From SEKAL Rovigo Microsurgery, Rovigo, Italy (Camellin); G.B. Bietti Eye Foundation-IRCCS, Rome, Italy (Savini, Carbonelli); Jules Stein Eye Institute, University of California, Los Angeles, and St Mary’s Eye Center, Santa Monica, California (Hoffer); and Studio Oculistico d’Azeglio, Bologna, Italy (Barboni).
The authors have no financial interest in the materials presented herein.
Study concept and design (G.S., Ma.C., K.J.H., Mi.C., P.B.); data collection (Ma.C.); analysis and interpretation of data (G.S., K.J.H., P.B.); drafting of the manuscript (G.S., K.J.H.); critical revision of the manuscript (Ma.C., Mi.C., P.B.); statistical expertise (G.S.); supervision (K.J.H.)
Correspondence: Giacomo Savini, MD, G.B. Bietti Eye Foundation-IRCCS, Via Livenza 3, Rome, Italy. Tel: 39 06 85356727; Fax: 39 06 84242333; E-mail: email@example.com
Intraocular lens (IOL) power calculation after corneal refractive surgery can lead to erroneous results due to three reasons: 1) the postoperative optical zone may be smaller than the area where conventional instruments (eg, manual keratometers and corneal topographers) take their readings to measure the corneal curvature (so-called “radius error” or “instrument error”)1–7; 2) the ratio between the anterior and posterior corneal curvature, which is assumed to be constant when the keratometric index is used to convert measured radii into diopters (D), is changed by surgery (so-called “index of refraction error” or “keratometric index error”)1,2,8–10; and 3) the IOL position (ELP) is miscalculated by those formulas predicting this value on the basis of corneal power (so-called “IOL formula error”).11
Although all errors are assumed to occur after excimer laser surgery, only errors 1 and 3 usually are considered responsible for IOL power miscalculation after radial keratotomy (RK). Several authors have claimed that after incisional surgery such as RK both the anterior and posterior corneal surfaces flatten in parallel, so that the ratio of their curvatures is maintained.12–16 Surprisingly, however, this ratio has not yet been assessed in vivo in postoperative RK eyes, despite modern technologies allowing measurements of both anterior and posterior corneal curvatures. Using a Scheimpflug camera (Pentacam; Oculus Optikgeräte GmbH, Wetzlar, Germany), this study aimed to evaluate the changes in anterior and posterior corneal curvature and their ratio in eyes that had undergone RK.
Patients and Methods
For this retrospective study, all participants were enrolled from a private practice (SEKAL Rovigo Microsurgery, Rovigo, Italy). Before being included in the study, each patient was informed of its purpose and gave written consent to participate. The study protocol had been approved by the local ethics committee. Study methods adhered to the provisions of the Declaration of Helsinki guidelines for research involving human participants.
The long-term postoperative Pentacam examinations were retrospectively reviewed (carried out with software version 1.16) of all patients who had undergone RK. The Pentacam is a Scheimpflug camera that measures the corneal radius on the basis of acquired images of the cornea. The slit light of the device successively illuminates 25 slits through the cornea while rotating for each slit by 1/25th of 180° around the apex. Because the transparent cells of the cornea disperse the light diffusely, the anterior and posterior surfaces of the cornea can be detected. This allows for calculation of the corneal radii for each point on both corneal surfaces.
During the examination, patients were asked to fixate on a light inside the machine and one examiner adjusted the joystick until perfect alignment was shown. The instrument automatically took 1 measurement by rotating the camera 360° and captured 25 Scheimpflug images within 2 seconds. For the purposes of this study, the front and back corneal radii measured by the instrument were analyzed using a 3-mm optical zone.
Patients were excluded if additional surgery had been performed, such as photorefractive keratectomy, or if the quality of the scans was poor, ie, when the quality specification indicated by the Pentacam display read “blink” or “lid.”
