#### Abstract

ABSTRACT

BACKGROUND: Photorefractive keratectomy causee marked alteration to anterior corneal topography, and is likely to induce major changes to the optical aberrations of the eye.

METHODS: Six diopters (D) of myopia correction was attempted on one eye of 50 patients, randomly allocated to one of three different treatments: 5-mm or 6-mm single ablation zone, or a double ablation (multizone; -5.00 D correction over 4.6 mm and -1.00 D over 6 mm). Topographic data was used to estimate corneal aberration coefficients. These were compared for effect of ablation zone, before and 1 year after photorefractive keratectomy. The coefficients were used to derive modulation transfer functions for the anterior corneal surface.

RESULTS: Corneal spherical aberrations and coma-like aberrations both increased significantly following photorefractive keratectomy (p < 0.001). The mean spherical aberration coefficient increased from 0.36 ±0.11 before, to 0.91 ± 0.37 after treatment, while the mean coma-like aberration coefficient changed from 0.28 ± 0.16 before, to 0.60 ± 0.31 after treatment. Ablation zone form had a significant effect on spherical aberration (p = 0.030), but not for coma (p = 0.96). The spherical aberration coefficient increased least for the 6-mm ablation (by 0.38 ± 0.17), compared with the 5-mm ablation (0.69 ± 0.45) and the multizone (0.62 ± 0.38). Corneal modulation transfer functions were reduced significantly following the photorefractive procedure. The effect was greatest for large pupil diameters and for spatial frequencies between 2 and 15 cycles per degree.

CONCLUSIONS: Corneal modulation transfer function calculations suggest that a significant loss of visual performance should be anticipated following photorefractive keratectomy, the effect being greatest for large pupil diameters. Results for three ablation zones show that induced aberrations are least for the largest (6 mm) ablation zone. [J Refract Surg 1997;13:246-254]

Excimer laser photorefractive keratectomy (PRK) has gained professional and patient acceptance in recent years, even among successful contact lens wearers.1 Its use in the surgical correction of myopia has been widely reported25 and results suggest that the refractive outcome begins to stabilize after about 6 to 12 months, with reasonable predictability for low corrections, ie, less than -5.00 diopters (D).24 However, where the attempted correction is more than -5.00 to -6.00 D, the induced change can be quite variable. Gartry2 reported that for attempted corrections of up to -3.00 D with a 4-mm ablation zone, more than 70% of patients achieved corrections within ± 1.00 D ofthat intended; for corrections above -6.00 D, less than 40% of patients achieved this level of success. Later studies6 have shown that larger ablation zones improve the predictability of outcome, although accuracy remains lower for the higher corrections.

There are important visual considerations other than refractive change that need to be considered to understand the visual consequences of the procedure. These include increased light scatter due to stromal deposits causing subepithelial haze7 and the visual effects of flare and halos apparently arising from the edges of the ablation zone.8 Additionally, induced corneal aberrations, with the consequent degradation of the retinal image, have been demonstrated following radial keratotomy910 and may be expected following PRK.

Studies of the aberrations of the cornea and of the eye11-13 have shown that the axial aberrations of greatest importance in the normal eye are spherical aberration and "coma-like" aberrations. Spherical aberration causes rays through the peripheral pupil to focus at positions displaced longitudinally from the focus of rays through the central pupil (paraxial rays). In a symmetrical optical system, spherical aberration is the only aberration affecting bundles of rays having a common point of convergence on the optical axis (axial pencils). In an asymmetric system such as the eye (or the cornea), the other primary aberrations, coma in particular, also affect axial pencils. Coma, although less familiar than spherical aberration, is equally simple conceptually. The asymmetry of refractive power across the pupil causes rays which pass through the peripheral pupil to focus at positions laterally displaced from the focus of rays passing through the central pupil (paraxial rays). Spherical aberration and coma are strongly pupil size dependent.14,15

Starting with corneal topography data taken before and 1 year after surgery, we examined changes in corneal axial aberrations using a "wavefront" method.13·16 Treating the cornea as a single refracting surface of known shape, the resulting distribution of optical pathlengths over the pupil- the wavefront- may be determined, thus defining the imaging properties of the cornea and making estimates of corneal aberrations possible. Large increases in spherical aberration and coma are associated with substantial reductions in corneal modulation transfer for large pupil diameters.15-17

Our principal aim was to determine the effect of PRK on optical aberrations. little has been published 18·19 on corneal aberrations and their visual effects following PRK, although the visual consequences of radial keratotomy have been investigated.9 Possible correlations between corneal aberrations, achieved refractive change at 1 year, and ablation zone diameter and form were investigated.

