Purpose
To determine novel diagnostic parameters for keratoconus, and to assess the correlation between anterior and posterior corneal surfaces based on vectorial astigmatism analyses.
Design
Retrospective case-control study.
Methods
Six hundred and ninety-eight eyes of 698 patients were enrolled in the study. Healthy corneas, or controls (C, n = 264), were compared to keratoconic corneas, further categorized as forme fruste (FFKc, n = 212) and overt keratoconus (Kc, n = 222). Corneal measurements were obtained from a Scheimpflug-based tomographer. Vectorial analyses were conducted in accordance with the method proposed by Thibos.
Results
Posterior corneal astigmatic power vector (APV) >0.23 diopter (D) yielded a test for overt Kc with sensitivity and specificity rates of, respectively, 81% and 77%, indicating a positive likelihood ratio (LR+) of 3.5 and a negative likelihood ratio (LR-) of 0.25. Posterior corneal overall blur vector (Blur) >6.45 D yielded a test slightly less sensitive and specific, with rates of 75% and 72%, respectively, associated to LR+ of 2.7 and LR- of 0.35. The highest (Spearman ρ) correlation coefficients between anterior and posterior corneal astigmatisms were associated with Blur, being 0.93 for Kc, 0.87 for C, and 0.81 for FFKc. The astigmatism vectors along the 45-degree (J 45 ) and 0-dregree meridians (J 0 ) and APV most often presented higher coefficient values for Kc and FFKc than for C ( P = .01).
Conclusions
Posterior corneal vectors APV and Blur constitute objective supplemental parameters for the diagnosis of Kc. Anterior and posterior corneal surfaces correlate in all groups, although it was not possible to accurately predict posterior astigmatism from anterior astigmatism.
Keratoconus (Kc) is a clinical term used to describe an ectatic condition in which the cornea assumes a conical shape as a result of noninflammatory thinning and protrusion. Such corneal thinning typically induces irregular astigmatism and myopia, often leading to a marked deterioration of visual acuity. Although both eyes are affected, Kc typically is manifested asymmetrically, usually at puberty, progressing into the fourth decade of life.
The estimated prevalence of Kc is approximately 50–230 per 100 000 in the general population. Severe forms of Kc are major reasons for corneal transplantation. Undiagnosed preoperative mild forms of Kc have been reported to be a principal reason for iatrogenic corneal ectasia following keratorefractive surgery.
At present, corneal topography of anterior surface, based on the Placido disk, remains the predominant method for detecting Kc. However, topography screening methods have inherent shortcomings. Moderate to severe Kc cases can easily be identified using typical clinical findings and topographic screening. But subclinical forms of the condition that may later develop ectatic changes still represent a diagnostic challenge.
Recently corneal tomography has increased the ability of ophthalmologists to identify corneal ectasia at a much earlier stage. Newer techniques, such as Scheimpflug-based tomography, have been developed to obtain a complete analysis of corneal geometry, permitting characterization of the anterior and posterior surfaces and pachymetric mapping. As Kc-associated changes apparently first arise on the posterior corneal surface, it has been suggested that corneal Scheimpflug tomography may readily detect topographically normal Kc cases. Recent studies, based on Scheimpflug tomography, have found that the shapes of anterior and posterior corneal surfaces correlate in a predictable way in the normal healthy eye, although conflicting observations have been reported.
Astigmatism is a vectorial variable: in addition to its magnitude, astigmatism has an orientation defined by its axis. A precise and complete analysis of corneal astigmatism must take this vectorial character into account.
The aims of our study were, first, to characterize the astigmatism of posterior corneal surface, based on vector analysis, for healthy corneas or normal controls (C), in comparison to keratoconic corneas, further categorized as forme fruste (FFKc) and overt Kc. Whether such characteristics could be useful as novel diagnostic parameters was also assessed. In parallel to this analysis, we sought secondarily to evaluate any correlations between vectors of anterior and posterior corneal surfaces. All analyses were conducted within each group, followed by comparisons between groups.
Methods
The research protocol of this retrospective case-control study was approved by the Ethics Committee of the University of São Paulo (São Paulo, Brazil). Our study is registered at http://www.clinicaltrials.gov (identifier NCT02698709 ). The tenets of the Declaration of Helsinki were followed throughout the study.
