The cornea's first surface smoothed by the tear film accounts for 65% to 70% of the refractive power of the human eye. Hence, irregularities in the surface of the cornea are likely to be a major contributor to the optical aberrations of the eye. Corneal surgeries to correct refractive errors and the development of videokeratoscopes capable of recording corneal shape in greater detail have allowed us to investigate the relationship between the shape of the corneal first surface and visual performance.
Refractive surgery is designed to alter the curvature of the central portion of the cornea, reducing it in myopes and increasing it in hyperopes. These surgeries (eg, radial keratotomy [RKJ, excimer laser photorefractive keratectomy [PRK], laser in situ keratomileusis ILASIK]) generally induce unusual corneal shapes rarely, if ever, observed in the normal cornea, and hence have the potential for creating a public health problem by introducing significant optical aberrations in otherwise normal eyes.1 Surgically-induced increases in optical aberrations of the cornea2"5 and/or model eye6 have been reported for RK and PRK.7 8 It has been demonstrated that the magnitude of the aberrations increase with RK5 or PRK8-induced change in refractive correction. However, the correlations of these new aberrations to actual measurements of visual performance are lacking.
The purpose of this investigation was to prospectively characterize the correlation between the optical aberrations of the corneal first surface and visual performance in refractive surgery patients and controls. We express the optical aberrations of the corneal first surface in terms of wavefront variance (WV) or log of the wavefront variance (LWV) and visual function in terms of visual acuity and the area under the log contrast sensitivity function (AULCSF). In this article, we report significant increases in the optical aberrations of the corneal first surface (LWV) that are correlated to decreases in visual performance (AULCSF).
PATIENTS AND METHODS
Twenty-three RK patients and nine normal patients, free of systemic and ocular pathology, were recruited from local eye clinics and the students and staff of the University of Texas Health Science Center at San Antonio. Radial keratotomy patients had refractive errors ranging from -2.00 to -9.25 diopters (D) of myopia prior to surgery (Tabie). To facilitate comparisons, the normal patients were selected to have refractive errors within the range of those anticipated for the RK patients following refractive surgery (Table). Data was collected from one eye of each subject. Written informed consent, approved by the University Institutional Review Board, was obtained from each patient after the nature and possible consequences of the studies were explained.
Best spectacle-corrected high contrast logMAR visual acuity was measured asing the Bailey-Lovie chart.9 Since neither Bailey and Lovie9 nor Ferris and colleagues10 detail a definitive endpoint criteria for logMAR acuity testing, we describe ours in detail. To define acuity, the number of letters correct were counted until the patient missed seven letters or an entire line. Procedurally, the patient started reading the chart where he/she was confident that they could read the entire line. If the patient missed a letter on the starting line they were asked to read successively larger lines until all letters of a line were read correctly. If an entire line was read correctly, it was assumed that the patient read all letters on larger lines. Final logMAR acuity was determined by multiplying the total number of letters correct by 0.02 and subtracting the result from 0.1 plus the logMAR acuity of the largest line scaled for the test distance (typically 12 feet). After surgery, acuities were corrected for magnification effect of moving the correction from the spectacle plane to the corneal plane, as described elsewhere.11,12 Magnification effects vary depending on the magnitude of the correction and the spectacle vertex distance. A -6.00 D myope with a 16 mm spectacle vertex distance would experience an approximately 10% increase in letter size if corneal refractive surgery yielded a perfect result, whereas, a +6.00 D hyperope would have an approximately 10% decrease in letter size.
Spherical Equivalent Refractive Correction (D) for Radial Keratotomy and Normal Eyes
Corneal topography was measured using a Tomey Technology, Inc. TMS-I videokeratoscope with software version 1.41 (New York, NY). Four videokeratographs were taken on each subject at each visit. The videokeratographs were reviewed and defective videokeratographs rejected (partially closed eye, tear break-up, etc.) and retaken. Data from the four videokeratographs from each visit were averaged to form the single data set representing corneal shape of the study eye for that particular visit.