Calculation of the Keratometric Index
Knowing the anterior and posterior corneal radius of the cornea and the corneal thickness (measured by the Pentacam) enabled calculation of the total corneal power according to Gullstrand’s equation for thick lenses, also known as the Gaussian optics formula, which reads as:
=refractive index of air (1.000), n1
=refractive index of the cornea (1.376), n2
=refractive index of the aqueous humor (1.336), r1
=radius of curvature of the anterior corneal surface (in m), r2
=radius of curvature of the posterior corneal surface (in m), and d=corneal thickness (in mm).17
From this value (which is also automatically measured by the Pentacam as the True Net Power), the fictitious keratometric index of the cornea was calculated for each eye using the thin lens formula for paraxial imagery, which reads as:
Sample Size Estimation and Control Group
Using PS version 3.0.12 ( http://biostat.mc.vanderbilt.edu/twiki/bin/view/Main/PowerSampleSize, accessed November 15, 2011), a sample size of 14 eyes per group was estimated to detect a difference in anterior corneal curvature of 0.04 mm (corresponding to 0.25 D ±0.04 mm with a power of 95% at a significant level of 5%). As a control group, a sample of 71 unoperated eyes from 71 patients included in a previous study comparing Pentacam and standard corneal topography were used.18
Unless otherwise indicated, all data are expressed as mean±standard deviation. An unpaired t test was used to compare mean values, if data followed a Gaussian distribution according to the method of Kolmogorov and Smirnov. Otherwise statistical comparison was achieved by means of Mann-Whitney test. Linear regression was performed to analyze relationships between variants. A P value <.05 was considered statistically significant. All statistical tests were performed using GraphPad InStat version 3a for Macintosh (GraphPad Software, San Diego, California). For patients who had bilateral surgery, only one eye, randomly chosen using a computer-generated, predetermined, randomization schedule, was considered.
Thirty-seven patients who had undergone RK before 1995 were identified. After poor quality examinations had been excluded, the final sample was 29 eyes from 29 patients (37.9% males; 20.6% right eyes). Mean number of radial incisions was 8.1±2.9 (range: 4 to 14 incisions). Mean patient age (46.3±8.0 years) was not statistically different in comparison to the control group (54.9±22.2 years, P=.069 Mann-Whitney test for nonparametric data).
The main results are summarized in the Table. The mean anterior corneal radius, mean posterior corneal radius, and mean anterior-to-posterior corneal curvature ratio were all significantly different between cases and controls. Using the Gaussian optics formula, a mean value of 35.04±3.07 D (range: 28.04 to 40.59 D) was calculated as the total corneal power in our sample. The mean value for the keratometric index was significantly higher than the same index calculated for the control group.
Table: Scheimpflug Measurements in Eyes That Underwent Previous Radial Keratotomy and Unoperated Eyes
Linear regression disclosed a statistically significant relationship between the number of radial incisions and 1) the anterior-to-posterior corneal curvature ratio (r=−0.4459, r2=0.1988, P=.0135), 2) the posterior corneal radius (r=0.7195, r2=0.5176, P<.0001), and 3) the anterior corneal radius (r=0.6470, r2=0.4186, P=.0001). In other words, the number of incisions was directly proportional to both posterior and corneal flattening and inversely proportional to the anterior-to-posterior corneal curvature ratio. Linear regression also revealed that the fictitious keratometric index tended to increase in eyes with higher numbers of radial incisions, although the relationship did not reach statistical significance (P=.0821, r=0.33, r2=0.11).
Our data show that RK changes the anterior-to-posterior corneal curvature ratio, thus contradicting previous statements.12–16 Hence, postoperative RK eyes are affected by the same three problems that make IOL power calculation challenging after excimer laser surgery: “radius error,” “keratometric index error,” and “IOL formula error.”1–11 In contrast, the few studies that previously analyzed the results of phacoemulsification and IOL implantation after RK focused only on the need to rely on the most central measurements of the corneal radius.15,19,20 In those studies, the major source of error was thought to be related to the small optical zone and oblate corneal shape, leading to overestimation of corneal power if measurements were taken on the refractive knee of the cornea (“radius error”). Our data suggest that the “keratometric index error” should also be considered.
