Study of Morpho-Geometric Variables to Improve the Diagnosis in Keratoconus with Mild Visual Limitation

The validation of new methods for the diagnosis of incipient cases of Keratoconus (KC) with mild visual limitation is of great interest in the field of ophthalmology. During the asymmetric progression of the disease, the current diagnostic indexes do not record the geometric decompensation of the corneal curvature nor the variation of the spatial profile that occurs in singular points of the cornea. The purpose of this work is to determine the structural characterization of the asymmetry of the disease by using morpho-geometric parameters in KC eyes with mild visual limitation including using an analysis of a patient-specific virtual model with the aid of computer-aided design (CAD) tools. This comparative study included 80 eyes of patients classified as mild KC according to the degree of visual limitation and a control group of 122 eyes of normal patients. The metric with the highest area under the receiver operating characteristic (ROC) curve was the posterior apex deviation. The most prominent correlation was found between the anterior and posterior deviations of the thinnest point for the mild keratoconic cases. This new custom computational approach provides the clinician with a three-dimensional view of the corneal architecture when the visual loss starts to impair.


Introduction
The human eye has four refractive surfaces, five refractive indexes, and four thicknesses [1]. The variation of any of these parameters affects the refractive state of the eye. Among all of them, the cornea is the most important parameter from a refractive point of view. A perfect optical system would be completely symmetrical and would be free of distortion and transverse chromatic aberration. However, the cornea is not a perfect biological structure because its surfaces do not present symmetry of revolution in a healthy scenario, which entails the existence of deformations, misalignments, and decentralizations between its anterior and posterior surfaces and between its singular points (apex, vertex, and minimum thickness point) [2]. However, in a pathological scenario, the progression of the asymmetry in the corneal architecture contributes to a decrease in its optical capacity, which causes a loss of the patients' visual quality [3]. This decrease in optical functionality may have its origin in a physio-pathological mechanism derived from a pathology called keratoconus. Keratoconus (KC) has an estimated prevalence of approximately 50-230 individuals Symmetry 2018, 10, 306 2 of 13 per 100,000 people in the general population [4]. This asymmetrical ectatic disorder is geometrically characterized by [5] the details below.
• a geometric decompensation or progressive distortion of the corneal curvature from a singular point denominated the corneal apex. • a decompensation of the spatial profile of pachymetry, which is described as an annular increase/decrease of its thickness from a singular point called the minimum thickness point.
Both characterizations involve a local geometric alteration in the cornea during keratoconus. Depending on the level of corneal deformation, it leads to a gradual deterioration of visual performance [6][7][8].
Several reports had the task to assess the different stages of KC and their corneal deformations by using different devices and analyses [9,10]. Most of the studies performed have only taken into consideration the morphological features to discriminate the different stages of the disease without considering other important clinical aspects directly correlated to the corneal visual disability [11].
As recently reported, the corneal geometric modeling has been proposed for the study of ectasia characterization [12]. Nevertheless, to the author's knowledge, this new tool has not been considered for the study of KC eyes with mild impaired visual function as graded along the evolution of the disease. Patient-specific 3D modeling may help to better recognize the changes that happen in the cornea when KC is developed and it correlates with vision decay as the disease evolves [11] (Figure 1). There is an important threshold between normality and, when the disease starts to clinically affect the patient, a better understanding of these cases could help the management of ectasia in the clinical practice.
The purpose of the current study was to determine the geometrical profile and novel correlations of the corneal deformation for KC eyes with mild visual limitation compared to normal corneas by using the morphogeometric custom modeling analysis. Our aim was to understand the modeled changes observed in the keratoconic cornea with a mild visual loss and also attempt to find a morpho-geometrical correlation.
Symmetry 2018, 10, x FOR PEER REVIEW 2 of 13  a geometric decompensation or progressive distortion of the corneal curvature from a singular point denominated the corneal apex.  a decompensation of the spatial profile of pachymetry, which is described as an annular increase/decrease of its thickness from a singular point called the minimum thickness point.
Both characterizations involve a local geometric alteration in the cornea during keratoconus. Depending on the level of corneal deformation, it leads to a gradual deterioration of visual performance [6][7][8].
Several reports had the task to assess the different stages of KC and their corneal deformations by using different devices and analyses [9,10]. Most of the studies performed have only taken into consideration the morphological features to discriminate the different stages of the disease without considering other important clinical aspects directly correlated to the corneal visual disability [11].
As recently reported, the corneal geometric modeling has been proposed for the study of ectasia characterization [12]. Nevertheless, to the author's knowledge, this new tool has not been considered for the study of KC eyes with mild impaired visual function as graded along the evolution of the disease. Patient-specific 3D modeling may help to better recognize the changes that happen in the cornea when KC is developed and it correlates with vision decay as the disease evolves [11] (Figure 1). There is an important threshold between normality and, when the disease starts to clinically affect the patient, a better understanding of these cases could help the management of ectasia in the clinical practice.
The purpose of the current study was to determine the geometrical profile and novel correlations of the corneal deformation for KC eyes with mild visual limitation compared to normal corneas by using the morphogeometric custom modeling analysis. Our aim was to understand the modeled changes observed in the keratoconic cornea with a mild visual loss and also attempt to find a morphogeometrical correlation.

