Keratometric Index Obtained by Fourier-Domain Optical Coherence Tomography

Purpose To determine the keratometric indices calculated based on parameters obtained by Fourier-domain optical coherence tomography (FD-OCT). Methods The ratio of anterior corneal curvature to posterior corneal curvature (Ratio) and keratometric index (N) were calculated within central 3 mm zone with the RTVue FD-OCT (RTVue, Optovue, Inc.) in 186 untreated eyes, 60 post-LASIK/PRK eyes, and 39 keratoconus eyes. The total corneal powers were calculated using different keratometric indices: Kcal based on the mean calculated keratometric index, K1.3315 calculated by the keratometric index of 1.3315, and K1.3375 calculated by the keratometric index of 1.3375. In addition, the total corneal powers based on Gaussian optics formula (Kactual) were calculated. Results The means for Ratio in untreated controls, post-LASIK/PRK group and keratoconus group were 1.176 ± 0.022 (95% confidence interval (CI), 1.172–1.179), 1.314 ± 0.042 (95%CI, 1.303–1.325) and 1.229 ± 0.118 (95%CI, 1.191–1.267), respectively. And the mean calculated keratometric index in untreated controls, post-LASIK/PRK group and keratoconus group were 1.3299 ± 0.00085 (95%CI, 1.3272–1.3308), 1.3242 ± 0.00171 (95%CI, 1.3238–1.3246) and 1.3277 ± 0.0046 (95%CI, 1.3263–1.3292), respectively. All the parameters were normally distributed. The differences between Kcal and Kactual, K1.3315 and Kactual, and K1.3375 and Kactual were 0.00 ± 0.11 D, 0.21 ± 0.11 D and 0.99 ± 0.12 D, respectively, in untreated controls; -0.01 ± 0.20 D, 0.85 ± 0.18 D and 1.56 ± 0.16 D, respectively, in post-LASIK/PRK group; and 0.03 ± 0.67 D, 0.56 ± 0.70 D and 1.40 ± 0.76 D, respectively, in keratoconus group. Conclusion The calculated keratometric index is negatively related to the ratio of anterior corneal curvature to posterior corneal curvature in untreated, post-LASIK/PRK, and keratoconus eyes, respectively. Using the calculated keratometric index may improve the prediction accuracies of total corneal powers in untreated controls, but not in post-LASIK/PRK and keratoconus eyes.


Introduction
Consideration of the keratometric index is essential for the assessment of total corneal power and the prediction of intraocular lens power. [1,2] Historically, because of the lack of information from the posterior corneal surface, the conventional keratometric index (1.3375) [3] or the keratometric index derived from Gullstrand schematic eye (1.3315) [4] combining the anterior corneal curvature were used to calculate the total corneal power. The equation is as follows: K = (N-1) / R, where K is the total corneal power, N is the keratometric index, 1 means the refractive index of the air, and R means the anterior corneal curvature in certain central zone. In theory, these keratometric indices (the conventional 1.3375 or the 1.3315 based on the Gullstrand schematic eye) which are lower than the real corneal refractive index of 1.376, compensate for the negative power of posterior corneal surface. Moreover, the equation above must be based on 2 assumptions: The anterior and posterior corneal curvatures have a constant and linear relationship. [5,6] However, this is not the case. Even in different schematic eyes, the ratio of anterior corneal curvature to posterior corneal curvature are not the same. [6] Furthermore, the ratios obtained by different devices from real human eyes are also vary. [7][8][9] Currently, there are three kinds of techniques that can detect the information of the anterior and posterior corneal surface and central corneal thickness (CCT) simultaneously, including Slit-scan system (Orbscan Ⅱ) [10,11], Scheimpflug camera system (Pentacam or Pentacam HR) [12,13] and optical coherence tomography system (Fourier-Domain OCT, FD-OCT) [14][15][16]. There have been reports in which the first 2 techniques were applied to obtain the ratio of anterior corneal curvature to posterior corneal curvature, and the keratometric index was calculated regarding the total corneal power based on Gaussian optics formula as a benchmark. [1,5,6,17] However, to the best to our knowledge, until now there have been no reports on the keratometric index calculated by data derived from RTVue FD-OCT (RTVue, Optovue, Inc.). The commercially available system RTVue FD-OCT with a speed of 26000 axial scans per second has an axial resolution of 5 μm and a transverse resolution of 15 μm. [16] The corneal mapping model had 6.0 mm line scans on 8 meridians with 1019 axial scans centered on the pupil, and the whole scan model was finished within 0.32 seconds. [16] Previous work from our research group showed that RTVue FD-OCT had good repeatability in measurements of corneal parameters (corneal curvature and CCT) from untreated eyes and eyes after corneal refractive surgery. [18,19] In this study, we used the RTVue FD-OCT system to measure the anterior and posterior corneal curvature and the CCT within central 3 mm zone in untreated controls, post-LASIK/PRK and keratoconus groups. The ratio of anterior corneal curvature to posterior corneal curvature and keratometric indices were then calculated, and the total corneal powers were assessed using these keratometric indices in each group.

