Keywords

1 Introduction

Early detection of corneal ectasia is a main concern for clinical ophthalmologists, in order to prevent the iatrogenic effects of several surgical procedures such as laser-assisted in situ keratomileusis (LASIK ) , lamellar cut, or excimer laser ablation. One retrospective study in 1364 patients has found a total of 69 eyes with a corneal topography suggesting forme fruste keratoconus (FFKC) after LASIK procedure [1]. Although it is a rare complication, the probability of an ectatic disease due to the surgically induced alteration of the corneal biomechanical structures is always present, and not only for those patients who have a previous ectatic cornea: in the same study, the rate of iatrogenic post-LASIK ectasia was 0.05 % (1/1992 eyes), and the total rate of post-LASIK ectasia for the entire study was 0.25 % (1/398). The rate of eyes with unrecognized preoperative FFKC that developed post-LASIK ectasia was 5.8 % (1/17) [1]. So even the use of the most conservative screening recommendations would not have precluded some patients from LASIK, as the one case of post-LASIK ectasia previously described, with no identifiable preoperative risk factors. Maybe in some cases it is not possible to elucidate how surgical procedures will lead to a biomechanical failure in response to forces from intraocular pressure (IOP), forces from the three antagonistic pairs of muscles that control eye movements (lateral and medial rectus muscles, the superior and inferior rectus muscles, and the superior and inferior oblique muscles), as well as other forces. But with a higher rate of surgical-related corneal ectasia development in those patients with previous ectatic signs, as observed before, there is a great interest in the development of new approaches for the improvement of sensitivity and specificity of the clinical diagnostic tools for subclinical stages of the ectatic disease detection. This chapter is aimed to explain how it is possible to establish new criteria for the subclinical keratoconus detection using a custom, geometrical approach, for an in vivo corneal analysis.

2 Materials and Methods

2.1 Sampling Procedures

We developed an observational case series study, evaluating a total of 120 eyes from 120 subjects with normal best spectacle corrected visual acuity, using one eye per patient, following a numerical sequence (dichotomous sequence 0 and 1) created by computer software in order to avoid interference potential correlations that could exist between the eyes of the same person. Participants with any ocular or corneal pathology, or those whose eyes had undergone any previous procedure, were excluded.

Sample was divided into two groups: healthy and subclinical keratoconus corneas. The first group (eyes with healthy cornea) did not present any ocular pathology and consisted of 89 healthy eyes of 89 patients with ages ranging from 7 to 66 years (mean age of 37.49 ± 15.11 years). The second group was formed by eyes with ocular pathology and consisted of 31 eyes of 31 patients diagnosed with subclinical keratoconus, with ages ranging from 16 to 55 years (mean age of 34.72 ± 11.12 years). The classification protocol for healthy or subclinical keratoconus cases was performed based on reported state-of-the-art clinical and topography evaluation [2]: healthy eyes had spectacle correction visual acuity ≥1 on the decimal scale (Snellen 20/20), no clinical signs of keratoconus, no scissoring on retinoscopy, no asymmetric bowtie (AB), inferior steepening (IS), skewed axes (SRAX), or asymmetric bowtie with skewed axes (AB/SRAX) pattern on topography. Subclinical keratoconus had spectacle correction visual acuity ≥1 on the decimal scale (Snellen 20/20); no slit-lamp findings; no scissoring on retinoscopy; and presence of AB, IS, SRAX, or AB/SRAX pattern on topography only.

All clinical data and corneal examinations were performed in Vissum Corporation (Alicante, Spain). Prior to the examination, informed consent was obtained from each patient, and the study was conducted in accordance with the ethical standards stated in the Declaration of Helsinki and approved by the local clinical research ethics committee.

2.2 Eye Exam

The preoperative examination of all selected eyes included the following tests: uncorrected distance visual acuity (UDVA), corrected distance visual acuity (CDVA), manifest refraction, Goldmann tonometry, biometry (IOLMaster, Carl Zeiss Meditec AG), and corneal topographic analysis with Sirius System® (CSO, Florence, Italy). All measurements were performed by the same experienced optometrist certified in Good Clinical Practice (GCP). Regarding the corneal topographic analysis , three consecutive measurements were performed and the average values were calculated for posterior analysis. A high performance corneal topographer with a combination between rotating Scheimpflug camera and Placido disk was used during the study to obtain the corneal topography, achieving accurate measurement of elevations, curvature, power, and thickness for the whole cornea. This topographer has a good level of consistency for taking measurements of sagittal and tangential curvature of both faces of the corneal refractive power, points of the anterior and posterior corneal surface, corneal pachymetry, and estimations of other biometric structures. This consistency has been previously proved to be accurate [3]. During the study, the Phoenix® (Phoenix, CSO, Florence, Italy) software was used for data registration.