Patients
The study included a total of 202 eyes of 202 patients (122 normal and 80 keratoconic cases) enrolled at Vissum Instituto Oftalmologico Alicante, Spain (Vissum) who were adequately informed about the clinical study and voluntarily signed their consent to participate. The study was ratified by

Patients
The study included a total of 202 eyes of 202 patients (122 normal and 80 keratoconic cases) enrolled at Vissum Instituto Oftalmologico Alicante, Spain (Vissum) who were adequately informed All patients were selected, according to the Cooperative Research Thematic Network (RETICS) grading [8,11] based on the limitation of spectacle corrected distance visual acuity (CDVA) and also taking into account corneal aberrations, internal astigmatism, and corneal biomechanical properties. Inclusion criteria were patients diagnosed as KC eyes with mild visual impairment (0.6 < CDVA ≤ 0.9 in decimal scale, or 20/33 < CDVA ≤ 20/22 Snellen), normal visual acuity achieved by fitting a rigid gas permeable contact lens, corneal topography revealing a localized steepening, and/or an asymmetric bowtie pattern with or without skewed radial axis. The exclusion criteria were the following. Any previous ocular surgery, ocular surface inflammation, moderate to severe dry eye or other active ocular comorbidity, or use of contact lenses within the four weeks prior to the first visit.
The control group comprised 122 normal eyes of 122 patients. This group was selected at random by subjects assessed in the refractive surgery department. Exclusion criteria for this range were the following: participants with any ocular disease, topographic irregularities or abnormal aberrometry, familial history of KC, contact lens wearing within four weeks, or those whose eyes had undergone any previous surgery.

Ophthalmological Examination
A detailed and uniform ophthalmologic examination was performed in all cases, according to the clinical standards [3]. Testing sessions consisted of a minimum of three corneal topographies for each cornea made with Sirius Tomographer (CSO, Florence, Italy), which was always carried out by the same experienced examiner. Only the best topographies with the highest acquisition quality for the Scheimpflug images were selected for providing data.

Morpho-Geometric Reconstruction of the Cornea
This analysis defined by the authors was conducted on all participants. The corneal morpho-geometric reconstruction procedure consists of the following successive stages (  All patients were selected, according to the Cooperative Research Thematic Network (RETICS) grading [8,11] based on the limitation of spectacle corrected distance visual acuity (CDVA) and also taking into account corneal aberrations, internal astigmatism, and corneal biomechanical properties. Inclusion criteria were patients diagnosed as KC eyes with mild visual impairment (0.6 < CDVA ≤ 0.9 in decimal scale, or 20/33 < CDVA ≤ 20/22 Snellen), normal visual acuity achieved by fitting a rigid gas permeable contact lens, corneal topography revealing a localized steepening, and/or an asymmetric bowtie pattern with or without skewed radial axis. The exclusion criteria were the following. Any previous ocular surgery, ocular surface inflammation, moderate to severe dry eye or other active ocular comorbidity, or use of contact lenses within the four weeks prior to the first visit.
The control group comprised 122 normal eyes of 122 patients. This group was selected at random by subjects assessed in the refractive surgery department. Exclusion criteria for this range were the following: participants with any ocular disease, topographic irregularities or abnormal aberrometry, familial history of KC, contact lens wearing within four weeks, or those whose eyes had undergone any previous surgery.

Ophthalmological Examination
A detailed and uniform ophthalmologic examination was performed in all cases, according to the clinical standards [3]. Testing sessions consisted of a minimum of three corneal topographies for each cornea made with Sirius Tomographer (CSO, Florence, Italy), which was always carried out by the same experienced examiner. Only the best topographies with the highest acquisition quality for the Scheimpflug images were selected for providing data.

