Detection of Corneal Ectasia Using OCT Maps of Pachymetry and Posterior Surface Mean Curvature

Abstract

Purpose:

To quantify the abnormal corneal thinning and posterior surface steepening that is observed in keratoconus with an Ectasia index.

Methods:

Optical coherence tomography (OCT) was used to image the corneas of normal subjects and patients with varying stages of keratoconus (manifest, subclinical, and forme fruste). Maps of corneal pachymetry and posterior surface mean curvature were generated, and an Ectasia index was calculated by multiplying Gaussian fits obtained from the two types of maps. Repeated 5-fold cross-validation was used to evaluate the ability of the Ectasia index to differentiate between normal and keratoconic eyes. The classification performance of the Ectasia index was compared to minimum pachymetry and maximum posterior mean curvature.

Results:

32 eyes from 16 normal subjects, 89 eyes from 63 manifest keratoconus patients, 16 eyes from 15 subclinical keratoconus patients, and 26 eyes from 26 forme fruste keratoconus patients were included in the study. During cross-validation, 100% of the manifest (89/89) and subclinical (16/16) keratoconus eyes were correctly classified by the Ectasia index. The average classification accuracy for the forme fruste keratoconus group was 63 ± 21% (16.4/26). The specificity for the normal group was 91 ± 10% (29.1/32). The Ectasia index had a higher sensitivity for keratoconus detection and similar specificity in comparison to minimum pachymetry and maximum posterior mean curvature.

Conclusions:

The Ectasia index could be a valuable additional metric for clinicians to consider when screening for keratoconus.

Introduction

Accounting for approximately two-thirds of the eye’s refractive power, the cornea plays an important role in the visual performance of the eye.¹ Corneal ectasia is a general term for a group of conditions in which the cornea becomes abnormally thin and takes on a conical shape.² This irregular corneal shape can cause visual distortions that cannot be corrected with spectacles. Keratoconus is the most common cause of corneal ectasia,³ and early detection is crucial during refractive surgery screening because undetected keratoconus is a major risk factor for developing iatrogenic ectasia.^4,5 Early detection is also important because treatments such as collagen cross-linking can be instituted at an early stage to halt disease progression.⁶

The current gold standard for keratoconus detection is corneal topography which is used to map the shape of the cornea. Early topographers relied on Placido disc reflections to determine the shape of the anterior corneal surface.⁷ More recent technologies such as scanning slit imaging (Orbscan II; Bausch & Lomb, Bridgewater, New Jersey), Scheimpflug imaging (Pentacam; Oculus Optikgeräte GmbH, Wetzlar, Germany), and optical coherence tomography (OCT) have made it possible to map the topography of both the anterior and posterior surfaces of the cornea.⁸ In addition to topography, quantifying the characteristic corneal thinning is an effective approach for keratoconus detection. Tomographic imaging has led to advancements in measuring pachymetry because it makes it possible to generate corneal thickness maps rather than making point measurements at discrete locations.^9,10 OCT has become a popular method for mapping corneal pachymetry due to its fast scanning speeds and high resolution.¹¹

Given that maps of both pachymetry and posterior surface topography can be generated by tomographic imaging, the Global Consensus on Keratoconus and Ectatic Diseases has stated that tomography is the most promising approach for detecting ectasia.¹² Following this guidance, we formulated a new metric for keratoconus detection, the Ectasia index, which is computed from OCT maps of corneal pachymetry and posterior surface mean curvature. Mean curvature provides an advantage over axial or tangential power because it is unaffected by astigmatism, thus making ectatic cones easier to recognize.¹³

Patients and Methods

Study Recruitment

Keratoconus patients and normal controls were recruited for this study. Participants were enrolled at the Casey Eye Institute (Oregon Health & Science University, Portland, Oregon) and the Affiliated Eye Hospital of Wenzhou Medical College (Wenzhou, China). Written informed consent was obtained from all participants, and the institutional review boards of both institutions approved the study protocol. The study was carried out in accordance with the tenets of the Declaration of Helsinki and the Health Insurance Portability and Accountability Act of 1996.

