The objective of this study was to identify and build an algorithm through an imaging process using a support vector machine (SVM) with the tomography variables of cases with, KC, highly susceptible corneas to ectasia (HSCE), and healthy corneas and to compare this algorithm to BAD-D (Belin_Ambrosio Display) and PRFI (Pentacam Random Forest Index). The study included 148 eyes with KC, 351 with healthy corneas, and 88 eyes with HSCE.

Patients were considered to be very asymmetric (VAE-NT) if the diagnosis of ectasia was confirmed in one eye based on the previously described criteria and the fellow eye had a normal front surface curvature (topometric) map. Objective criteria for considering normal topography was applied for defining the cases of VAE-NT, including objective front surface curvature metrics derived from Pentacam. Normal topography was rigorously considered based on objective criteria of a maximum curvature Kmax (Steepest Front Keratometry) <47.2 diopters, a paracentral inferior-superior (I-S value) asymmetry value at 6 mm (3-mm radii) < 1.45, and keratoconus percentage index (KISA%) score < 60. The cutoff point used to discriminate normal corneas and VAE-NT from KC corneas was the maximal posterior elevation (< 29 micron. This cutoff point had been determined in a previous study, using the same instrument and the same setting (30). The posterior elevation map was displayed with a 5-mm color-coded scale, and maximal posterior elevation was measured manually using the cursor in the central 5 mm.

The study included 148 eyes with KC, 351 with healthy corneas, and 88 eyes with suspected KC. The patients were divided into three groups:

• Control group - Normal eyes (CG): 351 eyes without KC of 351 patients who underwent LASIK or photorefractive keratectomy (PRK), stable after at least 18 months of follow-up, without any changes in the posterior elevation at the 18-month Pentacam in relation to the preoperative exam (surgeries performed in 2012-2018). The inclusion criteria for being a normal case was to have normal corneas on the general eye examination in both eyes, including normal slit lamp biomicroscopy, corrected distance visual acuity of 20/20 or better, overall subjective normal topography and tomography examinations.. Our objective topographic criteria were: both eyes with a KISA% index of less than 60%, Kmax of 47.2 D or less, and I-S difference of less than 1.45 D. Because no truly established tomographic parameter(s)/cut-off(s) for differentiating normal from keratoconus suspect eyes exist, we adapted our classification for normal eyes to the recent publication by Ambrósio et al.(31) by adding the criterion of "overall subjective normal topography and tomography examinations" based on the evaluation of experienced refractive surgeon (GCAJ). Only one eye was randomly selected for further statistical analysis. The CG included one eye randomly selected from 323 patients with normal cornea; one eye was randomly included per patient to avoid selection bias related to the use of both eyes from the same patient
• Very assimetric ectasia with normal topography group (VAE-NT G): 88 eyes of 88 patients with very asymmetric ectasia with normal topography (VAE-NT) in one eye and frank ectasia (VAE-E) in the fellow eye. The inclusion criteria followed previous studies (28, 32, 33) Eyes in this group with insufficient topographic findings to meet diagnostic criteria for keratoconus, and following features normal-appearing cornea on slit-lamp biomicroscopy, keratometry, retinoscopy. These cases were the less affected eye (fellow eye) of a keratoconic patient was included if the following criteria were met: KISA% index of less than 60%, I-S difference of less than 1.45 D, and Kmax of 47.2 D or less (ie, same topographic criteria as in normal eyes, except than in normal eyes, both eyes of the patient met the criteria). These patients can be considered with corneas highly susceptible to ectasia.
• Very asymmetric eyes with ectasia (VAE-E): The fellow eyes of the VAE-NT displaying a KISA% index of greater than 100% and at least one of the following biomicroscopic signs: Vogt striae, Fleischer ring, or focal stromal thinning. Oculus implemented their own staging system into the Pentacam software, which should mimic the Amsler/Krumeich systems: the Topographic Keratoconus Classification (TKC) (34). TKC classifies KC into four stages (plus four intermediate stages) and identifies other corneal pathologies, such as corneal refractive surgery or pellucid marginal degenerative (PMD). TKC classification of Pentacam tomographic index showing algum grau de KC variando de 1-4.
• Keratoconus group (KCG): 148 patients (one eye each) with bilateral clinical KC. The KCG included one eye randomly selected from 148 patients with keratoconus; one eye was randomly included per patient to avoid selection bias related to the use of both eyes from the same patient. The inclusion criteria were the same as for VAE-E, except that both eyes of the patient met the ectasia criteria.