Morpho-Geometric Reconstruction of the Cornea
This analysis defined by the authors was conducted on all participants. The corneal morphogeometric reconstruction procedure consists of the following successive stages (

Acquisition of the Point Clouds
The point clouds that represent the geometry of the corneal surfaces were generated from the data provided by a Sirius corneal topographer (CSO, Florence, Italy). This topographer offers an Excel file that includes information regarding both corneal surfaces for each patient. Within this information, the most reliable information to perform geometric modeling is the raw altimetry data of the anterior and posterior elevations (radii of Placido's disc rings), which have not been manipulated by any software process inside the topographer [13].

Geometric Reconstruction of Corneal Surfaces
The point clouds representative of corneal geometry are later imported by the surface reconstruction software Rhinoceros v5.0 (MCNeel & Associates, Seattle, WA, USA). This software uses a mathematical model to generate surfaces based on non-uniform rational B-splines (NURBS) [14] and its validity in the Biomedical Engineering [15][16][17][18] and Ophthalmology [19][20][21][22] fields has been widely demonstrated. For this study, the "patch" surface generation function was used to reconstruct both corneal surfaces. These surfaces were then connected by their vertex in relation to the optical axis and the perimetral surface was obtained.

Generation of the Solid Model of the Cornea
The reconstructed surfaces of each case by Rhinoceros were later imported into the solid modeling software SolidWorks (Dassault Systèmes, Vélizy-Villacoublay, France), which permitted to generate a solid model representative of the real and customized geometry of the cornea.

Characterization of the Cornea
After obtaining the 3D patient-specific model of the cornea in SolidWorks, it can be used to calculate certain morpho-geometric variables, which will characterize the analyzed cornea ( Figure 3). Table 1 shows a detailed description of the geometrical variables analyzed for the KC group during the present study. The point clouds that represent the geometry of the corneal surfaces were generated from the data provided by a Sirius corneal topographer (CSO, Florence, Italy). This topographer offers an Excel file that includes information regarding both corneal surfaces for each patient. Within this information, the most reliable information to perform geometric modeling is the raw altimetry data of the anterior and posterior elevations (radii of Placido's disc rings), which have not been manipulated by any software process inside the topographer [13].

Geometric Reconstruction of Corneal Surfaces
The point clouds representative of corneal geometry are later imported by the surface reconstruction software Rhinoceros v5.0 (MCNeel & Associates, Seattle, WA, USA). This software uses a mathematical model to generate surfaces based on non-uniform rational B-splines (NURBS) [14] and its validity in the Biomedical Engineering [15][16][17][18] and Ophthalmology [19][20][21][22] fields has been widely demonstrated. For this study, the "patch" surface generation function was used to reconstruct both corneal surfaces. These surfaces were then connected by their vertex in relation to the optical axis and the perimetral surface was obtained.

Generation of the Solid Model of the Cornea
The reconstructed surfaces of each case by Rhinoceros were later imported into the solid modeling software SolidWorks (Dassault Systèmes, Vélizy-Villacoublay, France), which permitted to generate a solid model representative of the real and customized geometry of the cornea.

Characterization of the Cornea
After obtaining the 3D patient-specific model of the cornea in SolidWorks, it can be used to calculate certain morpho-geometric variables, which will characterize the analyzed cornea ( Figure 3). Table 1 shows a detailed description of the geometrical variables analyzed for the KC group during the present study.
The main outcome measure of this study was to define the model that the keratoconic cornea follows when mild visual loss is associated with corneal deformation. The second outcome was the correlation coefficients, sensitivity, and specificity of this new KC detection method.

Morpho-Geometric Variable Acronym Description
Corneal volume (mm 3  The main outcome measure of this study was to define the model that the keratoconic cornea follows when mild visual loss is associated with corneal deformation. The second outcome was the correlation coefficients, sensitivity, and specificity of this new KC detection method.

Statistical Analysis
All data were analyzed using IBM SPSS 19.0 software (IBM Corp., Armonk, NY, USA). The statistical analysis included descriptive statistics for both normal and KC groups to demonstrate the distribution of the thirteen morpho-geometric variables in more detail. Normality was checked using the Kolmogorov-Smirnov test. When parametric analysis was possible, the Student t-test for unpaired data was used as a comparison between groups. When the normality condition was met, groups were compared using a Student t-test for unpaired data. For all other situations, a Mann-Whitney test was used. A p-value lower than 0.05 was considered significant in all statistical tests. Correlation between parameters was assessed using Pearson coefficients (for normally distributed data) or Spearman coefficients (not normally distributed). With the aim of quantifying the strength of the correlation between the two groups, a linear regression was executed.
For all metrics, we applied receiver operating characteristic (ROC) curves to determine the overall predictive accuracy by plotting sensitivity versus 1-specifity.