This topographer works in two clearly differentiated stages . The first stage performs a mapping of spatial data of the surface morphology of the anterior and posterior corneal surfaces. The second stage uses an internal algorithm, whose performance is unknown. This proceeds to the reconstruction of the corneal surface by an elevation map, a topographic map, and a map of curvature (tangential or sagittal) from both sides of the corneal surface, and later makes a qualitative analysis of these maps using different index rates. For the study performed in this paper, only raw data extracted from the first stage of the topographer was used, which warranties that no manipulation of the data by any software algorithm was executed.

2.3 Corneal Modeling and Geometrical Characterization Proposals

The procedure proposed consists of two main stages: the reconstruction of a 3D geometrical model of the cornea through computational geometry techniques and using raw data from a Sirius (CSO) corneal topographer, and the determination and calculation of several geometric variables from this model.

Geometrical modeling and analysis. The geometric reconstruction of the cornea was performed by executing the following steps, described with more detail in chapter 10 [4]: extraction of the point clouds from the corneal topographer, geometric surface reconstruction , and solid modeling. The resulting solid model of the cornea is then used to perform an analysis of determined geometric variables. The variables studied in this study are as follows: total corneal volume [mm3], anterior corneal surface area [mm2], posterior corneal surface area [mm2], total corneal surface area [mm2], sagittal plane area in apex [mm2], anterior and posterior apex deviation [mm], sagittal plane area at minimum thickness point (maximum curvature) [mm2], anterior and posterior minimum thickness point deviation (maximum curvature) [mm], centre of mass coordinates X, Y, Z of the solid model [mm], net deviation from the centre of mass in XY [mm], and volume of corneal cylinder R − x [mm3]. A more detailed description of these variables can be found in Table 11.1 .

Table 11.1 Geometric variables analyzed in the study
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2.4 Data Analysis

According to data engagement scores (K-S test), a Student’s t-test or U-Mann–Whitney Wilcoxon test was employed, as appropriate. ROC curves were established in order to determine what parameters could be used to classify diseased corneas, calculating optimal cutoffs, sensitivity, and specificity. All analyses were performed using Graphpad Prism 6 and SPSS 17.0 software.

3 Results

Table 11.2 summarizes the main outcomes of the variables analyzed in this study. The majority of modeled variables have statistically significant differences when comparing healthy with diseased corneas, as presented in Table 11.2 .

Table 11.2 Descriptive values (mean, standard deviation, 95 % CI, minimum, maximum, and 25th, 50th, and 75th percentiles) and differences between normal and subclinical keratoconus corneal variables modeled
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3.1 Importance of Volumetric Variables

Patients in the early keratoconus group showed a statistically significant decrease in total corneal volume when compared with healthy eyes (p < 0.05). This behavior is also found in the area of highest corneal irregularity. The volume of corneal cylinder with radius x is where there are statistically higher values for healthy eyes, with a similar trend for all radii adopted in the study, (x = 0.5, 1.0, 1.5, and 2.0 mm) (p < 0.05).

3.2 Surface and Area-Related Variables

Regarding the corneal surfaces, the areas for both anterior and posterior corneal surfaces are statistically lower in subjects with healthy corneas (p < 0.05). On the other hand, the total corneal surface area is higher in healthy corneas (p < 0.05), as well as the area of the sagittal plane that passes through the apex of the anterior surface (p < 0.05) and the area of the sagittal plane through the minimum thickness point of the anterior surface (p < 0.05).

3.3 Deviations of Several Geometrical Parameters

As expected, a minor deviation from the apex of the anterior and posterior surfaces, and also a minor deviation at minimum thickness points of both surfaces in the group of normal corneas were observed (p < 0.05). Regarding net deviation from the centre of mass in x, y, no significant differences between the groups of this study were observed (p < 0.05). The only parameter with no statistically significant differences between groups was the centre of mass (x , y , z) (p > 0.05). Therefore, it would not be a good predictor of differences between healthy corneas and corneas with subclinical keratoconus .