Contrast sensitivities were measured through 3 and 7 mm artificial pupils using a NeuroScientific Contrast Sensitivity apparatus (NeuroScientific Corporation, a subsidiary of Neurotech Corporation, Farmingdale, NY) at 6 horizontal sinusoidal spatial frequencies (4, 6, 8, 12, 16, 24 cycles per degree) using a two alternative, temporal forced choice paradigm. Mean screen luminance was 55 cd/m2. As with acuity measurements, spatial frequencies were adjusted by calculation to correct for the magnification effects induced by moving the refractive correction from the spectacle plane to the corneal plane.11,12 Magnification effects vary depending on the magnitude of the correction and the spectacle vertex distance. A -6.00 D myope with a 16 mm spectacle vertex distance would experience an approximately 10% decrease in spatial frequency (ie, increase in cycle width) if the corneal refractive surgery yielded a perfect result. A +6.00 D hyperope would have an approximately 10% increase in spatial frequency.
After signing the informed consent, performing routine clinical tests (case history, entrance acuities, etc.) and corneal topography measurements, the test eye was dilated and cyclopleged with 1% tropicamide. After the pupil was dilated to at least 7.5 mm, the eye's achromatic axis was determined using a hyperachromatic alignicator1315 which centers the eye's foveal achromatic axis with the center of a small 2 mm artificial pupil fixed in space 14 mm in front of the cornea. To achieve and maintain proper alignment, the head was stabilized using a bite bar mounted to a three axis compound vise. Once aligned, the test eye was refracted through a 3 mm artificial pupil using the endpoint criterion of maximum plus to best visual acuity. All visual function measurements were made using this 3 mm correction. Following acuity measurements, contrast sensitivity was measured through both a 3 and 7 mm artificial pupil. Patients and normal controls were tested prior to surgery and at one week, 4, 8, 12, 18, 24, 30, and 36 months after surgery. We chose a typical pupil size (3 mm) and relatively large pupil (7 mm) because normal eyes are generally diffraction-limited for pupil sizes equal to or less than 3 mm16 and patients following refractive surgery generally do not complain about the quality of their vision when their pupil size is 3 mm or smaller, but often do when their pupil size is large.
All corneal surgeries were performed in the practices of cooperating clinicians. The following is the typical protocol followed by AJC who performed the majority of the RK surgeries reported here. AJC follows a personal nomogram modified from a nomogram developed by Dr. Ralph Berkeley. After informing the patient of the potential risks of RK and after signing of surgical consent forms, the surgical eye was anesthetized with topical proparacaine. While the patient fixated the operating microscope filament, the surgeon marked the intersection of the line of sight on the cornea using blunt forceps. The size of the clear zone was determined by a nomogram based on the patient's refractive error, sex, and age. According to the size chosen, the clear zone size was marked on the cornea by pressing a ring into the cornea concentric with the blunt forceps mark. Using an ultrasonic pachymeter, the corneal thickness was measured in four corneal quadrants just outside this clear zone mark and at the center of the clear zone. The blade of the diamond micrometer knife was set to a length of 100% of the thinnest of these readings. A radial marker with three to eight marks, dependent on the patients refraction, age, and sex, was pressed onto the cornea to indicate the locations for incisions.
Radial cuts were made from the periphery of the cornea toward the central clear zone while holding the globe fixed with a forceps approximately 180°away. The blade was held perpendicular to the corneal surface and pushed toward the center with a single, uniform, slow movement. The sequence of incisions was from the 12 o'clock superior position, counterclockwise with the right hand and then clockwise with the left hand.
Figure 1 : A) Topographic map (TMS) of the remainder lens: measured surface elevations minus the best fitting preoperative sphere for an RK eye 1 week after surgery. B) Topographic map of the surface elevations of the surgical cornea from which have been subtracted the best-fit preoperative sphere and a fourth order polynomial fit to Figure 1A to better revea) the RK-induced corneal radial corrugations. Each color change is a 4 pm step up (positive numbers) or down (negative numbers) in elevation from the reference sphere (Fig 1A) or the reference surface defined by the reference sphere plus the fourth order polynomial fit to the difference between the actual elevations and the reference sphere (Fig 1B).