Patients and Methods
Inclusion criteria were patients who didn't receive prior corneal or ocular surgery in the untreated controls, or received uneventful LASIK at least 3 months or PRK at least 6 months previously in the post-LASIK/PRK group, or was diagnosed with keratoconus in the keratoconus group. All the results obtained by RTVue FD-OCT had good reliability (Measurement Reliability Rating GOOD displayed on the Pachymetry + CPwr map). Three groups of subjects were included in this study: 1. 186 eyes of 186 subjects in the untreated group; the mean age was 26.1 ± 5.6 years; the mean spherical equivalent was -2.53 ± 1.32 D; these subjects were selected from the patients examined before corneal refractive surgery in Wenzhou Eye Hospital (Wenzhou, China) from July 2011 to April 2012.
2. 60 eyes of 39 patients in the post-LASIK/PRK group; the mean age was 27.3 ± 6.2 years; the mean spherical equivalent before the laser surgery was -4.81±1.22 D; the mean spherical equivalent after the laser surgery was 0.02±0.33 D; these subjects were selected from the patients who received LASIK at least 3 months previously or PRK at least 6 month previously in Wenzhou Eye Hospital from July 2011 to April 2012.
3. 39 eyes of 27 patients in the keratoconus group; the mean age was 34.93 ± 11.41 years; the data were selected from the patients who were diagnosed as keratoconus in Synslaser Clinic (Tromso, Norway) from September 2012 to January 2013. All the patients did not receive any eye surgery previously. And 4 of them had apical scars, 5 of them had Vogt striae, and all the others had clean corneas.
The study was conducted at the Eye Hospital of Wenzhou Medical University and Synslaser Clinic (Tromso, Norway). The research was performed in accordance with the principles stated in the Declaration of Helsinki. The untreated controls and post-LASIK/PKR group from Wenzhou Eye Hospital was approved by the Office of Research Ethical Committee, Wenzhou Medical University; and the keratoconus group from Synslaser was approved by the National Committee for Medical and Health Research Ethics in Norway. All participants provided written informed consent after the nature of the study had been explained to them.
We obtained the anterior corneal curvature (R anterior ), posterior corneal curvature (R posterior ) and CCT within central 3 mm zone for each tested eye using RTVue FD-OCT. The ratio of the anterior and posterior corneal curvature in each eye was calculated as follows: The Gaussian optics formula calculates the actual total corneal power (K actual ) within central 3 mm zone by assuming the central cornea as a thick lens. And K actual in each eye was calculated as follows: K actual ¼ ðn 1 À n 0 Þ=R anterior þ ðn 2 À n 1 Þ=R posterior À ðCCT=n 1 Þ Â ½ðn 1 À n 0 Þ=R anterior Â ½ðn 2 À n 1 Þ=R posterior 2 where n 0 (1.000), n 1 (1.376) and n 2 (1.336) are the refractive indices of the air, the cornea and aqueous, respectively. We used the following equation to compute the real keratometric index (n) in each eye: The mean of n in each eye was computed and defined as N, next N was used to estimate the total corneal power (K cal ) in each eye as follows: The total corneal power estimated using the keratometric index obtained from Gullstrand model eye (1.3315) and the conventional keratometric index (1.3375) were calculated as follows: K 1:3315 ¼ ð1:3315 À 1Þ=R anterior 5 K 1:3375 ¼ ð1:3375 À 1Þ=R anterior 6 All the data were entered into MedCalc Version 11.4.2 for Windows. Correlation coefficient and paired t-test were used to compare values normally distributed in the three groups. Correlation coefficient and regression analysis were used to analyze the correlations between R anterior and R posterior , N cal and Ratio. Bland-Altman plots were applied to analyze the agreement between K cal and K actual , K 1.3315 and K actual , K 1.3375 and K actual . A P value of 0.05 or less was considered statistically significant. Table 1 shows the corneal parameters obtained by RTVue FD-OCT in untreated controls, post-LASIK/PRK group and keratoconus group. All the values conformed to be normally distributed by Kolmogorov-Smirnov test (all P > 0.05). The distributions of Ratio and keratometric indices (N) in untreated controls, post-LASIK/PRK group and keratoconus group are shown in Fig 1A, 1B, 1C, 1D, 1E and 1F, respectively.  