3.4 Sensitivity and Specificity for This Method

The predictive value of the modeled variables has been established through a ROC analysis (Fig. 11.1 ). A total of six variables have been identified with an area under the curve above 0. 63: Posterior apex deviation (area: 0.883, p < 0.000, std. error: 0.041, 95 % CI: 0.800–0.964), the cutoff value obtained was 0.0655 mm, with a sensitivity and specificity associated of 90.32 % and 34.83 %, respectively; anterior apex deviation (area: 0.758, p < 0.000, std. error: 0.059, 95 % CI: 0.641–0.875), the cutoff value obtained was 0.0010 mm, with a sensitivity and specificity associated of 64.52 % and 100.00 %, respectively; posterior minimum thickness point deviation (area: 0.758, p < 0.000, std. error: 0.053, 95 % CI: 0.654–0.862), the cutoff value obtained was 0.6215 mm, with a sensitivity and specificity associated of 90.32 % and 20.22 %, respectively; anterior minimum thickness point deviation (area: 0.744, p < 0.000, std. error: 0.054, 95 % CI: 0.638–0.851), the cutoff value obtained was 0.6795 mm, with a sensitivity and specificity associated of 90.32 % and 21.35 %, respectively; anterior corneal surface area (area: 0.672, p < 0.004, std. error: 0.059, 95 % CI: 0.557–0.790), the cutoff value obtained was 42.9460 mm2, with a sensitivity and specificity associated of 90.32 % and 15.73 %, respectively. Finally, the posterior corneal surface area (area: 0.638, p < 0.022, std. error: 0.061, 95 % CI: 0.519–0.757), the cutoff value obtained was 44.9985 mm2, with a sensitivity and specificity associated of 90.32 % and 19.10 %, respectively. Looking at these six variables, it can be concluded that the parameter that provides a higher rate of discrimination between normal corneal and corneas with subclinical keratoconus is the posterior apex deviation .

Fig. 11.1
figure 1figure 1

ROC curve modeling the sensitivity versus 1-specificity for variables diagnosing the existence of subclinical keratoconus disease (plotted only selected variables with area under the curve over 0.63)

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4 Discussion

Most of the indices employed by classic Placido disc topographers and tomographers devices use complicated formulas based on corneal curvature and thickness profiles for the detection of keratoconus. However, these devices have a number of limitations for analyzing completely the corneal topography, and their sensitivity and accuracy of the measurements are quite low in some cases, and therefore relevant information could be lost. Data are obtained directly from mathematical calculations that sometimes carry implicit assumptions to simplify the computation, and therefore, measurement error may increase. Due to this, it results of great interest to have detection indices for subclinical keratoconus that are based on the primary source of information, for example in the digitized data of the Placido rings, and that permit to improve the capacity of discrimination of this disease. Moreover, the independent analysis of the posterior and anterior corneal surfaces is not performed in an integrated way and requires the analysis of either surfaces separately, including also its aberrometric analysis , which provides a lot of different data that many times is redundant and sometimes difficult to interpret. This new method has shown new findings for the distinction between normal eyes and eyes with subclinical keratoconus, employing volumetric, pachymetric, surface area parameters, and deviations in the XY plane. Such parameters integrate both corneal surfaces and make aberrometric analysis of either of them unnecessary, creating a new, more simple, and global understanding of the limits of normality and early corneal pathology in the keratoconic eye.

Regarding volumetric parameters, the pathological group showed a statistically significant decrease of total corneal volume compared to healthy eyes. The same behavior was found in the volume of the corneal cylinders analyzed, detecting lower volumes for pathologic eyes. This trend was similar in all the radii studied (from 0.5 to 2 mm). Such changes may be due to the process of deterioration in keratoconus [5], which is triggered by the alteration of corneal collagen fibers, thus causing stromal thinning and breaks in Bowman membrane, initially in the subclinical degree. This way, the presence of orthogonality and homogeneity of the collagen fibers in healthy corneas is altered to an irregular distribution [6] and the bridges of collagen are affected in the pathological group. The analysis of this volumetric reduction has been identified in several studies as a parameter for the differentiation between normal and keratoconic eyes [7–11], where significant differences in the volume of the cornea were observed. In the case of this study, this difference is significantly compared to eyes with subclinical keratoconus where the degree of corneal protrusion is lower than in moderate cases, thus supporting the accuracy of the method proposed.

