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Keywords:

  • corneal asphericity;
  • keratoconus;
  • posterior elevation;
  • Scheimpflug imaging

Abstract.

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References

Purpose:  To explore the effects of corneal astigmatism and asphericity on posterior elevation values calculated by different reference bodies and to compare their predictive accuracy in the diagnosis of keratoconus.

Methods:  In this prospective observational case series, 44 eyes of 24 patients with keratoconus and 70 eyes of 41 refractive surgery candidates as a control group were measured by the Pentacam Scheimpflug camera. Discriminating ability and predictors of posterior elevation measurements obtained by best fit toric ellipsoid (BFTE) and best fit sphere (BFS) reference surfaces were compared by receiver operator characteristic curves (ROC) and generalized estimating equation (GEE) models. Bland–Altman plots were used to determine the agreement between different reference surfaces.

Results:  Receiver operator characteristic curve analysis showed that posterior elevation measured by a BFTE auto had a significantly higher area under ROC curves (0.99) value than BFTE 8-mm or BFS reference surfaces. ROC analysis identified cut-off values for BFTE auto (9.5-μm), for BFTE 8-mm (10.5-μm), for BFS auto (16.5-μm) and for BFS 8-mm (15.5-μm) reference surfaces. According to GEE models, corneal cylinder and posterior asphericity had the least effect in toric ellipsoid models. Bland–Altman plots showed a systematic bias at higher values of average posterior elevation measured BFS reference surfaces.

Conclusions:  Posterior corneal elevation value measured by the Pentacam camera can effectively discriminate keratoconus from normal corneas although measured values and cut-off points depend on the selection of reference body and corneal asphericity. Toric ellipsoid reference surface seems to be the most sensitive method to differentiate keratoconus.


Introduction

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References

Keratoconus is a bilateral, noninflammatory, asymmetric, progressive disorder characterized by corneal thinning and protrusion inducing myopia and irregular astigmatism. The diagnosis of more advanced keratoconus is not complicated, because of the typical biomicroscopic and topographic findings (Rabinowitz 1998; Barr et al. 2006; McMahon et al. 2006, Belin & Khachikian 2007). In the past the diagnosis of keratoconus was based on biomicroscopic findings, corneal topography and ultrasound pachymetry (Rabinowitz 1998; Barr et al. 2006). Placido disc-based corneal topography only examines the anterior surface of the cornea, and alteration in the reference point or viewing angle may result in inaccuracy of curvature measurement (Neshburn et al. 1995; Tomidokoro et al. 2000; Wilson 2000; Ambrósio et al. 2006; Fam & Lim 2006; Konstantopoulos et al. 2007; Swartz et al.2007). Height data give a more accurate representation of the true shape of the corneal surface because they are independent of axis, orientation and position (Rüfer et al. 2005; Fam & Lim 2006; Quisling et al. 2006; Ho et al. 2008; Nilforoushan et al. 2008). The Pentacam Comprehensive Eye Scanner (Oculus Optikgeräte GmbH, Wetzlar, Germany) uses a rotating Scheimpflug camera and measures both anterior and posterior corneal surfaces by an elevation-based system (Belin & Khachikian 2009). It allows the measurement of local elevation points by fitting the corneal shape to a best fit sphere (BFS) reference surface with variable diameters or to an ellipsoid surface. Examination of the posterior corneal surface is important in the early diagnosis of keratoconus as epithelial compensation can mask the presence of an underlying cone on the anterior surface (Reinstein et al. 2009). There are several previous papers concerning the discriminating potential of posterior elevation in keratoconus; however, there is no accordance in reference body selection, which makes the comparison of different study result difficult (Fam & Lim 2006; Quisling et al. 2006; De Sanctis et al. 2008; Nilforoushan et al. 2008; Schlegel et al. 2008; Khachikian & Belin 2009; Koller et al. 2009; Miháltz et al. 2009). The purpose of this study was to explore the effect of topographic parameters and corneal shape factor on the values of posterior elevation obtained by different reference surfaces and to compare their predictive accuracy in the diagnosis of keratoconus. According to our knowledge, this is the first study treating the problem of the diversity of posterior elevation values obtained by different calculating methods.