The study included 698 eyes of 698 patients. Two databases of patients were examined at the Instituto de Olhos Renato Ambrósio (Rio de Janeiro, Brazil), between July 12, 2004 and October 7, 2013. One of the databases contained the information on normal candidates for refractive surgery who did not develop any sign of corneal ectasia after laser in situ keratomileusis during a 2-year follow-up period, labeled as C (n = 264). The second database included information concerning keratoconic corneas, categorized as overt Kc (n = 222) if both eyes manifested classic Kc-suggestive topographic features, such as corneal steepness higher than 47.20 diopters (D), superior-inferior asymmetry higher than 1.40 D, and thinnest pachymetric reading lower than 500 μm ; or FFKc (n = 212) if only 1 eye exhibited such features. For C and overt Kc groups, only 1 eye was randomly selected per patient, in order to avoid any eventual correlation existing between the eyes of a single patient. For the FFKc group, only the unaffected eyes were enrolled in the study.
Contact lens wear was discontinued at least 3 weeks for rigid contact lens and 1 week for soft contact lens before the assessment. All corneal astigmatism measurements were obtained from a rotating Scheimpflug corneal tomographer (Pentacam; Oculus Optikgeräte GmbH, Wetzlar, Germany). The patient’s chin was placed on the chin rest, and the forehead was placed against the forehead strap. After blinking a few times, the patient was asked to open both eyes and stare at the fixation target. Proper alignment was obtained using a joystick, and then the automatic release mode started the scan using 25 single Scheimpflug images captured within 2 seconds for each eye. By “inclusion criterion,” it was meant that only patients with good-quality Scheimpflug scans (labeled “OK” by the device in the “Examination Quality Specification”) were selected. The exclusion criteria were previous eye surgery or trauma and any sort of corneal scarring that might interfere with keratometric data acquisition.
For each group (C, overt Kc, and FFKc), corneal astigmatism values were obtained as follows:
- (1)
Anterior astigmatism was calculated from simulated keratometric readings of central 3-mm optical zone (both steepest and flattest ones), multiplied by (1.376 − 1.0)/(1.3375 − 1.0), assuming that the refractive index of the air is 1.0, the refractive index of the cornea is 1.376, and the standardized corneal refractive index is 1.3375;
- (2)
Posterior astigmatism was calculated by ray tracing from Snell’s Law of refraction, taking into account the parallel incidence of light beams over the anterior corneal surface, the corneal width, the indices of refraction of the cornea (1.376), and the aqueous humor (1.336);
- (3)
For both anterior and posterior surfaces, astigmatism alignment (α) coincides with the steepest meridian of that surface.
Vector astigmatism analyses were conducted using the method proposed by Thibos for both anterior and posterior surfaces according to the following equations:
- (1)
Average keratometric reading (M) = (K steep + K flat )/2;
- (2)
Vector along the 0-degree meridian (J 0 ) = [−(K steep − K flat )/2] × cos2α;
- (3)
Vector along the 45-degree meridian (J 45 ) = [−(K steep − K flat )/2] × sen2α;
- (4)
Astigmatic power vector (APV) = (J 0 2 + J 45 2 ) 1/2 ;
- (5)
Overall blur vector (Blur) = (M 2 + J 0 2 + J 45 2 ) 1/2 .
The above-mentioned calculations were performed using Microsoft Excel (version 14.4.7; Microsoft, Inc., Redmond, WA, USA), and statistical analysis was performed using IBM SPSS (version 23.0; IBM, Inc., Armonk, NY, USA) for Macintosh. Descriptive evaluation of data was performed using the mean and median, interquartile range (IQR), and 95% confidence interval (95% CI). Normality of all data samples was checked by the Shapiro-Wilk test. Because normal sample distribution was seldom found among our data, nonparametric tests were chosen. The Mann-Whitney U test was used for comparisons between groups. The Spearman correlation coefficient (ρ) was used to assess the strength of the correlations between pairs of variables. A P value of less than .05 was considered statistically significant. Receiver operating characteristic (ROC) curves were used to determine the overall predictive accuracy of test parameters, as described by the area under the curve (AUC), to calculate the sensitivity and specificity rates and, hence, positive and negative likelihood ratios of such parameters.
