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Estimation accuracy of surgically induced astigmatism on the cornea when neglecting the posterior corneal surface measurement

2009; Wiley; Volume: 89; Issue: 5 Linguagem: Inglês

10.1111/j.1755-3768.2009.01732.x

1755-3768

Li-Sheng Cheng, Ching‐Yao Tsai, Ray Jui-Fang Tsai, Shiow‐Wen Liou, Jau‐Der Ho,

Ophthalmology and Visual Impairment Studies

Purpose: To evaluate the accuracy of corneal surgically induced astigmatism (SIA) estimation when neglecting the posterior corneal surface measurement. Methods: Fifty right eyes undergoing phacoemulsification were measured with a rotating Scheimpflug camera (Pentacam; Oculus Inc., Wetzlar, Germany) both before and after surgery. Clear corneal incisions with one suture were used in the phacoemulsification surgery. The keratometric corneal SIA (KSIA) was derived using the anterior corneal surface measurement and the keratometric index (1.3375) while neglecting the posterior corneal surface measurement. The Pentacam-derived total corneal SIA (PSIA) was derived by vergence tracing and polar value analysis [KP(135) and KP(180)] of the measurements on both corneal surfaces. Results: The mean arithmetic estimation errors of the KSIA for the PSIA were 0.16 ± 0.32 (−0.52 to 1.14) D for the KP(135), and −0.02 ± 0.30 (−0.75 to 1.29) D for the KP(180). There was a significant difference between the KP(135) components of the KSIA and PSIA. Bivariate analysis revealed a statistically significant difference between the combined means of the KSIA and PSIA. Overall, 24% had either a KP(135) component of the KSIA that differed by > 0.50 D from that of the PSIA or a KP(180) component of the KSIA that differed by > 0.50 D from that of the PSIA. The blurring strength caused by neglecting the posterior corneal measurement was > 0.50 D in 24% of eyes. Conclusion: Neglecting the posterior corneal surface measurement may lead to significant deviation in the corneal SIA estimation after phacoemulsification in a proportion of eyes. Preoperative astigmatism can be corrected at the time of cataract surgery using various methods, including peripheral corneal relaxing incision, selection of incision site and toric intraocular lens (IOL) (Carvalho et al. 2007; Amesbury & Miller 2009). Because surgically induced astigmatism (SIA) is a known consequence of creating the incision necessary for cataract surgery (Borasio et al. 2006; Altan-Yaycioglu et al. 2007), the amount of astigmatism to be corrected at the time of surgery must be the vector sum of the preoperative corneal astigmatism and any SIA (Eydelman et al. 2006). While many studies have investigated the SIA on the cornea after cataract surgery, the derivation of the SIA in those studies was based only on measurements of the anterior corneal surface (Pfleger et al. 1996; Kershner 1997; Rauz et al. 1997; Lyhne et al. 1998; Morlet et al. 2001; Kohnen et al. 2002; Borasio et al. 2006; Altan-Yaycioglu et al. 2007; Hill 2008). Although both the anterior and posterior corneal surfaces contribute to the total corneal SIA, the total corneal SIA is usually derived solely from the keratometer- or corneal topography-measured anterior corneal radius. This mathematical shortcut is used because of past difficulties in measuring the posterior corneal surface. The keratometric index (traditionally 1.3375 in most keratometers) was developed so that the omission of the posterior corneal surface measurement could be compensated for by measuring only the anterior corneal surface (Olsen 1986; Goss & West 2002). However, it has been shown that the traditional keratometric index might lead to a significant error in actual corneal power estimation in unoperated eyes (Fam & Lim 2007; Ho et al. 2008). In a recent study, we also demonstrated that neglecting the posterior corneal measurement might result in significant deviation in the corneal astigmatism estimation in a proportion of unoperated eyes (Ho et al. 2009). The astigmatism of the posterior corneal surface of unoperated eyes has been measured in several studies. Those studies used techniques such as Purkuinje imagery, pachymetry, Scheimpflug photography and slit-scan topography (Royston et al. 1990; Dunne et al. 1991, 1992; Prisant