After all the incisions were completed, several drops of the antibiotic Ciloxan and either Acular (ketorolac tromethamine, Allergan, Inc., Irvine, Calif) or Voltaren (diclofenac sodium 0.1%, Ciba Vision Ophthalmics, Duluth, GA) were instilled. The eye was not patched. The antibiotic was continued using a tapered regimen period of several weeks following surgery. Corticosteroids were used in some eyes beginning with the 24 hour follow-up visit, or initiated at a later visit, if the correction obtained postoperatively appeared at all short of the desired amount. Follow-up appointments were scheduled at 24 hours, 1, 3, and 6 weeks.
Corneal First Surface Aberrations- As in previous work, we used a Taylor polynomial3,17 and radial corrugation term to characterize the difference between corneal shape and two different reference surfaces: 1) a best fitting sphere to the preoperative cornea (Fig IA), and 2) the preoperative cornea. We designate the differences between these two reference surfaces the "remainder lens" and the actual cornea the "surgical lens." We suspected that RK might induce a radial corrugation in the surgical zone. To examine this possibility, we enhance the visibility of such surface irregularities by subtracting the elevations of both the best fitting sphere to the preoperative cornea and the polynomial fit to the remainder lens from measured elevations (Fig IB). The corrugation pattern revealed in Figure IB illustrates why we added the radial corrugation term to our analysis.
Converting the Taylor polynomial to a Zernike polynomial allows representation of the wavefront variance of the corneal first surface to be segregated into third order (coma-like aberrations), fourth order (spherical aberration-like aberrations), and radial corrugation sub-components, or used collectively to define a single quantity to characterize the overall optical quality of the corneal first surface.18 A detailed presentation of our data analysis method is provided in the Appendix.
Area Under the Log Contrast Sensitivity Function (AULCSF)- The log contrast sensitivity vs. log spatial frequency data (the latter corrected for magnification effects11·12) for both 3 mm and 7 mm pupil sizes were fit with a third order polynomial. This function is integrated between 4 and 24 cycles per degree to compute the area under the log contrast sensitivity function (AULCSF), a single quantity used to characterize the overall visual performance of the eye (Fig 2).19
Consistent with prior reports,20,21 there were no significant changes in best spectacle-corrected high contrast logMAR visual acuity from baseline (prior to refractive surgery measurements) for either the 3 mm or dilated pupil conditions.
Log Wavefront Variance and Area Under the Log Contrast Sensitivity Function (AULCSF)-We found that the correlation between the shape of the surgical and remainder lenses of normal and RK eyes was very high (r2=0. 987, p<0. 0001), and so we discuss here only the remainder lens results. This high correlation between the shapes of the remainder and surgical lenses does not imply that the preoperative corneas were spherical, only that the aberrations of RK eyes were large enough to make the magnitude of differences between the best-fitting spheres and the preoperative corneas relatively unimportant. In fact, the log wavefront variance of the remainder lens for normals is an expression of the difference between the two reference surfaces (best fitting sphere and preoperative cornea).
Figure 2: Graphical representation of the method for calculating the area under the log contrast sensitivity function (AULCSF). Contrast sensitivities were measured at six spatial frequencies corrected for the magnification effects of moving the correction from the spectacle plane to the corneal plane." '2 The log of the contrast sensitivity was in turn plotted as a function of log spatial frequency (circles) and a third order polynomial fit to the data (dotted curve). The fitted function was integrated between the fixed log spatial frequency limits of 0.6 and 1.4 cycles/degree and the resulting value defined the AULCSF. (Reprinted from the 1997 Technical Digest Series. Volume 1, Vision Science and Its Applications'9, with the permission of the Optical Society of America and the author.)
Normal Group- As anticipated within the normal group, an analysis of variance over all visits showed no significant differences over time for repeated measurements of mean log wavefront variance and mean AULCSF for either the 3 or 7 mm pupil.
