Geometrical custom modeling of human cornea in vivo and its use for the diagnosis of corneal ectasia

Novel Multivariable Evolutionary Algorithm-Based Method for Modal Reconstruction of the Corneal Surface from Sparse and Incomplete Point Clouds

Three-dimensional reconstruction of the corneal surface provides a powerful tool for managing corneal diseases. This study proposes a novel method for reconstructing the corneal surface from elevation point clouds, using modal schemes capable of reproducing corneal shapes using surface polynomial functions. The multivariable polynomial fitting was performed using a non-dominated sorting multivariable genetic algorithm (NS-MVGA). Standard reconstruction methods using least-squares discrete fitting (LSQ) and sequential quadratic programming (SQP) were compared with the evolutionary algorithm-based approach. The study included 270 corneal surfaces of 135 eyes of 102 patients (ages 11-63) sorted in two groups: control (66 eyes of 33 patients) and keratoconus (KC) (69 eyes of 69 patients). Tomographic information (Sirius, Costruzione Strumenti Oftalmici, Italy) was processed using Matlab. The goodness of fit for each method was evaluated using mean squared error (MSE), measured at the same nodes where the elevation data were collected. Polynomial fitting based on NS-MVGA improves MSE values by 86% compared to LSQ-based methods in healthy patients. Moreover, this new method improves aberrated surface reconstruction by an average value of 56% if compared with LSQ-based methods in keratoconus patients. Finally, significant improvements were also found in morpho-geometric parameters, such as asphericity and corneal curvature radii.

A three-dimensional morpho-volumetric similarity study of Down syndrome keratopathy vs. keratoconus

BACKGROUND

To compare and contrast morpho-volumetric features between Down syndrome (DS) cornea and non-DS keratoconic cornea by three-dimensional (3D) modelling.

METHODS

Forty-three subjects (43 eyes) with DS and 99 patients matching their age and sex (99 eyes) with keratoconus (KC) were included in this single-center cross-sectional study. Main outcome measures were high-order aberrations (HOA), central corneal thickness (CCT), spherical equivalent refraction, and morpho-volumetric parameters established using a 3D corneal model, such as deviation of anterior and posterior corneal apices (D_apexant/D_apexpost) and minimum thickness points (D_mctant/D_mctpost) from corneal vertex, areas of the anterior and posterior surfaces (A_ant/A_post), sagittal area passing through the anterior and posterior corneal apices (A_apexant/A_apexpost) and minimum thickness point (A_mctpost) and corneal volume of the complete cornea (V_total).

RESULTS

Age, gender, spherical equivalent refraction, CCT and V_total were similar between the net on-DS KC and DS groups (P > 0.05), while non-DS KC group had higher HOA than the DS group (P < 0.05). D_apexant, A_ant, A_post and A_apexant showed higher values in the DS group than in the non-DS KC group, whereas D_apexpost showed a reduction in the DS group when compared with the non-DS KC group (P < 0.05).

CONCLUSIONS

This study demonstrated that anterior and posterior corneal apex dynamics were specifically different in DS subjects, as the anterior apex tends to displace more prominently when compared to that from the non-DS KC group, while the posterior apex appears to be more stable than that in non-DS KC, which also support the theory that DS patients suffer from a specific keratopathy, distinctively different to KC but strongly related to it, and probably showing a diversity of corneal phenotypes in all cases of DS.

Emerging tissue engineering strategies for the corneal regeneration

Cornea as the outermost layer of the eye is at risk of various genetic and environmental diseases that can damage the cornea and impair vision. Corneal transplantation is among the most applicable surgical procedures for repairing the defected tissue. However, the scarcity of healthy tissue donations as well as transplantation failure has remained as the biggest challenges in confront of corneal grafting. Therefore, alternative approaches based on stem-cell transplantation and classic regenerative medicine have been developed for corneal regeneration. In this review, the application and limitation of the recently-used advanced approaches for regeneration of cornea are discussed. Additionally, other emerging powerful techniques such as 5D printing as a new branch of scaffold-based technologies for construction of tissues other than the cornea are highlighted and suggested as alternatives for corneal reconstruction. The introduced novel techniques may have great potential for clinical applications in corneal repair including disease modeling, 3D pattern scheming, and personalized medicine.