et al. 2002; Dubbelman et al. 2006; Ho et al. 2009). Some of those studies calculated the astigmatism of the posterior corneal surface on the basis of measurements in three or six fixed meridians (Royston et al. 1990; Dunne et al. 1991, 1992; Dubbelman et al. 2006). Two of them used a corneal elevation map, which was obtained by the Orbscan or the Pentacam to summarize the data from all meridians to calculate the astigmatism of the posterior corneal surface (Prisant et al. 2002; Ho et al. 2009). The Pentacam (Oculus Inc., Wetzlar, Germany) is a rotating Scheimpflug camera that images the anterior segment. It provides elevation maps of the anterior and posterior corneal surfaces, pachymetry maps and biometric measurements of the anterior segment (Barkana et al. 2005; Lackner et al. 2005). It measures 25 000 data-points over the cornea in < 2 seconds (Buehl et al. 2006). In this study, we analysed data obtained by the Pentacam of measurements of the anterior and posterior corneal surfaces before and after cataract surgery to derive the total corneal SIA. We compared the corneal SIA calculated using the data of both the anterior and posterior corneal surfaces with that calculated using only the data of the anterior corneal surface (i.e. the conventional calculation of SIA). The accuracy of the total corneal SIA estimation obtained using the conventional method (using the anterior corneal surface measurement only) was evaluated. After institutional review board approval, a retrospective review was performed on the data of patients whose right eyes were operated on for cataract removal and IOL implantation by the same surgeon between September and December 2007. All eyes with previous corneal or intraocular surgery and cases with poor-quality Pentacam scans were excluded. The following data were reviewed before and 2 months after surgery: measurements obtained by the Pentacam HR, which included central corneal thickness, the flat (Rf) and steep (Rs) central radii in the 3-mm zone on the anterior and posterior corneal surfaces, and the meridian of the Rf in the 3-mm zone on the anterior and posterior corneal surfaces. All operations were performed by the same surgeon using a two-plane, 2.75-mm incision placed just anterior to the limbus in the superotemporal quadrant (centred at 135°) of the clear cornea. Following a divide-and-conquer nucelofractis and irrigation/aspiration for cortex removal, a foldable IOL (SA60AT; Alcon, Fort Worth, Texas, USA) was implanted. At the conclusion of surgery, the wound was closed with one radial suture of 10-0 nylon. The suture was not removed when the eye was measured by the Pentacam 2 months after the surgery. The Appendix (available online as Supporting Information – Appendix S1) shows the derivation process of the total corneal SIA using the measurements of both corneal surfaces [Pentacam-derived SIA (PSIA)], or using only the measurements of the anterior corneal surface [keratometric SIA (KSIA)]. Because refractive data in the form of sphere, cylinder and axis are unsuitable for mathematical analysis, the polar value system (which converts net astigmatism to orthonormal components in dioptric space) was utilized for all calculations (Naeser & Hjortdal 1999; Naeser & Guo 2000; Naeser 2008). The estimation error for the Pentacam-derived total corneal SIA using the keratometric method (i.e. neglecting the posterior corneal surface measurement) was evaluated by the following criteria (Wang et al. 2004): The mean arithmetic estimation errors of the polar value components [KP(135) and KP(180)] of the KSIA for those of the PSIA. The percentage of eyes within a certain range of estimation error of the KP(135) of KSIA for the KP(135) of PSIA (e.g. within ±0.50 D), and the KP(180) of KSIA for the KP(180) of PSIA (e.g. within ±0.50 D). The percentage of eyes within a certain range of blurring strength that is caused by neglecting the posterior corneal measurement (e.g. within 0.50 D). For statistical evaluation, spss for Windows (Version 13.0; SPSS Inc., Chicago, Illinois, USA) was used. Variables were tested for normality by the Kolmogorov–Smirnov test. Descriptive statistics on univariate data were performed in the usual manner. A paired t-test was