PATIENTS AND METHODS

The patient group, selected on the basis of availability of refraction and topography data before and 1 year after PRK, was taken from that studied in a larger investigation.6·20 This previous study considered the effect of ablation zone size and form on refractive outcome and corneal healing following PRK for two refractive corrections (-3.00 and -6.00 D). For the primary study, ethical committee approval was obtained and signed, informed consent was received from all patients. All eyes had less than 1,50 D of astigmatism. Patients with any possible contraindications (eg, keratoconus, connective tissue disorders, diabetes, etc.) were excluded. Stability of refraction was confirmed prior to operation by careful examination of refractive history.

Of the sixty patients who received a -6.00 D attempted correction by PRK, to one eye only, full refractive and videokeratographic data were available for 53 patients. Patients were randomly divided into three groups according to ablation zone diameter and form: 5 mm (18 eyes), and 6 mm (18 eyes) single zones and 6 mm double-pass or multizone (17 eyes). The double pass multizone consisted of a correction of - 5.00 D over 4.6 mm, and -1.00 D over 6 mm, which produced an ablation depth equal to that of a 5 mm zone, with a blended edge. An experienced surgeon performed PRK using an Omnimed excimer laser (Summit Technology, Boston, Mass.) with an emission wavelength of 193nm, a fixed pulse repetition rate of 10 Hz and a radiant exposure of 180 mJ, following manual epithelial debridement.20,21

Steroids were not prescribed at any stage during this study, previous work having shown little longterm benefit associated with their application.22

The effectiveness of the procedure was monitored for the year following treatment and included refractive error and topography measurement with the TMS-I (Computed Anatomy, New York, NY). Estimates of the primary optical aberrations were calculated for each TMS-I image file (four sets of data generally being available for each patient, both before and after PRK), with both a small, 3-mm, and a large, 5.5-mm diameter pupil (aperture). Corneal shape was determined by estimating sagittal depths at each corneal point from topography data.16 Elementary geometry was employed to determine the optical path length from an axial point on the object through an arbitrary point on the cornea to an axial image point. The optical path length is actual path length times refractive index and is proportional to the extent of the path in units of wavelength. Therefore, equal path lengths over the pupil imply perfect constructive interference and an aberrationfree image. Conversely, variations in path lengths over the pupil result in aberrations. These aberrations may be classified by expressing the distribution of path lengths over the pupil as a linear combination of basis functions. These basis functions might, for example, be polynomials in rectangular pupil coordinates23 or Zernike circle polynomials.16 Zernike circle polynomials are a particularly convenient choice for basis functions as each of these functions can be identified with a specific aberration and its coefficient in the linear expansion is a measure of the strength ofthat aberration.

RESULTS

The values in this analysis exclude three patients (two from the 5-mm and one from multizone group), who suffered from extreme haze and marked regression. These patients were eliminated from the analysis as they did not represent the normal healing response, and were exceptions when considering the effect of PRK on corneal aberrations. Initial analysis of the Zernike polynomial coefficients relating to each of the different aberration terms was performed.13,16 Apart from refractive error, only two Zernike coefficients-spherical aberration and coma- were significantly altered by PRK. Analysis of variance (ANOVA) for spherical aberration and coma revealed a highly significant change (p < 0.001 for both terms) between values, calculated for a 5.5-mm pupil, before and 1 year after PRK (Figures 1 and 2; Table 1). Although for some eyes the single-surface corneal aberrations may actually be reduced by PRK, an increase in both spherical aberration and coma was more common (Fig 1). The change in spherical aberration was related to the ablation form (p = 0.03)- smallest for the 6 mm zone (Table 1, Fig 2). Further analysis by a Fisher's pairwise comparison indicated the greatest statistical difference was between the 5-mm and 6mm single ablation zones; no statistically significant difference was found in comparison of the 5-mm and multizone ablations. Coma did not vary with ablation zone (p = 0.96) (Table 1).

The increase in spherical aberration was directly proportional to the change in refractive error (p < 0.001). This relationship was strongest for the 5-mm and multizone ablation procedures (r2 = 0.861 and 0.848 respectively, and ? < 0.001 for both)(Fig 3A). This trend appears to be less pronounced for the Qmm (r2 = 0.182, ? .= 0.077) ablation zone. The coma term was also found to vary in direct proportion to the change in refractive error (p = 0.002) (Fig 3B), however, no significant effect of ablation zone was detected (r2 «s to 0.312, ? > 0.1). When analysis was restricted to patients with a refraction change within ±1.50 D ofthat intended, the difference in spherical aberration (as indicated by the increase in Zernike coefficient) between ablation zones was more significant (Table 3).

To determine the effect on visual performance, theoretical modulation transfer functions were determined using the aberration coefficients calculated from the topography data. We analyzed the results from patients who were considered to have relatively successful outcomes- those who achieved a change between 4.50 and 7.50 D for an intended correction of -6.00 D. This restriction was required to avoid the effect of the relationship between change in refraction and magnitude of spherical aberration and coma coefficients for the 5-mm and multizone ablations. The more effective procedures with these ablations resulted in large increases in optical aberration (Fig 3). Of the 53 eyes investigated, 27 fell into this category, with four of the 18 eyes undergoing a 5-mm ablation, 14 of the 18 eyes undergoing the 6-mm ablation, and nine of 17 multizone eyes achieving between 4.50 and 7.50 D.