Methods

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References

This institutional study was set at the Department of Ophthalmology, Semmelweis University, Budapest, Hungary. In this study, 44 eyes of 24 patients (15 men, 9 women) from keratoconus suspect cases to moderate keratoconus cases were included (age: 35.25 ± 10.67). Severe cases were excluded, because of potential stromal haze or scar formation, which may alter the optical transparency of the cornea and image acquisition of the Pentacam. Both eyes of each patient have undergone a complete ophthalmologic evaluation including slit-lamp biomicroscopy, keratometry, retinoscopy, ophthalmoscopy and Placido disc-based videokeratography. Keratoconus suspect cases were diagnosed when topographic abnormality was observed according to the Rabinowitz criteria without any slit-lamp findings (Rabinowitz 1995; Rabinowitz & Rasheed 1999). The criteria for diagnosing keratoconus were defined as the existence of central thinning of the cornea with Fleischer ring, Vogt’s striae or both by slit-lamp examination in addition to topographic findings. In the control group, 70 eyes of 41 refractive surgery candidates (24 men, 17 women) were included (age: 39.69 ± 15.77). Both eyes of each subject were used in the study, except for 12 fellow eyes because of previous refractive surgery or trauma. Control subjects were age-matched. Patients, who wore rigid contact lenses, were asked to stop using them for 4 weeks, and soft contact lenses were ceased for at least 1 week before assessment. All eyes were examined with the Pentacam HR (version number: 1.16 r: 23), used by three trained examiners without application of dilating or anaesthetic eye drops. The readings were taken as recommended in the instruction manual. Briefly, the patients were instructed to keep both eyes open and fixate on the black target, in the centre of the blue fixation beam. After attaining perfect alignment, the instrument automatically took 25 Scheimpflug images within 2 seconds. The measurement results were checked under the quality specification (QS) window, only the correct measurements (‘QS’ reads OK) were accepted; if the comments were marked yellow or red, the examination was repeated. For local posterior elevation measurements, four different reference surfaces were chosen: the BFS with autodiameter and fixed 8-mm-diameter settings and the best fit toric ellipsoid (BFTE) with autodiameter and fixed 8-mm-diameter settings. Compared to values of posterior elevation by BFS with fixed 8 mm diameter, those obtained by 9 mm showed an increased variance, indicating that further analysis would be less reliable (data not shown). For all methods, the float map was chosen, which means that the reference body has no fixed centre, and the average distance between posterior surface of the cornea and the sphere surface is optimized to be as small as possible. Elevation maps show the difference in height between cornea and reference body; their value is positive, when the measured point of the cornea is above the reference body, and negative, when it lies below. Posterior elevation data were read at the thinnest point of the cornea. Posterior corneal surface asphericity (Q value) was calculated at the sagittal angle ring at 30° centred on the apex. Statistical analyses were performed with SPSS 15.0 software (SPSS Inc., Chicago, Il, USA). Normal distribution assumption could be accepted for all of the variables according to the Shapiro–Wilks’ W test. For group comparisons of continuous variables, the independent sample t-test was used. A p value < 0.05 was considered statistically significant. Because binocular data of patients were evaluated in this study, we proposed the use of the bootstrap resampling technique as a tool to assess within-subject correlations. The basic idea of the bootstrap (Efron 1979) is to produce a random sample, which is obtained by sampling, with replacement, from the original pool of data. The bootstrap sample is then used to compute the estimate of the parameter, and this procedure (extraction of the random sample and computation of the estimate) is repeated 3000 times to create a nonparametric distribution of the parameters providing the estimated mean and the 2.5% and 97.5% confidence limits (95% CI). Receiver operator characteristic curves (ROCs) were used to compare discriminating ability and to determine cut-off values of posterior elevation measurements obtained by different reference surfaces. Intraclass (between eyes of the same patient) correlation was overcome using booststrap method deriving estimates of mean and confidence intervals for area under the ROC (AUROC). Comparison of AUROC values of different indices was made to test significant differences between reference surfaces. To explore the effect of corneal cylinder and asphericity on different calculation methods of posterior elevation, four independent generalized estimating equation (GEE) models were constructed using posterior elevation values calculated by the four reference surfaces as continuous dependent variables. GEE models take into account between-eye correlations by treating data from eyes of patients in statistical analysis as repeated measures (Zeger et al. 1988; Hanley et al. 2003). GEE is valid with data missing completely at random, i.e. analysing some patients with data of one eye only (Touloumi et al. 2001) as occurred in many previous studies. Comparisons of different regression models for a given dependent variable were assessed by the value of the Corrected Quasi Likelihood under Independence Model Criterion (QICC). Lower value of QICC indicates better fit to data (Zeger et al. 1988; Hanley et al. 2003). Finally, Bland–Altman limits of agreement were calculated to determine the agreement between the most different reference surfaces across posterior elevation values.