Radial Keratotomy with 3 mm Pupil- Before surgery the magnitude and distribution of log wavefront variance due to the third, fourth, and radial corrugation term of the RK eyes were not significantly different from those of the normal subjects (unpaired t-test). After surgery, the total log wavefront variance was significantly increased (paired t-test, p<0.01) and the distribution changed. For the 3 mm pupil, except for the 1 week after surgery, there was no significant change in AULCSF induced by surgery, indicating that the increase in log wavefront variance for the 3 mm pupil was not sufficient to induce a significant change in AULCSF.
Radial Keratotomy with 7 mm Pupil- We regressed the AULCSF against remainder lens log wavefront variance for each visit. We tested the compliance of our data to the basic assumptions of the linear regression model22 and found that they were met. Specifically, we were concerned that the variance over the range of log wavefront variances might not be constant. To verify constancy we did a variance ratio test of AULCSF between normals (low log wavefront variance) and postoperative RK eyes (high log wavefront variance). We found no significant difference in variance. Inspection of the residuals from the regression analysis did not indicate any significant deviations from normality. Although the variables on the ordinate and abscissa are not normally distributed and thus do not meet the requirements for a bivariate normal correlation model, they do meet the requirements for regression, and we can determine if the slope of the regression line is statistically significant.
In Figure 3, which shows regression plots for four of the nine visits (baseline, 12, 24, and 36 months), it can be seen that prior to surgery there was a low coefficient of correlation (r2 = 0.02, ? = 0.45) between AULCSF and log wavefront variance, and that the distributions of the AULCSFs and log wavefront variances are similar for RK eyes prior to surgery and normals. We conducted unpaired t-tests for differences in means and F-tests for differences in variances for both AULCSFs and log wavefront variances between normals and RK eyes prior to surgery. No tests were significant at the ? < 0.05 level; however, the difference in means of the AULCSFs between RK eyes and normal eyes prior to surgery approached significance (p = 0.057). This is in agreement with the findings23,24 that the total wave aberrations of the eyes of myopic patients tend to be larger than that for near emmetropic patients. We conclude from this r^jression that relatively small changes in the corneal log wavefront variance cannot account for the normal variation in AULCSF.
After surgery (Fig 3) for the 12, 24, and 36 month test intervals, the regressions between AULCSF and log wavefront variance were all significant (p <0.01) and coefficient of correlation was excellent (rp 2 =0.38 at 12 mo, rp 2 = 0.51 at 24 mo, and rp 2 = 0.66 at 36 mo). Correlations for other time periods were similarly strong (rp 2 = 0.66 at 1 wk, rp 2 = 0.49 at 4 mo, rp 2 = 0.48 at 8 mo, rp 2 = 0.64 at 18 mo, rp 2 = 0.62 at 30 mo).
Figure 3: Regressions of the area under the log contrast sensitivity as a function of the log wavefront variance of the remainder lens prior to RK surgery (upper left), 12 months (upper right), 24 months (lower left), and 36 months (lower right) after RK. Solid straight line in each panel is the best-fitting regression line (regression equation and rp 2 values are presented at the top of each panel). Bowed lines in each panel are the 95% confidence limits.
The mean decrease in postoperative AULCSF for the RK group at 1 week was 0.243, 0.180 at 4 mo, 0.190 at 8 mo, 0.136 at 12 mo, 0.125 at 18 mo, 0.152 at 24 mo, 0.186 at 30 mo, and 0.219 at 36 mo. A repeated measures ANOVA over all examinations revealed these differences in AULCSF to be significant (p < 0.05). Analysis using the statistical method of simultaneous contrasts25 revealed that the loss in AULCSF induced by surgery was significant at each of the eight postoperative examinations (p < 0.05).