used for comparison between the polar value components of the KSIA and PSIA. Bivariate statistical analysis was performed with Hotelling's T 2-test (Naeser 2008). The right eyes of 15 men and 35 women were included in this study. The mean age of these patients was 71.6 ± 9.1 (range 50–94) years. The mean preoperative (measurable in 35 eyes, immeasurable in the other 15 eyes because of dense cataract) and postoperative (measurable in 50 eyes) spherical equivalents were −2.95 ± 5.16 (range −16.25 to 3.125) and −0.04 ± 0.95 (range −2.25 to 3.125) D. The average PSIA and KSIA (expressed as net astigmatisms) were 0.24 D @ 51.1° and 0.10 D @ 65.9°, respectively. Table 1 summarizes the preoperative and postoperative data. There was no significant difference between the preoperative and postoperative central corneal thicknesses (555.9 ± 28.8 versus 557.4 ±28.9 μm; p = 0.552, paired t-test). Table 2 presents the average polar values [KP(135), KP(180)] and net astigmatisms for the anterior and posterior corneal surfaces, preoperatively and postoperatively, as well as SIA. (A) Scattergram of the KP(135) component of the Pentacam-derived posterior corneal surgically induced astigmatism (SIA) [KP(135)PSIA.back] versus that of the Pentacam-derived anterior corneal SIA [KP(135)PSIA.front]. (B) Scattergram of the KP(180) component of the Pentacam-derived posterior corneal SIA [KP(180)PSIA.back] versus that of the Pentacam-derived anterior corneal SIA [KP(180)PSIA.front]. Scattergram of the Pentacam-derived posterior corneal surgically induced astigmatism magnitude (PSIAback magnitude) versus the Pentacam-derived anterior corneal surgically induced astigmatism magnitude (PSIAfrontmagnitude). There was a significant correlation between the magnitude of the PSIAback and that of the PSIAfront (r = 0.428, p = 0.002). The regression formula is PSIAback magnitude = 0.1026 × (PSIAfront magnitude) + 0.1985. Estimation results for the PSIA using the KSIA (which neglects the posterior corneal surface measurement) in terms of polar value components are summarized in Table 3. The KP(135) and KP (180) values of the KSIA and the PSIA were all normally distributed (all p > 0.05, Kolmogorov–Smirnov test). The mean arithmetic estimation error of the KP(135)KSIA for KP(135)PSIA was 0.16 ± 0.32 (range −0.52 to 1.14). There was a significant difference between the KP(135)KSIA and KP(135)PSIA (p = 0.0008, paired t-test). That is, neglecting the posterior corneal measurement caused a significant difference in estimation of the net on-axis (curvital) power of the SIA. Among these eyes, 62% (31 eyes) and 84% (42 eyes) had a KP(135)KSIA that was within ±0.25 and ±0.50 D of the KP(135)PSIA, respectively. The mean arithmetic estimation error of the KP(180)KSIA for KP(180)PSIA was −0.02 ± 0.30 (range −0.75 to 1.29). There was no significant difference between the KP(180)KSIA and KP(180)PSIA (p= 0.6811, paired t-test). Among these eyes, 70% (35 eyes) and 92% (46 eyes) had a KP(180)KSIA that was within ±0.25 and ±0.50 D of the KP(180)PSIA, respectively. The Bland–Altman plots comparing the polar values of the KSIA and those of the PSIA are presented in Fig. 3A, B. The individual difference values between the KSIA and PSIA are shown as pairs of polar values [ΔKP(135), ΔKP(180)] in Fig. 4. The mean difference was on point (0.16 D, −0.02 D). This mean difference was 0.16 D @ 131.9° when expressed as net astigmatism. Bivariate analysis revealed a statistically significant difference between the combined means of the KSIA and PSIA (p= 0.0032, Hortelling's T2-test). The mean difference and the bivariate 95% confidence region for the mean difference between the KSIA and the PSIA are shown as pairs of polar values in Fig. 5. Bland–Altman plots comparing the polar values of the keratometric surgically induced astigmatism (KSIA) and those of the Pentacam-derived total corneal surgically induced astigmatism (PSIA). (A) Comparison of the KP(135) between the KSIA and PSIA. The 95% limits of agreement (LoA) were −0.46 to 0.78 D. (B) Comparison of the KP(180) between the KSIA and PSIA. The 95% LoA were −0.61 to 0.57 D. (Mean difference is represented by a solid line; 95% LoA are represented by dotted lines.). The difference between the