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.
Figure 1 : Corneal aberration, expressed as Zernike coefficients, before (X axis) and after (Y axis) photorefractive keratectomy for three ablation zones, using a 5.5 mm pupil. A) Spherical aberration coefficient: the increase in spherical aberration was generally less for the 6-mm zone than for either the 5-mm or multizone ablations. B) Coma coefficient: no significant differences were found between ablation zones.
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).
Figure 2: Corneal aberrations expressed as Zernike coefficients, before and 1 year after PRK. Individual box and whisker plots illustrate the range of values found for each set of observations- 50% of values lie within the box limits and 80% within the whisker limits. The horizontal line within the box is median value. Hollow circles are outliers. A) Spherical aberration coefficients calculated for a 5.5 and a 3-mm pupil before PRK (B5 is 5-mm ablation zone spherical aberration before PRK, and A5 is 5-mm ablation spherical aberration after PRK1 etc.). B) Coma coefficients calculated for a 5.5 and a 3-mm pupil.
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).
Spherical Aberration and Coma (Zernike Coefficients, Mean ± SD) before and 1 Year after Photorefractive Keratectomy
Age and Spherical Equivalent Refraction before and 1 Year after Photorefractive Keratectomy
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).
Figure 3: Relationship between change in spectacle correction (refractive error 1 year after PRK minus refractive error before PRK; X-axis) and the change in Zernike coefficient (coefficient after PRK minus coefficient before PRK; Y-axis) 1 year after PRK, for a 5.5-mm diameter pupil, with three different ablation zones. A) Spherical aberration coefficient: when regression occurs following surgery, the cornea reverts toward its original shape. This trend was significant for the 5-mm ablation (regression equation: 0.1 63x - 0.112, r2 = 0.861, shown by the solid line) and the multizone ablation (regression equation: 0.1 96x - 0.274, rp 2 = 0.848, dashed line). The relationship was not statistically significant for the 6-mm zone (regression equation: 0.065x + 0.044, rp 2 = 0.182, dotted line). B) Coma coefficient: a statstically significant relationship was found between change in refractive error and coma coefficient. No significant effect was found for ablation zone form (rp 2 < 0.32 for each zone).
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.
Figure 4: The effect of pupil diameter on corneal modulation transfer function (MTF)1 calculated from corneal wave functions consisting of the two Zernike circle polynomials identified with the average effects of coma and spherical aberration, for all eyes achieving a refractive change of ±1.50 D. Results for 3-mm and 5.5-mm pupil diameters are illustrated, both before and 1 year PRK ablation.
Figure 5: Estimated corneal modulation transfer function (MTF) for a corneal wave function consisting of the two Zernike circle polynomials identified with coma and spherical aberration, using mean values for each ablation zone. The solid lines represent the corneal modulation transfer function before PRK and the dotted lines, the corneal modulation transfer function 1 year after PRK. All values are calculated for a 5.5-mm pupil diameter.
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.
Figure 6: Estimated corneal modulation transfer function (MTF) for a corneal wave function consisting of the two Zernike circle polynomials identified with spherical aberration and coma, before and 1 year after PRK. A) Spherical aberration: the limits of the area were determined by adding and subtracting one standard deviation (SD) from the mean spherical aberration coefficient. The coma coefficient was given its mean value. The solid lines represent the corneal modulation transfer function before PRK and the dotted lines the corneal modulation transfer function after PRK, for the 6-mm ablation zone, calculated for a 5.5-mm pupil diameter. As the spherical aberration coefficient increases the modulation transfer function decreases. B) Coma: the limits of the area were determined by adding and subtracting one standard deviation from the mean coma coefficient. The spherical aberration coefficient was given its mean value, The solid lines represent the corneal modulation transfer function before PRK and the dotted lines the corneal modulation transfer function after PRK, for the 6-mm ablation zone, calculated for a 5.5-mm pupil diameter. As the coma coefficient increases the modulation transfer function decreases.
Statistical Significance (1-way ANOVA) of Ablation Zone Form for Different Pupil Diameters
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.
1. Migneco MK, Pepose JS. Attitudes of successful contact-lens wearers toward refractive surgery. J Refract Surg 1996;12: 128-133.
2. Gartry DS, Kerr Muir MG, Marshall J. Excimer laser photorefractive keratectomy, 18-month follow up. Ophthalmology 1992;99:1209-1219.
3. Shimizu K, Amano S, Tanaka S. Photorefractive keratectomy for myopia: One - year follow up in 97 eyes. J Refract Corneal Surg 1994;10(suppl):S178-S187.
4. Seiler T, McDonnell PJ. Excimer laser photorefractive keratectomy. Surv Ophthalmol 1995;40:89-118.
5. Kalski RS, Sutton G, Bin Y, Lawless MA, Rogers C. Comparison of 5-mm and 6-mm ablation zones in photorefractive keratectomy for myopia. J Refract Surg 1996;12:61-67.