Fig 2A, the mean R posterior from keratoconus group was significantly smaller than those from untreated and post-LASIK/PRK group (both P<0.05). And there was no statistical significance between the mean R posterior values from untreated controls and post-LASIK/PRK group (P>0.05). In Fig 2B, both the mean Ratio from post-LASIK/PRK group and keratoconus group were larger than the mean Ratio from untreated controls (both P<0.05), and the mean Ratio from post-LASIK/PRK group was larger than that from keratoconus group (P<0.05). In Fig 2C, both the mean keratometric indices (N cal ) from post-LASIK/PRK group and keratoconus group were smaller than the mean Ratio from untreated controls (both P<0.05), and the mean N from post-LASIK/PRK group was smaller than that from keratoconus group (P<0.05).

Results
In untreated controls, linear regression revealed that there were good correlations between R anterior and R posterior , Ratio and N. The regression equations were R posterior = 0.01021 + 0.8499×R anterior (r = 0.884, r 2 = 0.782, P<0.05) and N = 1.3752-0.03852×Ratio (r = -0.997, r 2 = 0.995, P<0.05) in Fig 3A and 3B. In post-LASIK/PRK group, linear regression revealed that there were good correlation between Ratio and N. The regression equations was N = 1.3775-0.04054×Ratio (r = -0.999, r 2 = 0.999, P<0.05) in Fig 3D. In keratoconus group, the regression equations were R posterior = -2.8393 + 1.218×R anterior (r = 0.854, r 2 = 0.728, P<0.05) and N = 1.3759-0.03917×Ratio (r = -0.999, r 2 = 0.999, P<0.05) in Fig 3E and 3F. Table 2 shows the total corneal power calculated with different keratometric indices in untreated controls, post-LASIK/PRK group and keratoconus group. Table 3 shows the comparisons between K cal and K actual , K 1.3315 and K actual , K 1.3375 and K actual in the three groups. There were no statistical significances between K cal and K actual in all three groups (all P = 1.00, paired t test). In untreated controls, K 1.3315 and K 1.3375 were 0.21 ± 0.11 D and 0.99 ± 0.12 D lager than K actual , respectively (both P<0.05). Fig 4 shows the Bland-Altman plots comparing the total corneal power calculated with different keratometric indices (K cal , K 1.3315 and K 1.3375 ) and the actual total corneal power calculated based on Gaussian optics formula (K actual ) in untreated controls, and the 95% confidence interval (CI) for K cal vs K actual , K 1.3315 vs K actual , and K 1.3375 vs K actual were -0.22 to 0.22 D, -0.01 to 0.42 D and 0.76 to 1.21 D, respectively. In post-LASIK/PRK group, K 1.3315 and K 1.3375 were 0.85 ± 0.18 D and 1.56 ± 0.16 D lager than K actual , respectively (both P<0.05). Fig 5 shows the Bland-Altman plots of K cal and K actual , K 1.3315 and K actual , K 1.3375 and K actual in post-LASIK/PRK group, and the 95% CI for K cal vs K actual , K 1.3315 vs K actual , and K 1.3375 vs K actual were -0.40 to 0.38 D, 0.50 to 1.19 D and 1.23 to 1.86 D, respectively. In keratoconus group, K 1.3315 and K 1.3375 were 0.56 ± 0.70 D and 1.40 ± 0.76 D lager than K actual , respectively (both P<0.05). Fig 6 shows the Bland-Altman plots of K cal and K actual , K 1.3315 and K actual , K 1.3375 and K actual in keratoconus group, and the 95% CI for K cal vs K actual , K 1.3315 vs K actual , and K 1.3375 vs K actual were -1.28 to 1.34 D, -0.82 to 1.93 D and -0.09 to 2.88 D, respectively.