To provide a clinical intuition for the loss in AULCSF induced by surgery, we measured the AULCSF as a function of myopic blur in five normal eyes and found that a decrease of approximately 0.25 in the AULCSF can be induced by 0.50 D of myopic blur.19,26
The magnitude of the wavefront variance is markedly increased (repeated measures ANOVA over all visits yields p < 0.001) following RK surgery. Figure 4 shows the baseline, 12, 24, and 36 month wavefront variance data. For example, at the 1 year postoperative examination, the average wavefront variance for the surgical eyes increased by a factor of 33.46. Dividing the total wavefront variance into its individual components at the 1 year visit, we found the average third order, fourth order, and radial corrugation terms were increased over baseline measurements 11, 136, and 181 times, respectively. Expressing the wavefront variance of the third order, fourth order, and radial corrugation terms as a percentage of the total wavefront variance at each examination (Fig 4) we found the that following RK surgery the wavefront variance was dominated by the fourth order aberrations (spherical aberration-like aberrations) by approximately the same amount that the third order aberrations (coma-like aberrations) dominated the aberration structure prior to surgery.
Figure 4: Log wavefront variance (LWV) of the remainder lens expressed in micrometers squared as a function of time for RK eyes and normal eyes. The distribution in percent of the total wavefront variance at each testing interval that is attributable to the third order, fourth order, and radial corrugation aberrations of the remainder lens is displayed in pie graph form. Notice that before surgery, the magnitude and distribution of the corneal aberrations of the RK eyes were very similar to those of the normal eyes and that after surgery the magnitude of the log wavefront variance is increased and that distribution has changed, reflecting a marked increase in the proportion of the total wavefront variance attributable to the fourth order (spherical aberration-like) terms.
Similarly, in the normal control eyes the third order aberrations dominate. These results on baseline and normal eyes are not unexpected, given the major role of the cornea in the refractive power of the eye and previous aberroscopy and other wavefront measures demonstrating that the major higher order aberrations of the entire normal eye are due to third order, coma-like aberrations. 17,27-30
Quantification of Corneal Aberrations
For eyes with large corneal aberrations, placido videokeratography has sufficient resolution to capture third and fourth order wave aberrations of the cornea. Given the large increases in aberration structure we have measured to date, we believe it prudent to expand the analysis to include at least the fifth and sixth order aberrations.
The radial corrugation aberration term presents a particularly interesting test for placido ring systems. As we report elsewhere31,32, if the transition between smoothly changing central cornea and the radially corrugated surgical area is abrupt, ringbased systems will fail to detect the radial corrugations. If the transition is smooth, then placido ringbased systems can, in principle, detect the radial corrugations. A question we have not answered isHow smooth does the transition have to be for the placido-based systems to work properly? Consequently, in the data we report here, we are uncertain whether we are detecting the full magnitude of the radial corrugations.
Correlation Between Aberrations and Visual Performance
We interpret the data to demonstrate that large increases in magnitude of corneal aberrations (on the order of 30+ times normal levels) at large pupil sizes induce significant decreases in visual performance as reflected by a loss in the AULCSF.
We note that the increase in the log wavefront variance and associated loss in contrast sensitivity are reflected in patients' subjective comments following RK. Specifically, RK patients in general often note decreased visual performance when the pupil is naturally large (night driving, going to the movies, or other low-light situations) and/or state that their vision (best corrected) is good but not as sharp as it was before surgery.
Figure 5: A) Log wavefront variance (LWV) of the remainder lens expressed in micrometers squared at the 2-year examination as a function of clear zone diameter. Notice that log wavefront variance increases as clear zone decreases. B) RK-induced change in the area under the contrast sensitivity function (minus numbers represent a loss in contrast sensitivity over baseline measurements) as a function of clear zone diameter. Notice the loss in the AULCSF increases as clear zone decreases.
In the same vein, it is noteworthy that low contrast acuity has been reported to be decreased following PRK33,34 and we8 and others7 have reported large increases in the aberration structure induced by PRK. These cross-sectional results on two different patient populations are consistent with the longitudinal prospective results reported here for RK.