Normal controls were defined as eyes with a normal slit-lamp examination, a normal topography map appearance, and a corrected distance visual acuity (CDVA) ≥ 20/20. Keratoconus eyes were divided into three groups:¹⁴

1. Manifest keratoconus: slit-lamp finding consistent with keratoconus (e.g. Vogt’s striae, Fleischer’s ring, Munson’s sign, Rizutti’s sign, apparent focal bulging and thinning); or a CDVA < 20/20 and topography characteristic of keratoconus (e.g. asymmetric bowtie with skewed radial axis, central or inferior steep zone).

2. Subclinical keratoconus: normal slit-lamp examination and a $\mathrm{C}\mathrm{D}\mathrm{V}\mathrm{A}\ge 20/20$, but topography characteristic of keratoconus.

3. Forme fruste keratoconus (FFK): no signs of keratoconus (normal slit- lamp exam, a $\mathrm{C}\mathrm{D}\mathrm{V}\mathrm{A}\ge 20/20$, and normal topography) but the contralateral eye has manifest or subclinical keratoconus.

Standard corneal topography maps were acquired using a Scheimpflug (Pentacam) or a scanning slit (Orbscan II) topographer. BAD-D was obtained for all eyes scanned by the Pentacam. Any eye with a history of ocular surgery was excluded from the study.

OCT Map Generation

All OCT scans were obtained using the Pachymetry+Cpwr radial scan pattern on the Avanti or RTVue Fourier-domain systems (Optovue Inc., Fremont, CA, both FDA approved). Images were acquired across eight equally spaced meridians of the cornea centered on the pupil, with each line scan having a length of 6 mm (Figure 1A). The scan pattern was repeated five times during a single scan for a total of 40 images per scan.

Figure 1.

A) Radial scan pattern used to obtain OCT images of the cornea. B) OCT image from an eye with keratoconus showing the segmented anterior and posterior corneal surfaces. C) Pachymetry and D) posterior mean curvature maps for the same eye.

The anterior and posterior surfaces of the cornea were segmented in each image (Figure 1B) using a custom edge detection algorithm (MATLAB, MathWorks Inc., Natick, MA).¹⁵ The posterior surface boundary was adjusted to remove the imaging artifact caused by the difference in refractive index between air and corneal tissue.¹⁴ The mean curvature of the posterior corneal surface was mapped using a custom OCT topography algorithm also created in MATLAB.¹⁶ Mean curvature provides a measurement of local surface curvature and is defined as:

$$C_m(x,y)=\frac{1}{2}\left[K_1\left(x,y\right)+K_2\left(x,y\right)\right]$$ (Eq. 1)

where $K_1$ and $K_2$ are the principal surface curvatures (in 1/m units) at point $\left(x,y\right)$ of the corneal elevation map.¹⁷ Both the pachymetry and mean curvature maps were cropped to a diameter of 5 mm to remove potential measurement errors at the scan boundary.

Gaussian Fitting of Pattern Deviation Maps

The pachymetry and mean curvature maps were converted to pattern deviation (PD) maps using a previously published process.¹⁸ In short, the maps were first normalized by dividing by the average value of the respective map. The PD map was then computed as the difference between the normalized patient map and a normalized population map representing the typical map pattern in healthy eyes. For pachymetry PD maps, negative values indicate a region with more thinning (relative to the overall corneal thickness) than a healthy eye. Similarly, regions with positive values on the mean curvature PD maps are interpreted as having more steepening than a healthy eye.

Gaussian fitting of the PD maps was performed to calculate the Ectasia index. For all fits, the width of the Gaussian waveform was fixed while the amplitude was allowed to vary. A different width was used for the pachymetry and posterior mean curvature PD maps to reflect the difference in the typical size of the keratoconic cone in each map. The pachymetric characteristic width was calculated in a previous study.¹⁹ The characteristic width for the posterior mean curvature PD maps was computed by Gaussian fitting the maps of the manifest keratoconus eyes with no bounds placed on the Gaussian width. The characteristic width was assigned to be the median value.