Results

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References

Table 1 summarizes mean and standard deviation values of topographic, asphericity and posterior elevation parameters in the two groups. Correlation analyses showed that corneal asphericity is strongly correlated with keratometric, pachymetric values and with the vertical distance of the minimum pachymetry from the corneal apex in the keratoconic group but not in the control group (Table 2).

Table 1.   Mean (SD) values of variables in the keratoconic and in the control groups.
VariablesKeratoconus (n = 44)Control (n = 70)t-test (p)
  1. BFS = best fit sphere; BFTE = best fit toric ellipsoid.

Keratometry steep (D)50.28 (5.77)43.97 (1.5)<0.001
Keratometry flat (D)46.59 (4.87)42.81 (1.29)<0.001
Cylinder (D)3.58 (2.79)1.19 (0.88)<0.001
Minimum pachymetry (MP) (μm)464.9 (54.9)553.1 (28.4)<0.001
Horizontal position of MP from apex (mm)−0.43 (0.40)−0.17 (0.16)<0.001
Vertical position of MP from apex(mm)−0.6 (0.39)−0.03 (0.18)<0.001
Posterior surface asphericity (Q)−0.7 (0.74)−0.09 (0.25)<0.001
Posterior elevation BFTE auto (μm)40.77 (22.9)−0.63 (6.88)<0.001
Posterior elevation BFTE 8 mm (μm)42.68 (33.44)1.38 (5.75)<0.001
Posterior elevation BFS auto (μm)56.30 (32.95)5.75 (5.26)<0.001
Posterior elevation BFS 8 mm (μm)67.57 (48.57)5.66 (5.02)<0.001
Table 2.   Correlations of posterior asphericity Q index to keratometry, minimum pachymetry and shift of minimum pachymetry in the keratoconus and in the control groups.
ParametersKeratoconusControlDifference
rprpp
  1. MP = minimum pachymetry.

Keratometry flat (D)−0.76<0.0010.21>0.05<0.001
Keratometry steep (D)−0.76<0.0010.18>0.05<0.001
Minimum pachymetry (μm) 0.58<0.0010.05>0.05<0.001
Horizontal position of MP from apex (mm) 0.02>0.050.12>0.05>0.05
Vertical position of MP from apex (mm)−0.37<0.010.03>0.05<0.001

Figure 1 depicts ROC curves for the different measurement methods of posterior elevation. As Table 3 shows, posterior elevation measured by BFTE autoreference surface had a significantly higher AUROC value than BFTE 8-mm, BFS 8-mm or BFS autoreference surfaces had. Table 4 shows the recommended cut-off values with the corresponding specificity and sensitivity levels.

image

Figure 1.  Receiver operator characteristic (ROC) curves for posterior elevations calculated by the four different reference surfaces.