Results
From a total of 202 eyes of 202 patients, the KC group comprised 80 eyes of 80 patients [29 women (36.2%) and 51 men (63.8%) with a mean age of 41.8 years ± 13.1 ranging from 16 to 72 years]. The control group was composed of 122 normal eyes of 122 patients (54 women (44.2%) and 68 men (55.8%)) with a mean age of 34.89 ± 7.8 years ranging from 19 to 64 years. There was no statistical difference regarding the age between groups (p > 0.05).
Regarding the KC group, the mean value of the posterior apex deviation (0.19 ± 0.10 mm) was higher than the anterior apex deviation (0.01 ± 0.02 mm) while the mean deviation at the minimum thickness point of the anterior and posterior curvatures was 1.11 ± 0.48 mm and 1.04 ± 0.45 mm, respectively. From the metrics of the center of mass coordinates X, Y, and Z, the value in Z reached the largest one with 0.78 ± 0.04 mm. The total corneal volume resulted in an average of 23.60 ± 2.28 mm 3 . For metrics from the total corneal surface, the anterior surface, and the posterior surface, the average achieved areas were 103.61 ± 1.62 mm 2 , 43.39 ± 0.35 mm 2 , and 44.70 ± 0.56 mm 2 , respectively. For the measurement of the sagittal plane area, the mean values reached were 3.91 ± 0.37 mm 2 (posterior surface) and 3.89 ± 0.39 mm 2 (at the minimum thickness point of the posterior surface). The descriptive values of the thirteen corneal morpho-geometric variables and their distribution in more detail are summarized in Table 2 for both keratoconic and control groups.  In comparison to the control group, the differences between groups were statistically significant for overall corneal metrics, which includes total volume (p < 0.001), anterior surface area (p < 0.001), anterior apex deviation (p < 0.001), anterior minimum thickness point deviation (p < 0.001), posterior surface area (p < 0.001), posterior sagittal plane apex area (p < 0.001), sagittal plane area at minimum thickness point (p < 0.001), posterior apex deviation (p < 0.001), posterior minimum thickness point deviation (p < 0.001), center of mass Y (p < 0.001), and center of mass Z (p = 0.006). In this regard, the modeled variables with no statistical difference for groups discrimination were the center of mass X (p = 0.073) and the total corneal surface area (p = 0.205).
When applying the ROC analysis, the highest area under the curve (AUC) was reached by the corneal posterior apex deviation. Considering an AUC greater than 0.7, the variables found were a  Figure 4.  Table 3 summarizes the statistically significant correlations between all the modeled morphogeometric variables for the KC group. Table 4 also shows the significant correlations for the normal group.   Table 3 summarizes the statistically significant correlations between all the modeled morpho-geometric variables for the KC group. Table 4 also shows the significant correlations for the normal group.  The regression analysis among the mild KC group ( Figure 5) revealed significant and strong correlations between the morpho-geometric variables (p = 0.000), which is shown below.

Normal Group (n = 122) Measurement Correlation Correlation Coefficient p Value
Apostapex/CV (mm 3  The regression analysis among the mild KC group ( Figure 5) revealed significant and strong correlations between the morpho-geometric variables (p = 0.000), which is shown below.
Total corneal volume = 5.757 × Posterior sagittal plane apex area + 1.197 (R 2 = 0.953) Sagittal plane area at minimum thickness point = 0.16 × Total corneal volume + 0.136 (R 2 = 0.955) According to the regression analysis for the normal group (Figure 6), the most significant correlations between the corneal metrics extracted from the reconstructed model are shown below (p = 0.000).
Center of mass Z = 0.0195 × Total cornea surface area − 1.255 (R 2 = 0.907) According to the regression analysis for the normal group (Figure 6), the most significant correlations between the corneal metrics extracted from the reconstructed model are shown below (p = 0.000).