Vector analysis was used to determine the typical spatial relationship between the location of maximum relative thinning (minimum value on the pachymetry PD map) and the location of maximum relative steepening (maximum value on the posterior mean curvature PD map) for the same eye. All three keratoconus groups were combined for the vector analysis, and the points of maximum relative thinning and maximum relative steepening were identified within a keratoconus-specific search area (Figure 2). The search area was computed in a previous study and represents the 99% confidence region for cone location in manifest keratoconus eyes.¹⁹ Eyes for which one or both of these points were located at the edge of the map or the boundary of the search area were removed from the analysis. The average offset vector between the two points was calculated.

Figure 2.

Locations of minimum pachymetry PD values (red circles) and maximum posterior mean curvature PD values (blue triangles) for all of the keratoconus eyes. The yellow arrow indicates the average offset vector between the minimum pachymetry PD location and the maximum posterior mean curvature PD location. Points located at the boundary of the map or search area were excluded from the calculation of the average vector. S = superior, T = temporal, I = inferior, N = nasal.

Ectasia Index Calculation

The Ectasia index was computed from Gaussian fits of the pachymetry and posterior mean curvature PD maps (Figure 3). First, the location of maximum relative thinning was identified on the pachymetry PD map within the search area mentioned earlier. Gaussian fitting was then performed on a 4 mm diameter sub-region of the map centered at this location. This sub-region could include portions of the map outside of the search area but was cropped at the edge of the map. The center of the Gaussian fit for the posterior mean curvature PD map was shifted by the offset vector described above. If the location of maximum relative thinning was located near the edge of the map, the magnitude of the shift was reduced so that the Gaussian center for the posterior mean curvature PD map remained within the map boundary. The two Gaussian maps were multiplied together to generate an Ectasia map ($G_E$):

$$G_E=100\times \sqrt{G_{pachy}(x,y)\times G_{mc}(x,y)}$$ (Eq. 2)

where $G_{pachy}$ and $G_{mc}$ are the Gaussian fits of the pachymetry and posterior mean curvature PD maps, respectively, The Ectasia index was calculated as:

$$EctasiaIndex=-\sqrt{\left|G_E(x_c,y_c)\right|}\times sign\left(G_E(x_c,y_c)\right)$$ (Eq. 3)

where $G_E$ is the Ectasia map and $(x_c,y_c)$ is the center location of the Gaussian shape on the Ectasia map. For eyes with more than one good OCT scan, the Ectasia index values were averaged.

Figure 3.

The process used to compute the Ectasia index. A 2D symmetric Gaussian waveform was fit to a 4 mm diameter region of both the pachymetry and posterior mean curvature PD maps. The Gaussian fit was centered on the minimum value of the pachymetry PD map within the search area (dashed circle). The Gaussian center for the posterior mean curvature PD map was shifted 0.11 mm in the nasal direction and 0.39 mm in the inferior direction relative to the pachymetric Gaussian center. The two Gaussian maps were multiplied together to produce the Ectasia map from which the Ectasia index was calculated.

Statistical Analysis

The map and Gaussian fit characteristics were analyzed using the Shapiro-Wilk test to determine if they were normally distributed within each group. The average values from each keratoconus group were compared to the normal group using t-tests or non-parametric Wilcoxon rank-sum tests. Pearson and Spearman (non-parametric) correlations were used to quantify the strength of the relationship between the Gaussian fit characteristics. The repeatability of the Ectasia index across repeated scans of the same eye was examined using the intra-class correlation coefficient (ICC).