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Table 3.   Area under the ROC curve values with 95% confidence limits and pairwise comparisons of different reference surfaces.
Reference surfaceAUROC95% CLpComparison (p)
  1. AUROC = area under the ROC curve, BFS = best fit sphere, BFTE = best fit toric ellipsoid, CL = confidence limits, ROC = receiver operator characteristic.

BFTE auto0.990.98–1.00<0.001
BFTE 8 mm0.960.92–0.99<0.0010.04
BFS auto0.960.90–0.99<0.0010.05
BFS 8 mm0.940.89–0.98<0.0010.02
Table 4.   Sensitivity (Sn) and specificity (Sp) values in % for different cut-off levels (μm) of the four elevation parameters, including specificity of 100%.
BFTE autoBFTE 8 mmBFS autoBFS 8 mm
Cut-offSnSpCut-offSnSpCut-offSnSpCut-offSnSp
  1. Recommended cut-off levels are bolded. BFS: Best Fit Sphere; BFTE: Best Fit Toric Ellipsoid.

6.598917.5958414.5938612.59589
7.595948.5939214.5939213.59592
8.595959.5939515.5939714.59195
9.5959710.5919516.5939815.59198
11939711.5889717.5909816.58698
148910014.58610021.08610021.086100

The effect of posterior corneal cylinder and asphericity on fitting the posterior corneal surface was assessed by four independent GEE models using posterior elevation values calculated by the four reference surfaces as dependent variables. Corneal cylinder had no significant effect on posterior elevation calculated by BFTE auto (p > 0.05) and BFTE 8 mm (p > 0.05) in contrast to posterior elevation values calculated by BFS 8 mm or BFS auto (p = 0.004 and p = 0.03, respectively). Although posterior asphericity showed significant effect on posterior elevation values calculated by either toric or spherical reference surfaces, regression models showed better accuracy of fit and smaller influence in case of BFTE auto and BFTE 8-mm compared to BFS auto and BFS 8-mm reference bodies.

The Bland–Altman plot showed a systematic bias at higher values of posterior elevation measured by BFS 8 mm compared to BFTE auto (Fig. 2). Quadratic term had the best fit to data (r2 = 0.79, p < 0.001), indicating the overestimation of posterior elevation values using spherical reference surfaces primarily beyond 50 μm. An example of different reference body fitting methods and a schematic representation of posterior elevation calculating methods are depicted on Fig. 3.

image

Figure 2.  Bland–Altman plot for comparison of best fit toric ellipsoid auto and best fit sphere (BFS) 8-mm reference surfaces. The graph shows mean difference of 18.9 μm (95% limits of agreement: −16.8 to 55.1 μm), indicating the overestimation of posterior elevation by fixed 8-mm BFS which tendency can be fit by a quadratic curve (r2 = 0.79, p < 0.001).

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image

Figure 3.  Posterior elevation maps of a keratoconic patient with a best fit toric ellipsoid autoreference body (Top Left) and a fixed 8-mm best fit sphere reference body (Top Right). Schematic cross-sectional view of the cornea and ellipsoid reference body (Bottom Left) and spherical reference body (Bottom Right) in the steepest meridian (99°). Areas coloured red correspond to corneal elevation relative to reference surface, elevation: + value. Areas coloured blue correspond to corneal depression relative to reference surface, elevation: − value. Site of the thinnest point marked: degree (°).

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Finally, ROC analysis was performed to test the discriminating ability of posterior elevation between normals and keratoconus suspects using auto-BFTE setting. The lower AUROC value (0.84, 95% CL: 0.71–0.97; p < 0.001) indicated that posterior elevation is a weaker sole predictor of suspect cases than a predictor of keratoconus. By setting the posterior elevation cut-off value at 7.5 μm, suspect keratoconus cases could be detected with 60% sensitivity and 90% specificity.