Keratoconus: An updated review

Keratoconus is a bilateral and asymmetric disease which results in progressive thinning and steeping of the cornea leading to irregular astigmatism and decreased visual acuity. Traditionally, the condition has been described as a noninflammatory disease; however, more recently it has been associated with ocular inflammation. Keratoconus normally develops in the second and third decades of life and progresses until the fourth decade. The condition affects all ethnicities and both sexes. The prevalence and incidence rates of keratoconus have been estimated to be between 0.2 and 4,790 per 100,000 persons and 1.5 and 25 cases per 100,000 persons/year, respectively, with highest rates typically occurring in 20- to 30-year-olds and Middle Eastern and Asian ethnicities. Progressive stromal thinning, rupture of the anterior limiting membrane, and subsequent ectasia of the central/paracentral cornea are the most commonly observed histopathological findings. A family history of keratoconus, eye rubbing, eczema, asthma, and allergy are risk factors for developing keratoconus. Detecting keratoconus in its earliest stages remains a challenge. Corneal topography is the primary diagnostic tool for keratoconus detection. In incipient cases, however, the use of a single parameter to diagnose keratoconus is insufficient, and in addition to corneal topography, corneal pachymetry and higher order aberration data are now commonly used. Keratoconus severity and progression may be classified based on morphological features and disease evolution, ocular signs, and index-based systems. Keratoconus treatment varies depending on disease severity and progression. Mild cases are typically treated with spectacles, moderate cases with contact lenses, while severe cases that cannot be managed with scleral contact lenses may require corneal surgery. Mild to moderate cases of progressive keratoconus may also be treated surgically, most commonly with corneal cross-linking. This article provides an updated review on the definition, epidemiology, histopathology, aetiology and pathogenesis, clinical features, detection, classification, and management and treatment strategies for keratoconus.

Descemet's membrane area and posterior corneal power may predict the Descemet membrane folds after deep anterior lamellar keratoplasty in patients with advanced keratoconus

AIMS

To investigate possible predictive topographic characteristics for the development of Descemet's membrane (DM) folds after the uneventful deep anterior lamellar keratoplasty (DALK).

METHODS

A retrospective study included 56 eyes of 56 consecutive patients who underwent uneventful DALK using the big-bubble technique to treat advanced keratoconus. At baseline and each visit, best-corrected logMAR visual acuity (BCVA), slit-lamp findings, endothelial cell density, topographic parameters were recorded. DM area is calculated using morphogeometric modelling.

RESULTS

Twelve (21.4%) of them exhibited DM folds, whereas the remaining 44 (78.6%) did not exhibit any DM folds after the surgery. The mean follow-up time was 36.3 ± 16.7 (range, 12-71) months. The mean posterior corneal power was - 13.8 ± 0.6 D in patients with DM folds, whereas - 13.0 ± 0.8 D in those without DM folds (p = 0.016). The mean DM area was 53.6 ± 2.3 (50.9-57.9) mm² in patients with DM folds, whereas 51.6 ± 1.7 (47.1-53.9) mm² in those without DM folds (p = 0.001). The ROC curve showed that two best cut-off value for the posterior corneal power and DM area were 13.75 D and 53.8 mm², respectively, to predict the occurrence of DM folds.

CONCLUSION

DALK surgery seems to cause DM folds in patients with large DM area and high posterior corneal power.

Effects of intracorneal ring segments implementation technique and design on corneal biomechanics and keratometry in a personalized computational analysis

The implementation of intracorneal ring segments (ICRS) is one of the successfully applied refractive operations for the treatment of keratoconus (kc) progression. The different selection of ICRS types along with the surgical implementation techniques can significantly affect surgical outcomes. Thus, this study aimed to investigate the influence of ICRS implementation techniques and design on the postoperative biomechanical state and keratometry results. The clinical data of three patients with different stages and patterns of keratoconus were assessed to develop a three-dimensional (3D) patient-specific finite-element model (FEM) of the keratoconic cornea. For each patient, the exact surgery procedure definitions were interpreted in the step-by-step FEM. Then, seven surgical scenarios, including different ICRS designs (complete and incomplete segment), with two surgical implementation methods (tunnel incision and lamellar pocket cut), were simulated. The pre- and postoperative predicted results of FEM were validated with the corresponding clinical data. For the pre- and postoperative results, the average error of 0.4% and 3.7% for the mean keratometry value ([Formula: see text]) were predicted. Furthermore, the difference in induced flattening effects was negligible for three ICRS types (KeraRing segment with arc-length of 355, 320, and two separate 160) of equal thickness. In contrast, the single and double progressive thickness of KeraRing 160 caused a significantly lower flattening effect compared to the same type with constant thickness. The observations indicated that the greater the segment thickness and arc-length, the lower the induced mean keratometry values. While the application of the tunnel incision method resulted in a lower [Formula: see text] value for moderate and advanced KC, the induced maximum Von Mises stress on the postoperative cornea exceeded the induced maximum stress on the cornea more than two to five times compared to the pocket incision and the preoperative state of the cornea. In particular, an asymmetric regional Von Mises stress on the corneal surface was generated with a progressive ICRS thickness. These findings could be an early biomechanical sign for a later corneal instability and ICRS migration. The developed methodology provided a platform to personalize ICRS refractive surgery with regard to the patient's keratoconus stage in order to facilitate the efficiency and biomechanical stability of the surgery.