The ability of the Ectasia index to distinguish between normal and keratoconus eyes was compared to minimum pachymetry and maximum mean curvature using repeated 5-fold cross-validation (80% training, 20% test, 5 repeats). Within each fold, a receiver operating characteristic (ROC) curve was constructed from the training set using all keratoconus eyes as the positive cases. The metric value corresponding to 95% specificity was selected as the cutoff and used to classify the eyes in the test set. The diagnostic sensitivity for each keratoconus group and the specificity were calculated from the test set. The cutoff, sensitivity, and specificity values were averaged across the 25 folds and compared with a McNemar test. The cross-validation algorithm was created using MATLAB, and the statistical comparisons were performed in R (R Foundation for Statistical Computing, Vienna, Austria).

Results

Keratoconus eyes were characterized by higher curvature of the posterior corneal surface and lower corneal thickness compared to normal eyes (Table 1). Example topography and corneal thickness maps of a subclinical keratoconus and a FFK eye were shown in Supplemental Figure 1. Among the keratoconus groups, the manifest keratoconus group had the highest maximum posterior mean curvature and the lowest minimum pachymetry. The FFK eyes were most similar to normal, with their mean values just beyond one standard deviation of the normal eyes.

Table 1.

Number of eyes and average values of diagnostic metrics for each group

Patient Group	# Eyes (Subjects)	Minimum Pachymetry (μm)	Maximum Posterior Mean Curvature (1/m)	Ectasia Index (%)
Manifest Keratoconus	89 (63)	438 ± 34*	232 ± 32**	19.4 ± 6.9**
Subclinical Keratoconus	16 (15)	454 ± 52*	208 ± 17*	13.7 ± 4.6**
Forme Fruste Keratoconus	26 (26)	491 ± 35*	170 ± 12	3.7 ± 3.9*
Normal	32 (16)	516 ± 19	162 ± 5	0.1 ± 1.0

^*2-tailed t-test p < 0.006

^**2-tailed Mann-Whitney U test p < 0.0001

For keratoconus eyes, most of the peak thinning and steepening locations were found in the inferior and inferotemporal octants, with fewer located in the central 2 mm zone or temporal octant (Figure 2). For normal eyes, the locations of the minimum pachymetry PD value and the maximum mean curvature PD value (within the search area) were often observed at the boundaries of the map or search area (not shown). This suggested that the global maximum/minima were located outside of the search area and were therefore unlikely to be related to keratoconus.

The steepening of the posterior corneal surface was generally located in a more inferotemporal position compared to the pachymetric thinning (Figure 2). The offset vector from the pachymetry PD minimum to the mean curvature PD maximum pointed in the direction 15.7° clockwise from the -y axis. The average distance between the two points was 0.41 ± 0.34 mm. The characteristic Gaussian width was also different for the two types of PD maps, with a median full-width-half-maximum (FWHM) of 4.1 mm for posterior mean curvature versus 3.4 mm for pachymetry.

For both types of PD maps, the amplitudes of the Gaussian fits were significantly larger for all three keratoconus groups compared to normal (Table 2). The PD map patterns were also more Gaussian in shape for the keratoconus eyes compared to normal. The Gaussian amplitudes and the correlation with the Gaussian function from the two PD maps were correlated for the keratoconus eyes but not for the normal eyes (Figure 4). The pachymetry PD minimum and mean curvature PD maximum were closest in proximity for the manifest keratoconus eyes and furthest apart for the normal eyes.

Table 2.

Gaussian fit results and distance between pachymetry PD minimum and posterior mean curvature PD maximum for each group

	Gaussian Amplitude (%)		Gaussian Cross-Correlation		Distance Between Pachymetry PD Minimum and Mean Curvature PD Maximum (mm)
Patient Group	Pachymetry	Mean Curvature	Pachymetry	Mean Curvature
Manifest Keratoconus	−16 ± 6*	67 ± 28*	0.90 ± 0.08**	0.81 ± 0.15**	0.49 ± 0.25*
Subclinical Keratoconus	−12 ± 4**	50 ± 21*	0.90 ± 0.09**	0.85 ± 0.07**	0.67 ± 0.28*
Forme Fruste Keratoconus	−4 ± 4**	15 ± 15**	0.73 ± 0.18*	0.54 ± 0.19*	1.31 ± 0.76**
Normal	−1 ± 1	0 ± 4	0.42 ± 0.27	0.37 ± 0.21	1.85 ± 0.65

^*2-tailed t-test p < 0.03

^**2-tailed Mann-Whitney U test p < 0.005

PD = pattern deviation

Figure 4.