All subjects underwent complete eye examination as well as refraction assessment, biomicroscopy, retinoscopy, fundoscopy, topography, and tomography assessment. All patients were assessed at the Visum Eye Center between January 2012 and January 2018.

This study adhered to the tenets of the Declaration of Helsinki and was approved by the Research Ethics Committee of the Sao Jose do Rio Preto Faculty of Medicine. All patients were informed about the objectives of the study, and they signed written informed consent forms before being enrolled.

External validation was conducted with 140 patients, whose data were not included in building the algorithm. They met the same inclusion criteria as the others, with a total of 82 eyes of 82 patients with healthy corneas, 19 eyes of 19 patients with VAE-NT, and 39 eyes of 39 patients with KC.

PENTACAM TOMOGRAPHY: All eyes were examined by rotating Scheimpflug corneal and anterior segment tomography (Pentacam HR; Oculus GmbH, Wetzlar, Germany). Image quality was checked so that only cases with acceptable-quality images were included in the study. An experienced fellowship-trained corneal specialist (GCAJ) reviewed all the cases so that they were correctly classified in the KC and VAE-NT groups. The raw data (u12 files) were obtained from all cases; therefore, the same customized software (version 1.20r118) was used to process all the export files, and all Scheimpflug variables were directly downloaded from the Pentacam software using the "call-all" function.

MATHEMATICAL ALGORITHM: To build the equation extracted from SVM, 58 variables were used, some of them were extracted from the spreadsheet.. After the construction of these 58 feature vectors (FV), an SVM-derived index was created, which was called the corneal tomography multivariate index derived from a support vector machine (CTMVI). Considering that each patient represents a point on a cartesian plane with 58 dimensions (each coordinate representing one of the 58 FV), the role of SVM is to find the hyperplane that best separates the CG, KCG, and VAE-NT G subjects. A hyperplane is algebraically described by a linear equation; in this case, there are 59 coefficients, 58 of which are related to the FV and one independent coefficient representing the bias (which is a possible parallel dislocation of a given hyperplane). The analyzed FV were:

ARC (3 mm Zone): Anterior radius of curvature in the 3.0 mm zone centered on the thinnest location of the cornea; ARTmax: Ambrosio relational thickness maximum; ARTmin: Ambrosio relational thickness minimum; BAD D: Belin/Ambrosio enhanced ectasia total deviation value ;BAD Daa: Deviation of the ART average; BAD Dam: Deviation of the ART max; BAD Db: Deviation of back elevation difference map; BAD De: Deviation from the posterior elevation at the thinnest considering BFS 8 mm; BAD Df: Deviation of front elevation difference map; BAD Df: Deviation of minimum thickness; BAD Dk: Deviation from Kmax; BAD Dp: Deviation of average pachymetric progression;BAD Dr: Deviation from the more negative value on the relative thickness map; BAD Dy: Deviation from the vertical displacement of the thinnest point from the apex; C.Vol D 3mm: corneal volume of 3 mm diameter area; C.Vol D 5mm: corneal volume of 5 mm diameter area; C.Vol D 7mm: corneal volume of 7 mm diameter area; C.Vol D 10mm: corneal volume of 10 mm diameter area; D2 mm / Pachy Min: The quotient of D2 mm / Pachy Min; D2 mm: Average corneal thickness of 2 mm circle centered on the thinnest location; D4 mm / Pachy Min: The quotient of D4 mm / Pachy Min; D4 mm: Average corneal thickness of 4 mm circle centered on the thinnest location; D6 mm / Pachy Min: The quotient of D6mm / Pachy Min; D6 mm: Average corneal thickness of 6 mm circle centered on the thinnest location; D8 mm / Pachy Min: The quotient of D8 mm / Pachy Min; D8 mm: Average corneal thickness of 8 mm circle centered on the thinnest location; Ele B BFS 8 mm Max. 4 mm Zone: Elevation parameter derived from the back surface centered at the point with highest value within the 4 mm (diameter) using the 8 mm best-fit sphere; Ele B BFS 8mm Apex: Elevation parameter derived from the back surface centered at the apex calculated using the 8 mm best-fit sphere; Ele B BFS 8mm Thinnest: Elevation parameter derived from the back surface centered at the thinnest point using the 8 mm best-fit sphere; Ele B BFTE 8 mm Max. 4 mm Zone: Elevation parameter derived from the back surface centered at the point with highest value within the 4 mm (diameter) using the 8 mm best-fit toric ellipsoid; Ele B BFTE 8mm Apex: Elevation parameter derived from the back surface centered at the apex calculated using the 8 mm best-fit toric ellipsoid; Ele B BFTE 8mm Thinnest: Elevation parameter derived from the back surface centered at the thinnest point using the 8 mm best-fit toric ellipsoid; Ele F BFS 8 mm Max. 4 mm Zone: Elevation parameter derived from the front surface centered at the point with highest value within the 4 mm (diameter) using the 8 mm best-fit sphere; Ele F BFS 8mm Apex: Elevation parameter derived from the front surface centered at the apex calculated using the 8 mm best-fit sphere; Ele F BFS 8mm Thinnest: Elevation parameter derived from the front surface centered at the thinnest point using the 8 mm best-fit sphere; Ele F BFTE 8 mm Max. 4 mm Zone: Elevation parameter derived from the front surface centered at the point with highest value within the 4 mm (diameter) using the 8 mm best-fit toric ellipsoid; Ele F BFTE 8mm Apex: Elevation parameter derived from the front surface centered at the apex calculated using the 8 mm best-fit toric ellipsoid; Ele F BFTE 8mm Thinnest: Elevation parameter derived from the front surface centered at the thinnest point using the 8 mm best-fit toric ellipsoid; IHA: Index highest asymmetry; IHD: Index highest decentration; ISV: Index of surface variance; IVA: Index of vertical asymmetry; KI: Keratoconus index; Pachy Min: Corneal thickness at the thinnest point; Pachy Min Y: Position of minimum corneal thickness in relation of Y axis centered on cornea apex; PRC (3mm Zone): Posterior radius of curvature in the 3.0 mm zone centered on the thinnest location of the cornea; Rel Pachy Min: Relative corneal thickness at the thinnest point; RMS HOA (CB): root mean square of high order aberration of cornea back; RMS HOA (CF): root mean square of high order aberration of cornea front; RMS HOA (Cornea): root mean square of high order aberration of total cornea; RPIavg: Average pachymetric progression index; RPImax: Maximum pachymetric progression index; RPImin: Minimum pachymetric progression index; Z 3 -1 (CB): 3rd order vertical coma aberration cornea back; Z 3 -1 (CF): 3rd order vertical coma aberration of cornea front; Z 3 -1 (Cornea): 3rd order vertical coma aberration total cornea; Z 5 -1 (CB): 5th order vertical coma aberration of cornea back; Z 5 -1 (CF): 5th order vertical coma aberration of cornea front. All Zernike measurements were made for a corneal diameter of 6 mm.

Inclusion Criteria:

Patients were considered to be very asymmetric (VAE-NT) if the diagnosis of ectasia was confirmed in one eye based on the previously described criteria and the fellow eye had a normal front surface curvature (topometric) map. Objective criteria for considering normal topography was applied for defining the cases of VAE-NT, including objective front surface curvature metrics derived from Pentacam. Normal topography was rigorously considered based on objective criteria (27, 28) of a maximum curvature Kmax (Steepest Front Keratometry) <47.2 diopters, a paracentral inferior-superior (I-S value) asymmetry value at 6 mm (3-mm radii) < 1.45, and keratoconus percentage index (KISA%) score < 60 and (29). The cutoff point used to discriminate normal corneas and VAE-NT from KC corneas was the maximal posterior elevation (< 29 µm). This cutoff point had been determined in a previous study, using the same instrument and the same setting. The posterior elevation map was displayed with a 5-mm color-coded scale, and maximal posterior elevation was measured manually using the cursor in the central 5 mm.

Exclusion Criteria:

The following exclusion criteria were adopted: history of ocular trauma; chronic use of eye medication, glaucoma; dry eye syndrome; corneal scarring; neurotrophic keratopathy; severe meibomian gland dysfunction; vulnerable state owing to physical or mental illness and with language-related difficulties; pregnant or breastfeeding.

Population served at an ophthalmological center in a city with an area covered by an estimated population of one million inhabitants. Patients who sought the service for refractive surgery or for the evaluation and treatment of keratoconus.