Discussion
Keratometric index is critical in both the calculation of total corneal power and the prediction of intraocular lens power. Clinically, the commonly used keratometric indices include the conventional 1.3375 and the 1.3315 based on the Gullstrand schematic eye. However, the keratometric indices calculated in real eyes using Scheimpfulg camera system [1] and Slit-scan system [6] were smaller than 1.3375 and 1.3315. To the best to our knowledge, this is the first study to calculate keratometric index based on data derived from RTVue FD-OCT. In our study, we used the RTVue FD-OCT to measure the anterior and posterior corneal curvature within central 3 mm zone and central corneal thickness in untreated, post-LASIK/ PRK and keratoconus eyes. Then we used the data obtained to calculate the mean ratio of the  anterior corneal curvature to the posterior corneal curvature (Ratio) and the mean calculated keratometric index (N cal ) in each group. In untreated controls, it was shown that the Ratio was 1.176 ± 0.022, and N cal was 1.3299 ± 0.00085. Jin et al. [17] calculated a Ratio of 1.223±0.028 and a keratometric index of 1.3280 ± 0.0011 in 352 Chinese untreated eyes, and a Ratio of 1.205±0.027 and a keratometric index of 1.3287 ± 0.0010 in 205 German untreated eyes using data derived from Pentacam HR. Ho et al [5] used the data obtained by Pentacam to calculate a     Consequently, a larger total corneal power will be calculated based on a larger posterior corneal curvature (Formula 2), thus a larger N cal will be calculated (Formula 3). The differences of R posterior obtained by RTVue FD-OCT, Pentacam Scheimpflug camera system and Slit-scan system RTVue maybe caused by distinct measurement principles on which each device is based. RTVue FD-OCT with a speed of 26000 axial scans per second has an axial resolution of 5 μm. The corneal mapping model contained 6.0 mm line scans on 8 meridians with 1019 axial scans centered on the pupil, and the whole scan model was finished within 0.32 seconds. [16,20] The Pentacam using a rotating Scheimpflug camera to image the anterior segment, provides the anterior and posterior corneal surfaces, pachymetry maps. And it measures 50000 or 125000 data points in less than 2 seconds. [21][22][23] The OrbscanⅡis based on a slitscan combining Placido ring technology. The data collected are processed to generate approximately 9000 data points over a 10 mm corneal diameter, and the Placido ring reflections are used to supplement slit-scan data to generate curvature-based map. [ In our study, it was shown that Ratio from post-LASIK/PRK group (1.314 ± 0.042) was the largest; followed by Ratio from keratoconus group (1.229 ± 0.118); whereas Ratio from untreated controls was the smallest (1.176 ± 0.022) (all P<0.05). On the contrary, N cal from post-LASIK/PRK group (1.3242 ± 0.00171) was the smallest; followed by N cal from keratoconus group (1.3277 ± 0.0046); whereas N cal from untreated controls was the largest (1.3299 ± 0.00085). We further analyzed the correlation and linear regression between Ratio and N cal in each group. It demonstrated that N cal was negatively correlated to Ratio in each group (N = 1.3752-0.03852 × Ratio (r = -0.997, r 2 = 0.995, P<0.05) (Fig 3B),N = 1.3775-0.04054 × Ratio (r = -0.999, r 2 = 0.999, P<0.05) (Fig 3D),N = 1.3759-0.03917 × Ratio (r = -0.999, r 2 = 0.999, P<0.05) (Fig 3F). Here, we can try to explain the reason why N cal was closely negatively correlated to Ratio from the origin of the 2 parameters. We can combine formula 2 and formula 3 in Patients and Methods part. Then we obtained the equation as follows: ðn 1 À n 0 Þ=R anterior þ ðn 2 À n 1 Þ=R posterior À ðCCT=n 1 Þ Â ½ðn 1 À n 0 Þ=R anterior Â ½ðn 2 À n 1 Þ=R posterior ¼ ðn À 1Þ=R anterior where n 0 (1.000), n 1 (1.376) and n 2 (1.336) are the refractive indices of the air, the cornea and aqueous, respectively.