keratometric surgically induced astigmatism (KSIA) and the Pentacam-derived total corneal surgically induced astigmatism (PSIA) shown as pairs of polar values. Individual values and 50%, 95% normal regions for the observations are shown. The mean difference and the bivariate 95% confidence region of the mean difference between the keratometric surgically induced astigmatism (KSIA) and the Pentacam-derived total corneal surgically induced astigmatism (PSIA) expressed as pairs of polar values. In total, 38 eyes (76%) had a KP(135)KSIA within ±0.50 D of the KP(135)PSIA and a KP(180)KSIA within ±0.50 D of the KP(180)PSIA; 12 eyes (24%) had either a KP(135)KSIA that differed by > 0.50 D from the KP(135)PSIA or a KP(180)KSIA that differed by > 0.50 D from the KP(180)PSIA. In terms of blurring strength caused by neglecting the posterior corneal measurement, 32 eyes (64%) and 12 eyes (24%) had a blurring strength that was > 0.25 and > 0.50 D, respectively. In this study, we used a rotating Scheimpflug camera (the Pentacam) to measure the curvatures of the anterior and posterior corneal surfaces before and after cataract surgery. We showed that there was a statistically significant difference between the combined means of the KSIA and PSIA. Among all studied eyes, 24% had either a KP(135)KSIA that differed by > 0.50 D from the KP(135)PSIA or a KP(180)KSIA that differed by > 0.50 D from the KP(180)PSIA. To the best of our knowledge, there is no published study addressing the issue of SIA on the posterior corneal surface after cataract surgery. One of the reasons might be the difficulty in measuring the posterior corneal surface in clinical settings, especially before the advent of the Orbscan and Pentacam. Another reason might be that the difference in the refractive indices across the posterior corneal surface (1.336 − 1.376 = −0.04) is relatively small compared with that across the anterior corneal surface (1.376 − 1 = 0.376); therefore, the refractive change induced on the posterior corneal surface might be assumed to be small enough to be neglected. However, bivariate analysis in this study revealed a statistically significant difference between the combined means of the KSIA and PSIA. The result suggests that neglecting the contribution of the posterior corneal surface may cause a significant error in estimating the total corneal SIA. The outcome of all intraoperative astigmatism-reducing methods depends upon accurate estimation of the total corneal SIA because the amount of astigmatism to be corrected at the time of surgery must be the vector sum of the preoperative corneal astigmatism and any SIA (Eydelman et al. 2006). Our study found that measuring only the anterior corneal surface may have resulted in either a KP(135)KSIA that differed by > 0.50 D from the KP(135)PSIA or a KP(180)KSIA that differed by > 0.50 D from the KP(180)PSIA in 24% of eyes. In these eyes, the blurring strength caused by not considering the posterior corneal surface measurements is > 0.50 D, perhaps leading to suboptimal results in the intraoperative astigmatism correction of these eyes. In addition, our study revealed that there was a statistically significant difference in SIA between measurements derived solely from the anterior cornea versus both anterior and posterior corneal surfaces. The difference was significant for KP(135), but not for KP(180). This observation can be explained as follows: the ratio of the KP(135) of the posterior corneal SIA to that of the anterior corneal SIA was 4.28 ± 28.42 (range −2.98 to 200.56), while the ratio of the KP(180) of the posterior corneal SIA to that of the anterior corneal SIA was −0.17 ± 1.10 (range −6.81 to 1.91). It is evident from these data that variation in the posterior-to-anterior ratio was much larger for KP(135) than for KP(180). Because all incision wounds in this study were centred at 135° and closed with a radial suture, the variable depth of the suture bite and the variable degree of suture tightness might be partially responsible for the larger variation in the relationship between the KP(135) values (i.e. the on-axis components) of the anterior and posterior corneal SIAs. On the other hand, the relationship between the KP(180) values (off-axis