With regard to the area of the corneal surfaces , eyes with subclinical keratoconus show significant differences for both surfaces when compared with healthy corneas, being these areas higher in the pathological group. This result was expected because of the protrusion and existence of an irregular corneal area [5, 12, 13], due to an increment in the radius of curvature that causes an increase in the surface area. However, this behavior was not found when the total corneal surface area was obtained. Significant differences of the area of the total corneal surface were found between both groups, being higher in the group of healthy corneas. As previously mentioned in the section of solid modeling, anterior, posterior, and peripheral surfaces were considered for the calculation of the total corneal surface area. In the healthy corneas the peripheral corneal area is the possible cause of this fact, achieving a higher total corneal surface area. These values are consistent with those published by different studies on subclinical keratoconus, which report that the geometry and surface area of both corneal surfaces are affected because of the decreased number of stromal lamellae and lower interconnection lamellar surface at the level of the irregular corneal area [14, 15]. However, the presence of a higher total surface area in the healthy group is not as important as a higher total corneal volume accompanied by a high-density network of collagen fibers, making the cornea more resistant to the forces and therefore delaying the progression of keratoconus. This trend can also be appreciated with respect to the area of the sagittal plane that passes through the apex point of the anterior corneal surface, as well as to the area of the sagittal plane that passes through the minimum thickness point of the anterior surface. Statistically significant differences of these area parameters were found between groups, obtaining higher values for both parameters in the group of healthy corneas. The higher corneal volume in the healthy group previously mentioned may be the possible cause of these outcomes.

In addition, when analyzing the deviation of the apex points of both surfaces (average distance from the Z axis to the apex of the anterior/posterior corneal surfaces), significant differences between groups were observed, obtaining the largest deviation in the group of eyes with subclinical keratoconus [5, 16]. Concretely, in the case of deviation of the apex of the anterior surface, no observations were made in healthy corneas (0.00 ± 0.00 mm) and a minimal deviation with subclinical keratoconic corneas was detected (0.01 ± 0.03 mm). This might be related to the stage of lethargy in which the pathology can still be found in the anterior corneal surface. On the contrary, a deviation of the apex on the posterior surface of the cornea does exist in healthy corneas (0.08 ± 0.02 mm), possibly due to the existence of the toricity manifested in subjective refraction [17]. However, this deviation is significantly higher in eyes with subclinical keratoconus (0.16 ± 0.08 mm). This variation of the curvature could be detected by corneal tomography or topography [18]. On the other hand, the results showed by the deviation of the minimum thickness (maximum curvature) points of both surfaces (average distance from the Z axis to the minimum thickness points of the anterior/posterior corneal surfaces) were statistically different between groups, being higher in eyes with subclinical keratoconus (1.15 ± 0.33 mm for anterior surface and 1.07 ± 0.31 mm for posterior surface) with respect to healthy eyes (0. 88 ± 0.27 mm for anterior surface and 0.81 ± 0.25 mm for posterior surface). This fact is influenced by the presence of an irregular corneal surface creating a protrusion in the keratoconic case, thus increasing corneal curvature and therefore incrementing the distance of deviation [19]. Some researchers have evaluated certain ratios of corneal irregularity, concluding that they were significantly higher in keratoconic corneas than in normal corneas [20]. Saad et al. showed the comparison of a group of normal eyes with subclinical keratoconic eyes, demonstrating that only the combination of all indices of irregularity, extracted from the minimum thickness area of the cornea, allows a 92 % of accuracy in differentiation of these groups [11].

In this sense, we attempt to understand the performance provided by this technique for discrimination of both groups by each of these variables. The best results in the determination of the disease were obtained by the posterior apex deviation variable (area: 0.883, p < 0.000, std. error: 0.041, 95 % CI: 0.800–0.964). This variable, having a higher area under the ROC curve, provided a more discriminatory capacity. This may be due to the existence of structural instability in subclinical keratoconic corneas. For instance, the decrease of corneal volume in these cases was observed. The posterior corneal surface is more susceptible to variations due to the forces that are exerted on the tissue and for this reason the posterior apex deviation is one of the variables that most reliably represents the early changes in patients with early forms of the disease. Several studies conclude the great importance and interest regarding the posterior corneal surface. At the beginning of the disease, structural changes occur at the rear face of the cornea and an efficient analysis of this surface would be very useful to perform a positive and early identification of the subclinical keratoconus. These findings suggest that important clinical analysis of posterior corneal surface clearly contributes to early manifestation of subclinical keratoconus.