The theoretical corneal modulation transfer function before and 1 year after PRK, calculated using mean values of spherical aberration and coma for each zone of those eyes undergoing a -6.00 D correction, are shown in Figure 5. The modulation transfer function before PRK was significantly higher than 1 year after PRK (in particular for lower spatial frequencies), indicating that a significant loss in contrast sensitivity may be expected following PRK for all ablation zones. Photorefractive keratectomy was more successful in eyes with -6.00 D/6-mm ablations than for either the -6.00 D/5-mm or the -6.00 D multizone ablations.

The theoretical corneal modulation transfer function (derived from the mean spherical aberration value ± 1 standard deviation, using the average coma coefficient) of those eyes undergoing a -6.00 D/6-mm correction are shown in Figure 6A, illustrating the degree to which induced spherical aberration affected modulation transfer function, and was representative of the spread found for the other two ablation zones. Figure 6B, derived from the coma values (mean ± 1 standard deviation) and the average spherical aberration coefficient for the 6-mm zone, shows that the effect of coma on modulation transfer function is masked by that of spherical aberration, and resulted in relatively little spread of the data. For smaller pupil diameters (3 mm), the effects ceased to be significant (Table 1, Fig 2), despite their apparently high degree of statistical significance (Table 3).

DISCUSSION

Corneal optical aberrations, in terms of Zernike coefficients, were estimated before and 1 year after PRK for 50 myopic eyes; a correction of -6.00 D was attempted for all eyes using one of three different ablation zone forms. The magnitudes of the two primary aberration coefficients, spherical aberration and coma, showed significant increases following PRK (Table 3).

Correlations between spherical aberration, coma, and other parameters associated with PRK were also investigated. Both the mean and standard deviation of spherical aberration after surgery were less for those eyes with the larger (6-mm) single ablation zone than for both the smaller (5-mm) and multizone ablation. A similar relationship was not found for coma. Both corneal haze and refractive regression were least with the 6-mm ablation zone.6 Strong correlations were found between induced spherical aberration and the amount of refractive regression for the two smaller ablation zones. It is, perhaps, not surprising that the amount of this aberration decreased as the cornea regressed towards its original refractive power.

Corneal modulation transfer function, based on topography measurements, was significantly reduced as a resuìt of PRK. It cannot be concluded that a reduction in contrast sensitivity occurs since the role of the ocular lens is unknown. It is conceivable, although unlikely, that aberrations of the lens compensate for those of the cornea. A more probable explanation is that large reductions in corneal modulation transfer function are expressed as comparable reductions in contrast sensitivity. This is consistent with previous investigations in which many patients experience reduced contrast sensitivity as a consequence of PRKA 2^ 25 The loss in modulation transfer function was greatest for spatial frequencies between 5 and 15 cycles per degree. It was most significant for large pupil diameters (> 5 mm) (Fig 4), suggesting significant visual detriment in low luminance conditions.

There are caveats to these findings. First, the attempted correction, -6.00 D, was quite large. It seems likely that induced aberrations wouid be smaller for lower corrections. The corneal topography data is subject to error, but the trends found are convincing. Other qualifications that concern pupil size, spherical aberration and coma, are pupil dependent. The calculations on corneal topography data were carried out for corneal cord diameters of 5.5 mm (ie, apparent pupil diameters). This 5.5-mm pupil determined by the corneal topographer may not have been centered with respect to the ablation zones. The aberration estimates may depend on the amount that the 5.5-mm pupil coincides with the ablation zone. This may be a factor in the smaller induced spherical aberration for the largest (6 mm) ablation zone. The fact that induced coma apparently does not depend on ablation zone size or form suggests that it is dependent on the accuracy of centration, which varies independently of ablation zone form.

Corneal astigmatism, regular or irregular, was not considered. A smooth surface can display only regular astigmatism at each point, ie, the principal meridians at each point must be perpendicular. Irregular astigmatism- where the principal meridians are not perpendicular- implies abrupt changes in corneal curvature, ie, corneal irregularities extend over distances less than pupil diameter. We did not see any small scale irregularities in our corneal topography data and did not take their consequences into account.

In irregular astigmatism, the principal meridians are not perpendicular and abrupt changes in corneal curvature occur, resulting in corneal irregularities that extend over distances smaller than the pupil diameter. Future investigations of PRK should include measurements of contrast sensitivity, as visual acuity measurements alone are not sensitive to the loss of visual performance at low and middle spatial frequencies.

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Table 1

Spherical Aberration and Coma (Zernike Coefficients, Mean ± SD) before and 1 Year after Photorefractive Keratectomy

Table 2

Age and Spherical Equivalent Refraction before and 1 Year after Photorefractive Keratectomy