components) of the anterior and posterior corneal SIAs would be less affected by the radial suture at 135°. That is, the relationship between the KP(180) values of the anterior and posterior corneal SIAs would be more constant than that between the KP(135) of the anterior and posterior corneal SIAs. Because the precondition for keratometric SIA validity in estimating the total corneal SIA is that the anterior corneal SIA and posterior corneal SIA have a relatively constant relationship (Fam & Lim 2007), the more variable posterior-to-anterior relationship for KP(135) compared with KP(180) may underlie the observation that there was a statistically significant difference in the KP(135) between the keratometric SIA and the Pentacam-derived total corneal SIA, but not the KP(180). Another possibility is that the anterior and/or the posterior corneal surface was measured incorrectly. In Scheinmpflugg imaging, the measurement of the posterior surface is affected by the distortion of the anterior surface. This is not well described in Pentacam technology. The posterior corneal surface has a smaller radius of curvature than the anterior corneal surface. Identical changes in the radius of curvature of the anterior and posterior corneal surfaces (e.g. Δ = 1 mm) will induce a larger change in the curvature on the posterior corneal surface than on the anterior corneal surface. In addition, the more central location of the cut on the posterior corneal surface is expected to induce a greater 'shape' change in the central portion of the posterior corneal surface than the more peripheral cut on the anterior corneal surface would in the central portion of the anterior corneal surface. These factors may explain our finding that the PSIAback magnitude was on average 29.8% that of the PSIAfront, which was higher than the ratio of the difference in the refractive indices across the posterior corneal surface to that across the anterior corneal surface, i.e. (1.376 − 1.336)/ (1.376 − 1) = 10.6%. The traditionally and most commonly used keratometric index of 1.3375 was chosen only for convenience, rather than for optical significance, because it makes the two values (7.5 mm and 45.0 D) agree exactly (Holladay 1997). Based on the preoperative and postoperative data of this study, the optimal effective corneal refractive index (i.e. the optimal keratometric index) would be 1.3278 (337.5 × 43.23/44.52 = 327.8) or 1.3270 (337.5 × 42.99/44.37 = 327.0), respectively. These values reflect more exactly the average relationship between the anterior and posterior corneal surfaces than does the value of 1.3375. However, we found that a keratometric index value of 1.3278 or 1.3270 did not improve the estimation accuracy of the total corneal SIA of cataract surgery above the value of 1.3375 either in terms of the percentage of eyes with a KP(135)KSIA within ±0.50 D of the KP(135)PSIA and a KP(180)KSIA within ±0.50 D of the KP(180)PSIA (72% for the keratometric index of 1.3278 or 1.3270 versus 76% for the keratometric index of 1.3375), or a blurring strength within 0.50 D (70% for the keratometric index of 1.3278 or 1.3270 versus 76% for the keratometric index of 1.3375). This indicates that when neglecting the posterior corneal surface measurement, the estimation accuracy of the total corneal SIA cannot be improved by changing the traditional keratometric index to a more physiological one. In summary, our study found that the SIA of the posterior corneal surface might contribute significantly to the total corneal SIA. Omission of the posterior corneal surface measurement when calculating the total corneal SIA can lead to significant inaccuracies in estimating the total corneal SIA in some eyes. As the demand for intraoperative correction of astigmatism during cataract surgery rises, further studies are needed to evaluate whether including measurements of the posterior corneal surface in estimating the total corneal SIA improves the accuracy of the total corneal SIA estimation, and thus enhances the results of intraoperative correction of astigmatisms. The authors have no proprietary or commercial interest in any materials mentioned in this article. Appendix S1. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.