (from 1.184 to 2.2252 D). The underestimated values should be taken into account when considering the actual corneal powers in the calculation of IOL power.

In conclusion, direct corneal power measurements using automatic keratometry or videokeratography underestimate the actual corneal flattening after photorefractive surgery. The underestimation is lowest by measuring the power of the first photokeratoscopic ring on videokeratography. The measured corneal power can be adjusted by a linear regression formula to decrease the risk of error in underestimating the IOL power and hyperopia in cataract surgery post photorefractive surgery. However, a prospective study to examine the accuracy of the formula and the results of IOL prediction is needed.

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