Results
The mean age of the patients was 36.7 years. The median age was 32.4 years, with an IQR of 20.8 years. The subgroups of patients and their respective demographic data are summarized in Table 1 .
| C | FFKc | Kc | |
|---|---|---|---|
| Eyes (n) | 264 | 212 | 222 |
| R/L (n) | 130/134 | 104/108 | 112/110 |
| F/M (n) | 138/126 | 85/127 | 91/131 |
| Patient age (y) | |||
| Mean | 44.0 | 30.8 | 33.7 |
| Median | 44.6 | 31.1 | 27.8 |
| IQR | 19.6 | 14.7 | 13.8 |
Table 2 compares vector parameters of posterior corneal surfaces between groups. The majority of parameters assessed exhibited statistically significant differences between groups ( P value < .05). Exceptions were (1) the orientation of the steepest meridian between FFKc and overt Kc; (2) the toricity (defined as the difference between the steepest and the flattest corneal keratometric readings) of group C compared to that of FFKc; (3) the astigmatic component J 45 , which exhibited no difference among all groups; and (4) the astigmatic power vector (APV), which exhibited no difference between C and FFKc groups.
| C | FFKc | Kc | P Value a | |||
|---|---|---|---|---|---|---|
| C vs FFKc | C vs Kc | FFKc vs Kc | ||||
| K steep (D) | ||||||
| Mean | −6.49 | −6.40 | −7.48 | .030 | .000 | .000 |
| Median | −6.50 | −6.40 | −7.20 | |||
| IQR | 0.30 | 0.40 | 1.18 | |||
| α steep (°) | ||||||
| Mean | 82.0 | 90.8 | 88.4 | .006 | .038 | .916 |
| Median | 89.0 | 92.5 | 89.6 | |||
| IQR | 19.0 | 32.8 | 62.1 | |||
| ΔK (D) | ||||||
| Mean | 0.33 | 0.35 | 0.83 | .300 | .000 | .000 |
| Median | −0.30 | 0.30 | 0.70 | |||
| IQR | 0.20 | 0.20 | 0.60 | |||
| M (D) | ||||||
| Mean | −6.32 | −6.23 | −7.60 | .001 | .000 | .000 |
| Median | −6.30 | −6.20 | −6.85 | |||
| IQR | 0.30 | 0.35 | 1.00 | |||
| J 0 (D) | ||||||
| Mean | −0.15 | −0.12 | −0.14 | .004 | .299 | .541 |
| Median | −0.14 | −0.12 | −0.12 | |||
| IQR | 0.11 | 0.15 | 0.37 | |||
| J 45 (D) | ||||||
| Mean | 0.00 | 0.00 | −0.03 | .360 | .758 | .806 |
| Median | 0.01 | −0.01 | 0.00 | |||
| IQR | 0.09 | 0.15 | 0.47 | |||
| APV (D) | ||||||
| Mean | 0.17 | 0.17 | 0.41 | .403 | .000 | .000 |
| Median | 0.15 | 0.15 | 0.35 | |||
| IQR | 0.10 | 0.10 | 0.30 | |||
| Blur (D) | ||||||
| Mean | 6.32 | 6.23 | 7.08 | .000 | .000 | .000 |
| Median | 6.30 | 6.20 | 6.85 | |||
| IQR | 0.30 | 0.35 | 1.01 | |||
The AUC of the ROC curve, plotted for posterior corneal APV between C and overt Kc, shown in Figure 1 , reached 0.855, the highest value found in our study. A cutoff value of 0.50 D yielded a test for overt Kc with sensitivity and specificity rates, respectively, of 27% and 100%. This cutoff value corresponds to the highest value found for C. An alternative cutoff value of 0.23 D yielded a sensitivity of 81%, with a specificity of 77%. Consequently, a positive likelihood ratio (LR+) of 3.5 and a negative likelihood ratio (LR-) of 0.25 were calculated.
The AUC of the ROC curve, plotted for posterior corneal blur (Blur) between C and overt Kc, shown in Figure 2 , reached 0.790. A cutoff value of 7.11 D yielded a test for overt Kc with sensitivity and specificity rates of 38% and 100%, respectively. Such a cutoff value, arbitrarily chosen, corresponds to the highest value found for C. An alternative cutoff value of 6.45 D yielded a test with a sensitivity of 75%, with a specificity of 72%. Hence an LR+ of 2.68 and an LR- of 0.35 were calculated.