6. O'Brart DPS, Corbett MC, Lohmann CP, Kerr Muir M, Marshall J. The effects of ablation diameter on the outcome of excimer laser photorefractive keratectomy. A prospective, randomized, double-blind study. Arch Ophthalmol 1995;113:438-443.
7. Lohmann.CP, Timberlake GT, Fitzke FW, Gartry DS, Kerr Muir M, Marshall J. Corneal Light scattering after excimer laser photorefractive keratectomy: the objective measurements of haze. J Refract Corneal Surg 1992;8:114-121.
8. Lohmann CP, Fitzke FW, O'Brart DPS, Kerr Muir M, Marshall J. Halos- a problem for all myopes? A comparison between spectacles, contact lenses and photorefractive keratectomy. Refract Corneal Surg 1993;9(suppl):S72-S75.
9. Applegate RA, Howland HC, Buettner J, Cottingham AJ, Sharp R, Yee R. Radial keratotomy (RK) corneal aberrations, and visual performance. Invest Ophthalmol Vis Sci 1995;36(suppl):S309.
10. Applegate RA, Hilmantel G, Howland HC. Corneal aberrations increase with the magnitude of the refractive keratotomy refractive correction. Optom Vis Sci 1996:73:585-589.
11. Howland HC, Howland BA. A subjective method for the measurement of monochromatic aberrations of the eye. J Opt Soc Am 1977;67:1508-1518.
12. Walsh G, Charman WN, Howland HC. Objective technique for the determination of monochromatic aberrations of the human eye. J Opt Soc Am A 1984;1:987-992.
13. Hemenger RP, Tomlinson A, Oliver K. Optical consequences of asymmetries in normal corneas. Ophthal Physiol Opt 1996;16:124-129.
14. Bennett AG, Rabbetts RB. Accommodation and near vision. The inadequate - stimulus myopias. In: Bennett AG, Rabbetts RB. Clinical Visual Optics. 2nd Ed. Butterworths; London, England; 1989:135-165.
15. Hemenger RP, Tomlinson A, Caroline PJ. Role of spherical aberration in contrast sensitivity loss with radial keratotomy. Invest Ophthalmol Vis Sci 1989;30:1997-2001.
16. Hemenger RP, Tomlinson A, Oliver K. Corneal optics from videokeratographs. Ophthal Physiol Opt 1995;15:63-68.
17. Applegate RA, Gansel KA. The importance of pupil size in optical quality measurements following radial keratotomy. Refract Corneal Surg 1990;6:47-54.
18. Oliver KM, Hemenger RP, Corbett MC, O'Brart DPS, Verma S, Tomlinson A, Marshall J. Corneal aberrations one year after photorefractive keratectomy for three types of ablation zone. Optom Vis Sci 1995;72(suppl):183.
19. Martinez CE, Applegate RA, Howland HC, Klyce SD, McDonald MB, Medina JP. Changes in corneal aberration structure after photorefractive keratectomy. Invest Ophth Vis Sci 1996;37(suppl):S933.
20. Corbett MC, Verma S, O'Brart DPS, Oliver KM, Heacock G, Marshall J. Effect of ablation profile on wound healing and visual performance 1 year after excimer laser photorefractive keratectomy. Br J Ophthalmol 1996;80:224-234.
21. O'Brart DPS, Corbett MC1 Verma S, Heacock G, Oliver KM, Lohmann CP, Kerr Muir MG, Marshall J. Effecte of ablation diameter, depth, and edge contour on the outcome of photorefractive keratectomy. J Refract Surg 1996;12:50-60.
22. Gartry DS, Kerr Muir MG, Lohmann CP, Marshall J. The effect of topical corticosteroids on refractive outcome and corneal haze after photorefractive keratectomy A prospective, randomized, double-blind trial. Arch Ophthalmol 1992;110:944-952.
23. Howland HC, Glasser A, Applegate RA. Polynomial approximations of corneal surfaces and corneal curvature topography. Ophthalmic and Visual Optics Technical Digest (Optical Society of America, Washington, DC) 1992:3:34-37.
24. Butuner Z, Elliott DB, Gimbel HV, Summon S. Visual function one year after excimer laser photorefractive keratectomy. J Refract Corneal Surg 1994;10:625-630.
25. Verdon WA, Bullimore MA, Maloney RK Prospective vision changes one year after photorefractive keratectomy. Optom Vis Sci 1994;71(suppl):16.
Spherical Aberration and Coma (Zernike Coefficients, Mean ± SD) before and 1 Year after Photorefractive Keratectomy
Age and Spherical Equivalent Refraction before and 1 Year after Photorefractive Keratectomy