A) The amplitudes of the Gaussian fits from the pachymetry and posterior mean curvature PD maps increased in a correlated fashion for the keratoconus eyes. The amplitudes were not correlated for the normal eyes. B) The cross-correlations between the Gaussian function and the pachymetry and posterior mean curvature PD maps of keratoconus eyes were correlated. A correlation was not observed for the normal eyes.

The ectatic pattern of coincident corneal thinning and posterior surface steeping was evident for the keratoconus eyes (Figure 5), resulting in larger Ectasia index values (indicated by dark red color on the Ectasia map). Such a pattern was not observed for the normal eyes, and the average value of the Ectasia index was near zero (Table 1). The Ectasia index was largest for the manifest keratoconus group and decreased for the subclinical and FFK groups, respectively. The ICC for the Ectasia index across all of the keratoconus eyes was 0.98.

Figure 5.

Representative pattern deviation (PD) and Ectasia maps for an eye from each group. Keratoconus eyes were characterized by thinner pachymetry and steeper posterior mean curvature relative to normal eyes. The coincidence of the pachymetric thinning and posterior surface steepening resulted in a larger Ectasia index for the keratoconus eyes. This pattern was more pronounced for the manifest and subclinical groups than for the forme fruste group.

A higher overall classification accuracy was found for the Ectasia index compared to minimum pachymetry and maximum mean curvature, with the difference between the Ectasia index and minimum pachymetry reaching statistical significance (Table 3). When each keratoconus group was evaluated separately, the Ectasia index was statistically more sensitive than minimum pachymetry in detecting manifest keratoconus and more sensitive than maximum mean curvature in detecting FFK. The specificity of the Ectasia index did not differ statistically from the specificity of the two other metrics.

Table 3.

Summary of repeated 5-fold cross-validation results

			Sensitivity by Keratoconus Group (%)
Diagnostic Metric	Cutoff Value	Overall Accuracy (%)	Manifest	Subclinical	Forme Fruste	Specificity (%)
Minimum Pachymetry (μm)	492.3 ± 1.3	85 ± 5*	93 ± 5*	69 ± 23	54 ± 23	94 ± 8
Maximum Mean Curvature (1/m)	172.4 ± 1.0	87 ± 4	99 ± 2	100 ± 0	32 ± 19*	93 ± 11
Ectasia Index (%)	−1.35 ± 0.16	92 ± 4	100 ± 0	100 ± 0	63 ± 21	91 ± 10

^*McNemar test p < 0.05

Discussion

The motivation behind the design of the Ectasia index was to capture the characteristic pattern of corneal thinning and posterior surface steepening in eyes with keratoconus.²⁰ These features are clearly demonstrated in Table 1, with the keratoconus groups having thinner corneas and higher posterior surface curvature than normal eyes. We combined corneal thickness and curvature information by multiplying Gaussian fits of pachymetry and posterior mean curvature PD maps.

The large Gaussian amplitudes and high cross-correlation with the Gaussian function for the keratoconus eyes justified our use of Gaussian fitting (Table 2, Figure 4). We have previously shown high cross-correlation between the Gaussian function and maps of pachymetry and mean curvature for keratoconic corneas,^19,21 and Gaussian functions have been used by others to model the characteristic cone shape.^22,23 The plots in Figure 4 showed that for keratoconus eyes, the Gaussian amplitudes increased in a correlated way for both types of PD maps, suggesting that multiplication could generate larger magnitudes of the Ectasia index. By contrast, the Gaussian amplitudes were low and uncorrelated for normal eyes.