The equation can be simplified as: n ¼ 1:376 þ ð0:011 Â CCTÞ=R posterior À 0:04 Â Ratio In the simplified formula above, the value of (0.011×CCT)/R posterior was very small. We assumed that CCT and R posterior were 520 um and 6.5mm, respectively, then the value of (0.011×CCT)/R posterior was calculated as 0.00088, which could be ignored comparing the constant of 1.376 in the same formula. Thus, we obtained a new formula: n = 1.376-0.04 × Ratio, which was very similar to the regression formulas in untreated, post-LASIK/PRK and keratoconus group. It means that N cal and Ratio obtained from untreated, post-LASIK/PRK and keratoconus eyes have excellent similar linear relationship. In our study, the total corneal powers were calculated using N cal in each group (K cal ), the keratometric index of 1.3315 derived from Gullstrand schematic eye (K 1.3315 ) and the conventional keratometric index of 1.3375 (K 1.3375 ). And we also compared K cal , K 1.3315 and K 1.3375 to the total corneal powers calculated based on Gaussian optics formula (K actual ). In all the 3 groups, K cal and K actual were comparable (all P = 1.00). K 1.3315 was 0.21 ± 0.11 D larger than K actual in untreated controls, and the difference increased to 0.56 ± 0.70 D in keratoconus eyes, and the difference was 0.85 ± 0.18 D. Similarly, K 1.3375 were 0.99 ± 0.12D, 1.40 ± 0.76D and 1.56 ± 0.16 D larger than K actual in untreated, keratoconus and post-LASIK/PRK eyes, respectively. In Ho et al's study [5] in which Pentacam Scheimpflug camera system was applied, K cal and K actual were also comparable in untreated controls, but the 95% CI was larger than that in our study (-0.46 D to 0.46 D in Ho et al's, -0.21 D to 0.21 D in ours). The differences between K 1.3315 and K actual , K 1.3375 and K actual were larger than those in our study (0.85 D and 1.21 D in Ho et al's study). And also the 95% CI were larger than ours (-0.03 D to 0.89 D and 0.75 D to 1.67 D in Ho et al's study; -0.01 to 0.42 D and 0.76 to 1.21 D in ours). It demonstrated that the agreement between K cal and K actual obtained by RTVue FD-OCT was better than that the one obtained by Pentacam Scheimpflug camera system in untreated eyes. In Wang et al's study [25] using Galilei Scheimpflug camerasy system to obtain data from untreated eyes and myopic-LASIK/PRK eyes, K 1.3375 was 1.30 D larger than K actual in untreated eyes, and the difference increased to 1.51 D in eyes after corneal refractive surgery. In Jin et al's study [17], K 1.3375 was 1.26 D larger than K actual in untreated eyes, and the difference increased to 1.71 D in eyes after corneal refractive surgery. Table 4 showed the differences between K 1.3375 and K actual obtained by distinct devices in untreated eyes and post-LASIK/PRK eyes. In our study, we found that the trends of the differences between K 1.3315 and K actual , K 1.3375 and K actual coincided with the trend of Ratio, and opposited to the trend of calculated keratometric index in the 3 groups.
The limitations of this study included: 1) a small number of eyes were included in keratoconus group; 2) the repeatability of corneal parameters obtained by RTVue FD-OCT in keratoconus group has not been proved; 3) For post-LASIK/PRK group, only eyes after myopic-LASIK/ PRK were included.
In conclusion, the ratio of anterior corneal curvature to posterior corneal curvature obtained by RTVue FD-OCT in untreated eyes is smaller than those obtained from Scheimpflug camera system and Slit-scan system in published studies, and also the calculated keratometric index obtained by RTVue FD-OCT in untreated eyes is larger than those obtained from Scheimpflug camera system and Slit-scan system in published studies. The calculated keratometric index was negatively related to the ratio of anterior corneal curvature to posterior corneal curvature in untreated, post-LASIK/PRK, and keratoconus eyes. Using the calculated keratometric index may improve the prediction accuracies of total corneal powers in untreated eyes, but not in post-LASIK/PRK and keratoconus eyes.