Discussion

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References

Improved patient selection to avoid post-LASIK ectasia has become an area of active research and interest. The early diagnosis of keratoconus based on curvature topography and pachymetric measurement is often challenging. More recent studies, based on the elevation data obtained by Orbscan and Pentacam measurements, suggest that posterior corneal elevation is an early and sensitive sign of keratoconus (Tomidokoro et al. 2000; Rao et al. 2002; Fam & Lim 2006; Quisling et al. 2006; Emre et al. 2007; De Sanctis et al. 2008; Nilforoushan et al. 2008; Schlegel et al. 2008; Khachikian & Belin 2009; Koller et al. 2009; Miháltz et al. 2009; Reinstein et al. 2009). Another advantage of analysing the posterior surface of the cornea is that this map is not influenced by tear-film irregularities. This study reports the effect of reference body selection on posterior elevation measurement in keratoconic eyes. In this study, we used the bootstrap resampling technique to overcome between-eye correlations of data in the same study person as it was proposed in several papers previously (Martus et al. 2000; Ciolino et al. 2008). Another alternative would have been to use only one eye from each patient but because of relatively small sample size we gave preference to binocular data analysis over random selection of one eye only.

Keratoconus classically causes inferior steepening, corneal protrusion and astigmatism (Rabinowitz 1998). In our study, eyes with keratoconus showed statistically significant difference in astigmatism and posterior surface asphericity compared to the control group. Keratoconic patients had more prolate corneas (more negative posterior Q values) because of corneal protrusion. This finding is in accordance with the significant correlation we found between posterior corneal asphericity and keratometric, pachymetric values in keratoconus patients. There was no similar correlation in the control group.

The corneal surface is variably aspheric and toric; this diversity is even more pronounced in keratoconic patients. Approximating posterior corneal surface to a conic is useful as it permits the description of its shape by the apical radius and the rapidity of steepening or flattening from the apex. The ellipso-toric model besides corneal asphericity incorporates the difference in curvature between the two principal meridians (Calossi 2007). Therefore, an aspherical and toric reference surface like a toric ellipsoid would lie closer to the actual corneal surface and enhances local changes more sensitively than a reference sphere. In our study, multiple regression analysis indicated that corneal cylinder influenced posterior elevation calculations when spherical reference bodies were used, but not when toric ellipsoid surfaces were chosen. Corneal asphericity had significant effect in all fitting methods, even though it showed the least influence on posterior elevation measured by toric ellipsoid reference surface. These findings underlie the importance of corneal asphericity and toricity when analysing elevation data.

Receiver operating characteristic curve analysis showed that toric ellipsoid reference surface had significantly better ability for discriminating keratoconus from normal subjects than spherical reference surface had. The optimized cut-off for equally important sensitivity and specificity was calculated in Table 4. Using BFTE autosetting is associated with a decreased risk of masking keratoconus cases as higher specificity is associated with higher sensitivity at the optimized cut-off compared to other reference surface settings (Table 4). Although a specificity of 100% would mean that the test recognizes all actual negatives and no positives are erroneously tagged, this would be associated with a considerably decreased sensitivity level, ruling out its clinical use (Table 4).