The shorter distance between the locations of maximum relative thinning and steepening also contributed to the higher Ectasia index values for keratoconus eyes (Table 2). We found a characteristic difference in the locations of maximum relative thinning and maximum relative steepening for the keratoconus eyes, with the steepening being more inferotemporal (Figure 2). For this reason, we shifted the center of the Gaussian fit for the posterior mean curvature PD maps by the offset vector. This improved the ability of the Ectasia index to separate keratoconus eyes from normal eyes since it is characteristic of keratoconus eyes but not normal eyes.

We compared the Ectasia index to minimum pachymetry and maximum posterior mean curvature to determine how a metric which combined thickness and curvature information would perform relative to either type of measurement on its own. Minimum pachymetry has been shown to differ significantly between normal and keratoconus eyes,^{10, 11, 24} and it is currently used as a component of the ABCD keratoconus grading system.²⁵ Maximum mean curvature is similar conceptually to the traditional maximum keratometry metric that is measured from axial power maps.²⁶

The Ectasia index was more accurate in classifying normal and keratoconus eyes than both minimum pachymetry and maximum posterior mean curvature (Table 3). This result is consistent with other studies which have shown that combining corneal thickness and curvature information is more effective than relying on only one of these measurements.^27–29 Rabinowitz et al. tested twelve different variables and concluded that combining videokeratography and pachymetric measures was the most effective strategy for separating normal and keratoconic eyes.³⁰ Another study by Prakas et al. suggested that pachymetric features could be used along with topographic criteria to screen for keratoconus.³¹ Xu et al. constructed discriminant functions using Pentacam measurements of topography and pachymetry and found that including both corneal surfaces and pachymetry resulted in higher sensitivity and specificity.³²

Interestingly, the results comparing the Ectasia index to minimum pachymetry and maximum posterior mean curvature differed across the patient groups. The Ectasia index outperformed minimum pachymetry for all three keratoconus groups, although statistical significance was only achieved for the manifest group. Sensitivity was similar between the Ectasia index and maximum posterior mean curvature for the manifest and subclinical groups, but a statistical difference was found showing that the Ectasia index outperformed maximum posterior mean curvature for the FFK group. The diagnostic power of different metrics may not be equivalent for the early and late stages of keratoconus,^{32, 33} and by capturing both thickness and curvature information, the Ectasia index can be effective in detecting keratoconus across the spectrum of disease severity.

BAD-D is a metric reported by the Pentacam which combines various measurements including anterior and posterior surface elevation and minimum pachymetry.³⁴ Among the 17 FFK eyes for which both the Ectasia index and BAD-D were measured, two eyes with a normal BAD-D value (< 1.6) were detected by the Ectasia index. Three FFK eyes had a normal Ectasia index and an abnormal BAD-D value. We have previously published another metric termed the coincident thinning (CTN) index which uses pachymetry and epithelial thickness PD maps.¹⁹ There were five FFK eyes that were detected by the Ectasia index but missed by the CTN index, and two FFK eyes missed by the Ectasia index but identified by the CTN index. This suggests that the subtle early signs of keratoconus may vary, and combining epithelial thickness measurements with the Ectasia index could improve keratoconus screening. Biomechanical information obtained from optical coherence elastography could also be added to the analysis to further enhance the diagnostic sensitivity.

There were several limitations to this study. The sample size was relatively small for the subclinical and FFK groups which limited the statistical power of our analyses. The scan pattern was another limitation because it was composed of only 8 meridians, each with a length of 6 mm. Scanning 8 meridians meant that we could use at most fourth order Zernike terms to construct the corneal surface. The 6 mm scan diameter is not large enough to detect peripheral corneal abnormalities such as pellucid marginal degeneration. Lastly, mean curvature mapping of the cornea and the Ectasia index are not yet FDA-approved for clinical use.

In conclusion, we have introduced the Ectasia index, a new metric for keratoconus detection. We demonstrated that the Ectasia index is highly effective in differentiating between normal and keratoconic eyes and could therefore be a useful additional metric for clinicians to consider during keratoconus screening.