The keratometric index is a fictitious number that all instruments use to convert the curvature of the anterior corneal surface into the dioptric power of the whole cornea (modeled as a single refracting surface). This index, which provides excellent results for IOL power calculation in unoperated eyes, is unrelated to the anatomy and physical properties of the eye and depends on a fixed ratio between the anterior and posterior corneal curvature. Conventionally, it has been set to 1.3375, although studies evaluating the posterior corneal curvature calculated that the mean keratometric index of unoperated eyes is lower, ranging between 1.3273 and 1.3290.17,21–24 The data of the present investigation show that after RK the mean keratometric index (1.3319) is significantly higher (P<.0001) compared to the mean value of 1.3285 that we previously found in virgin eyes.18 Interestingly, the 1.3319 value is the same that had been previously calculated by means of intraoperative pachymetry measurements during RK.25,26 As a consequence, even if the radius error is corrected (by measuring the corneal curvature inside the postoperative optical zone) and the IOL formula error is compensated (by the Aramberri Double-K method),11 inaccurate IOL power calculation can still occur in postoperative RK eyes because of the keratometric index error. This can be avoided if the corneal power is measured by means of 1) the Gaussian optics formula or 2) ray-tracing based on Snell law, as both methods do not rely on any keratometric index. The former, which is automatically displayed on the Pentacam as the True Net Power, has never been tested for IOL power calculation and may theoretically lead to incorrect results after LASIK.27 The latter, which is automatically displayed on the Pentacam as the Total Refractive Power, on the Galilei (Ziemer, Port, Switzerland) as the Total Corneal Power, and on the Sirius (CSO, Firenze, Italy) as the Mean Pupil Power, may provide better results than the Gaussian optics formula after LASIK,27 and has been shown to lead to accurate calculations in unoperated eyes.28
After RK, the change in the anterior-to-posterior corneal curvature ratio occurs in an opposite direction compared to excimer laser surgery, where only the anterior corneal curvature is flattened. In a sample of 35 eyes that had undergone myopic photorefractive keratectomy (PRK) or LASIK and were subsequently analyzed by the Pentacam (and partially published previously),29 the mean ratio was 1.34±0.05, which is higher than the same ratio in unoperated eyes (1.22±0.03) and postoperative RK eyes (1.12±0.07). Consistent with this result, when compared to the control group, postoperative RK eyes revealed a 22.15% flattening of the mean anterior corneal radius and 33.44% flattening of the mean posterior corneal radius. These findings show that, after RK, the surgically induced corneal flattening is more relevant on the posterior surface. This may explain why Hanna et al,30 in their computer simulation of the effects of RK, found that the refractive change was greater than the corneal power change by approximately 26%. If, in fact, the corneal power is calculated only from the anterior corneal curvature, the relevant contribution of posterior flattening cannot be accounted for. The reason why corneal flattening is more evident on the posterior rather than on the anterior corneal surface is not clear. As a possible explanation, we can suppose that a partial remodeling of the epithelium and steepening of the anterior corneal surface occurs after RK. Such a steepening may be the consequence of corneal epithelial compensatory hyperplasia. This has been shown in eyes that had undergone myopic LASIK and PRK, especially when a small (<5.0 mm) optical zone is used.31–33 In these cases, epithelial thickening at the corneal vertex has been detected, as if the corneal epithelium behaved in such a way as to reverse the change in stromal curvature by remodeling itself to mirror the volume of stromal tissue removed. Similarly, epithelial hyperplasia has been observed in a variety of diseases leading to stromal loss or ectasia.34 It is likely that epithelial hyperplasia and central corneal steepening also take place after RK.35
We also detected a statistically significant relationship between the number of radial incisions and corneal flattening. This is in accordance with previous studies of the 1980s and 1990s, which showed that eight-incision RK could attain higher refractive change than four-incision RK when the same optical zone was selected.36,37 We observed that the anterior-to-posterior corneal curvature ratio was inversely related to the number of incisions; hence, our data suggest that the higher the number of incisions, the more evident the flattening of the posterior corneal curvature relative to the anterior corneal curvature. Again, this finding may be explained by corneal epithelium remodeling, which may lead to greater thickening in eyes with more severe curvature changes between the mid-peripheral refractive knee and central optical zone.
This study has some limitations and further investigation is warranted. First, we did not measure the preoperative anterior and posterior corneal curvature, as the Pentacam was not available when RK was performed several years ago. Therefore, we could not directly assess the change in corneal radius, but had to compare postoperative RK eyes to a separate control group of unoperated eyes. Second, corneal measurements were taken at 3 mm, as this is the standard diameter displayed by the Pentacam, and most instruments use this diameter to measure the corneal curvature to be used in the setting of IOL power calculation. Slightly different results might have been achieved using a smaller optical zone diameter for the analysis. Third, we did not know the exact surgically induced refractive change for all patients, therefore, we could not perform a linear regression analysis to correlate corneal curvature and refractive changes. Fourth, the repeatability of corneal curvature measurements by Pentacam in RK eyes has not yet been studied and may be worse than in normal unoperated eyes.
Corneal curvature measurements by Scheimpflug imaging showed that the anterior-to-posterior radius ratio changes after RK, with a major contribution from the posterior curvature, which is subject to a more marked flattening compared to the anterior curvature. The variation in the anterior-to-posterior radius ratio relative to virgin eyes is the main outcome of this study and this finding invalidates the standard keratometric index (usually 1.3375) that is adopted to obtain corneal power from anterior corneal curvature measurements. Therefore, we can conclude that IOL power calculation in postoperative RK eyes can lead to postoperative refractive surprises not only because of the radius and IOL power formula errors, as previously thought, but also because of the keratometric index error, as in postoperative LASIK/PRK eyes.
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Scheimpflug Measurements in Eyes That Underwent Previous Radial Keratotomy and Unoperated Eyes
||Mean±Standard Deviation (95% Confidence Interval)
|Post RK Eyes
|Anterior corneal radius (mm)
|Posterior corneal radius (mm)
|Anterior-to-posterior corneal radius ratio