Distribution of Aberrations
The distribution of the aberrations of the eye are markedly changed following RK. The most notable change is that the fourth order aberrations (spherical auei ration-like) at larger pupil sizes are dominant. This is in direct contrast to the normal or preoperative eye where the third order (coma-like) aberrations are dominant. This switch in dominance is a direct result of the fact that the shape of the postoperative cornea at the edge of larger pupils remains relatively unchanged as compared to the central cornea. For the same reason (a relatively abrupt change in shape within the large pupil) a similar reversal of third and fourth order aberration dominance has been observed using our methods8 and the methods of others7 for the PRK eye.
Aberrations, Contrast Sensitivity, and Clear Zone Size
As we have reported elsewhere,5 corneal aberrations increase with the RK-induced change in refraction. Since clear zone size generally decreases with increasing myopic refractive error to be corrected, it is expected that RK-induced aberrations will decrease as clear zone diameter increases and the induced loss in contrast sensitivity will decrease as clear zone diameter increases. We confirmed these expectations by regressing log wavefront variance against clear zone size (Fig 5A) and regressing the induced change in AULCSF against clear zone size (Fig 5B) at the 2-year postoperative examination. As anticipated, the regressions revealed that surgically induced log wavefront variance decreases (p < 0.01) and the induced loss in contrast sensitivity decreases (p < 0.01) as clear zone diameter increases. Specifically, 40% of the variance in log wavefront variance and 56% of the induced change in contrast sensitivity can be accounted for by the size of the clear zone.
The number of incisions did not vary enough in our test population to evaluate the correlation between number of incisions and either log wavefront variance or AULCSF.
Ideal Compensating Optic
The ideal compensating optic for foveal viewing eliminates the eye's defocus and higher order aberrations, making the eye diffraction limited for all pupil sizes of physiologic interest.35 Although relatively simple in principle, designing an ideal compensating optic for large pupils is difficult to implement. Consider PRK where corneal thickness can, and often is, a limiting factor. That is, for a fixed maximum ablation depth, the higher the correction the smaller the maximum possible ablation diameter. For high refractive errors where there is not enough corneal thickness to allow the cornea to be ablated over the largest possible physiologic pupil, other modes of correction, once perfected, may provide superior optical performance. For example, large aperture compensating optics could be designed in the form of a contact lens and/or a phakic or an aphakic intraocular lens or implemented as a combination procedure.
Regardless of form, in order to design the ideal compensating optic for foveal imaging, the aberration structure of the individual eye (as opposed to the cornea alone, as presented in this paper and all other papers using corneal topography) must be defined by measurement.35 The aberration structure of the eye can be measured using several techniques. Three of the more promising techniques for real-time clinical use are: Hartmann-Shack devices36,37, an objective crossed-cylinder aberroscope28,38, and the spatially resolved refractometer recently patented by Webb and Penny.39,40
Seeing Into Eyes
Although we have focused the discussion on improving the eye's view of the world by minimizing the eye's ocular aberrations, it is worth noting that higher order ocular aberrations not only lead to a lower contrast view of the world for the patient, they also provide a lower contrast view of the fundus to the practitioner or fundus photographer. Thus the more uncorrected aberrations an eye has (whether naturally, from pathology, or clinical manipulation) the poorer the view of the fundus. In fact, Williams and co-workers have recently measured the optical aberrations of the normal eye using a HartmannShack device and input their measurements to a deformable mirror to correct the aberrations of the eye and were able to noninvasively view rods and cones in the human eye.41,42
We have demonstrated: 1) Radial keratotomy induces an increase the optical aberrations of the eye; 2) The RK-induced increase in optical aberrations for large pupils (7 mm) but not small (B mm) is correlated to a decrease in contrast sensitivity; 3) Radial keratotomy, like PRK, shifts the distribution of aberrations from third order dominance (coma-like aberrations) to fourth order dominance (spherical-like aberrations); 4) Radial keratotomy induced aberrations and loss in contrast sensitivity are reduced with increasing clear zone diameter. It should be possible to reduce the pupil size-dependent optical and visual performance deficits, by minimizing abrupt changes in corneal shape within the pupil and considering the preoperative aberrations of the eye in the design of the optimal correction.
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Spherical Equivalent Refractive Correction (D) for Radial Keratotomy and Normal Eyes