Discussion
The validation of new methods for the diagnosis of incipient cases of KC or with mild visual loss is of great interest in the field of ophthalmology since there are several clinical treatments that would permit the end of further development of the disease [23]. For this reason, this work tries to perform a morphological analysis of the corneal structure's response to both the linear decompensation and the annular profile defined in the singular points of corneal surfaces. This procedure will contribute to a better differentiation between the corneas in a healthy scenario and in an incipient stage of the development of the disease based on a new approach and interpretation of the corneal architecture in KC corneas with visual limitations.
The first study [24] in KC corneas with mild visual limitation analyzed the corneal thinning and found that such thinning was moved with respect to the corneal vertex as an asymmetric response to the development of the pathology. Subsequently, another study analyzed the geometric response in normal eyes and the initial phases of KC. However, their conclusions were insufficient because they did not obtain consistent values of thinning measures in corneas with similar geometries [25]. A recent study showed that, when morphological analysis and corneal thickness of eyes are combined with KC, both are involved in the pathogenesis of the disease [26]. However, the geometric profile and the relationships that allow modeling of the progression of KC with mild visual loss have not yet been analyzed from these geometric models.
Other authors [25,27,28] consider a finite element model for KC aimed to simulate the behavior of the deformation on model corneas. However, they did not take into account the patient-specific corneal tomography. Alternatively, another study [29] that included progressive KC eyes was performed by gathering the elevation data from Zernike coefficients. Unlike our method, the x, y, and z coordinates from the elevation maps of Pentacam were linearly interpolated into the Zernike polynomials by a natural cubic spline. For this approach, the discretization of the model was derived from estimated data by using the blending function method. Therefore, the corneal surface reconstruction algorithm could not be properly inferred by this fitting procedure, which has been discussed in the literature [30][31][32]. In addition, the small sample size could be considered a drawback of these previously mentioned reports.
This analysis outlines the presence of mild visual impairment in the current series using a grading system primarily based on the criteria of visual evolution. In this regard, the present study set out the 3D characterization with patient-specific geometry of these KC cases in stages where a loss of visual function begins to occur. While the corneal refractive power is mostly determined by the anterior curvature [33], changes from the posterior surface are usually related to mild visual degradation [34]. The present report portrays the first study to assess the correlations of this geometrical method between the anterior and posterior corneal surfaces of keratoconic eyes with mild visual dysfunction.
In the present study, almost all mean differences were statistically significant (p = 0.00) between KC corneas with mild visual limitation and normal eyes. The proposed variables were obtained from the raw data of Sirius using a 3D point cloud, which generated a reliable solid model striving for consistent noise-suppressing properties. This Scheimpflug-Placido system used in a recent study [35] demonstrated more robust measurements in terms of repeatability (coefficients of variation = 0) and also outstanding levels of reproducibility and inter-device agreement in comparison to other devices studied.
Regarding the ROC analysis, the apex deviation of the posterior surface showed the highest discriminant coefficient (AUC, 0.904), which occurs because the apex is the maximum curvature point of the corneal surface According to a previous publication [36], the posterior curvature might have an impact on visual performance. We postulate that measuring the posterior apex deviation value is the most proficient way of characterizing the geometric profile of the KC stage in which a decrease of the visual acuity begins to occur. Moreover, the anterior apex deviation also shows an acceptable discrimination capability (AUC, 0.866). However, its sensitivity was lower (76.3%) in this investigation.
Other authors [37] recently reported that topographic indices and posterior elevation values from the Galilei device were significantly correlated with visual function.
This study also assessed the relationship of the geometrical pattern of the anterior and posterior corneal curvatures. Other authors, for a different purpose, found strong statistical correlations between the anterior and posterior shape factors for keratoconic corneas [38]. Regarding the minimum thickness point deviations from both corneal surfaces, we found significant differences between groups. Furthermore, for keratoconic eyes, the strongest correlation value yielded in this investigation was between the anterior and posterior deviations of the thinnest point (R 2 = 0.997, p = 0.000). Lopes et al. [39] demonstrated a robust correlation between apex deviation and the pachymetric progression index of the front and back elevations with CDVA of the analyzed patients.
Although there are other methods [40][41][42] describing corneal volume reduction among the disease evolution, in our study, this metric was investigated in KC eyes based on the beginning of visual impairment. With respect to the total volume, we found a significant difference in comparison to the control group. We also found a significant positive correlation between the corneal volume with the sagittal plane apex area of the posterior surface (R 2 = 0.953, p = 0.000) and with the sagittal plane area at a minimum thickness point (R 2 = 0.955, p = 0.000). Likewise, the correlations described were strongly achieved for normal eyes that were analyzed.
In conclusion, the morphological analysis of the corneal response with geometric models to both the linear decompensation and the annular profile in the mentioned singular points support the hypothesis of a focal weakening in incipient phases of the KC development. The most predictive accuracy using this geometrical reconstruction of KC eyes associated with mild visual loss resulted clearly from the posterior apex displacement. The anterior and posterior deviations of the thinnest point were considerably correlated among mild keratoconic corneas in the specific geometry of the 3D model, which was obtained with the new method described. The proposed morpho-geometric metrics showed significant differences between groups, which may lead to a further advancement of a more tailored disease management based on the evolution of corneal visual impairment. This may also presumably be extended to other Scheimpflug systems. This computational custom approach determines the characterization profile of keratoconic modeling in eyes with mild visual limitation. This procedure provides the clinician with a three-dimensional view of corneal architecture when mild visual loss happens and allows a reliable diagnosis of mild forms of the disease.