The selection of reference body influences the magnitude of posterior elevation and thus the identified cut-off values for discriminating keratoconic corneas from normal. There are several previous papers reporting posterior elevation cut-off values characteristic of keratoconus; however, there is no accordance in reference body selection, which makes the comparison difficult. De Sanctis et al. (2008) have found a posterior elevation cut-off value of 35 μm for keratoconus and 32 μm for subclinical keratoconus using a fixed 9-mm-diameter BFS. In a previous study using autodiameter BFS, we have found a posterior elevation cut-off value of 15.5 μm with 95.1% sensitivity and 94.3% specificity for discriminating normal eyes from keratoconus (Miháltz et al. 2009). Rao et al. (2002) have found a posterior elevation greater than 40 μm by a BFS reference body as a diagnostic index for keratoconus using Orbscan data. Fam et al. identified a cut-off value of 16.5 μm for the anterior elevation using a limbus-to-limbus fit BFS reference body as the most sensitive index with ROC curve analysis for discriminating keratoconus with Orbscan (Fam & Lim 2006). The disparity between the different results obtained by Pentacam and Orbscan can be explained by the different scanning methods, but also by the reference body selection. A larger diameter BFS results in larger posterior elevation values, which explains the greater posterior elevation values found by De Sanctis et al. (2008). Our results confirm that toric ellipsoid reference body seems to compensate for extreme values, which can be seen in the Bland–Altman plots and is proved by the smaller posterior elevation cut-off value (9.5 and 10.5 μm versus 15.5 and 16.5 μm for spherical reference surfaces) identified by this fitting method. In contrast to the previously described diverse posterior elevation cut-off values from different study populations, our results are based on comparison of different calculating methods on the same data set. Bland–Altman plot analysis showed that there was a systematic bias of larger measurements by fixed 8-mm BFS reference surface than by toric ellipsoid and spherical autoreference surfaces. This analysis confirms that elevation parameters calculated by spherical reference surfaces are in accordance with results based on the toric ellipsoid reference bodies in normals, but the typically higher values of posterior elevation in keratoconic eyes are systematically overestimated using BFS reference surfaces.

Corneal asphericity was correlated with keratometric and pachymetric results, in which parameters are characteristic indicators of keratoconus progression. Toric ellipsoid reference bodies approximate this aspheric corneal surface better than spherical models, as it is proven by smaller posterior elevation values provided by this fitting method. Bland–Altman curves show that BFS is primarily less suitable to fit the more aspheric and toric (i.e. advanced) cases. The correlation between asphericity and elevation can be better understood when looking at the schematic illustration of posterior elevation calculating method on Fig. 3. An increased prolateness results in higher elevation values in the centre. It is also apparent that when a toric ellipsoid reference surface is used, the central vaulting above the reference surface has less variation and posterior elevation values around the cone apex are smaller than with a BFS.

The selection of reference body is particularly important when evaluating the progression of the disease or the effect of corneal cross-linking treatment. Corneal astigmatism increases with progression (Rabinowitz 1998), and according to the study of Koller et al. (2009), corneal asphericity changed with time in both riboflavin-treated and riboflavin-untreated keratoconus eyes. Our findings suggest that the use of toric ellipsoid reference body is the best method to compensate for these progressive changes in the calculation of posterior elevation.

Our results confirm that posterior corneal elevation value measured by the Pentacam camera can effectively discriminate keratoconus from normal corneas and that the selection of reference body and corneal asphericity has an influence on the measured values. Fitting an automatic toric ellipsoid reference surface seems to be the best method to differentiate elevation data taken from an astigmatic cornea from the elevation data of an ectatic cornea. Using this approach, with a cut-off level of 7.5-μm normal cases can be differentiated from keratoconus suspects with high accuracy (90% of specificity) and moderate sensitivity (60%), which is in good correspondence with previous findings (De Sanctis et al. 2008). However, without the assessment of clinical parameters and the topographic pattern, the diagnosis of keratoconus should not be based on elevation data alone.

Acknowledgement

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References

Contributions to Authors in each of these areas: design and conduct of the study (IK, KM); collection, management, analysis and interpretation of the data (IK, KM, ME); and preparation, review or approval of the manuscript (IK, JN, ZN).

Statement about Conformity with Author Information: the institutional ethical committee of Semmelweis University waived the need for approval of the study. The research followed the tenets of the Declaration of Helsinki, and informed consent was obtained from all of the subjects after explanation of the nature and possible consequences of the study.

References

  1. Top of page
  2. Abstract.
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgement
  8. References