Quantitative comparison of corneal surface areas in keratoconus and normal eyes

Keratoconus is a highly prevalent corneal disorder characterized by progressive corneal thinning, steepening and irregular astigmatism. To date, pathophysiology of keratoconus development and progression remains debated. In this study, we retrospectively analysed topographic elevation maps from 3227 eyes of 3227 patients (969 keratoconus and 2258 normal eyes) to calculate anterior and posterior corneal surface area. We compared results from normal eyes and keratoconus eyes using the Mann–Whitney U test. The Kruskal–Wallis test was used to compare keratoconus stages according to the Amsler–Krumeich classification. Keratoconus eyes were shown to have statistically significantly larger corneal surface areas, measured at the central 4.0 mm and 8.0 mm, and total corneal diameter. However, no significant increase in corneal surface area was seen with increasing severity of keratoconus. We suggest that these results indicate redistribution, rather than increase, of the corneal surface area with keratoconus severity.

Three-Dimensional Morphogeometric and Volumetric Characterization of Cornea in Pediatric Patients With Early Keratoconus

PURPOSE

To present morphogeometric and volumetric characteristics of the cornea and its diagnostic value in pediatric patients with keratoconus (KC) using 3-dimensional (3-D) corneal modeling.

DESIGN

Cross-sectional study.

METHODS

This single-center (VISSUM Innovation, Alicante, Spain) study comprised 49 eyes of 49 pediatric patients (age ≤16 years) with KC and 31 eyes of 31 healthy pediatric controls. Eyes were graded as early (n = 21) and mild KC (n = 28) based on the RETICS (Thematic Network for Co-Operative Research in Health) classification system. The 3-D corneal model was generated using raw topographic data. Deviation of anterior (D_apexant) and posterior (D_apexpost) apex and minimum thickness points (D_mctant, D_mctpost), D_apexant-D_apexpost difference, total corneal volume (V_total), volumetric distribution (VOL_AAP, VOL_PAP, and VOL_MCT), and percentage of relative volume increase (VOL_AAPrel, VOL_PAPrel, and VOL_MCTrel) between 2 consecutive radii centered to anterior/posterior apex and thinnest point were evaluated.

RESULTS

D_apexpost and D_apexant-D_apexpost difference were higher in the early and mild KC groups compared to the control group (P < .05). Eyes with early and mild KC had decreased V_total compared with the control group (P < .05). D_apexpost, D_apexant-D_apexpost difference, and VOL_MCTrel between 1.0 and 1.4 mm diameters had area under receiver operating characteristics curve (AUROC) values over 0.93 in discrimination of early KC from normal.

CONCLUSIONS

This is the first study presenting morphogeometric and volumetric characterization of cornea in pediatric patients with early and mild KC using a 3-D corneal model. Integration of the morphogeometric and volumetric parameters to topography software can add value in early detection of KC in pediatric patients.

Evidence of a Down Syndrome Keratopathy: A Three-Dimensional (3-D) Morphogeometric and Volumetric Analysis

The aim of this study was to investigate whether a different and abnormal corneal profile is present in Down syndrome (DS) by personalized three-dimensional (3D) modelling. This single-centre cross-sectional study included 43 patients with DS (43 eyes) and 58 age-sex-matched control subjects (58 eyes) with normal karyotype and topography. Refraction, central corneal thickness (CCT), aberrations (high-order, coma and spherical), asphericity and morphogeometric/volumetric parameters based on a 3D corneal model that was generated from raw topographical data were evaluated. Deviation of anterior/posterior apex (D_apexant/D_apexpost) and thinnest point (D_mctant/D_mctpost) from corneal vertex, anterior/posterior surface area (A_ant/A_post), sagittal area passing through the anterior/posterior apex (A_apexant/A_apexpost) and thinnest point (A_mctpost), total corneal volume (V_total) and volumetric progression for each 0.05 mm step of the radius value centred to the thinnest point (VOL_MCT) and anterior/posterior apex (VOL_AAP/VOL_PAP) comprised the morphogeometric/volumetric parameters. In the DS group, 58.1% of the eyes presented abnormal topography. High-order and coma aberrations, asphericity, D_apexant, A_ant, A_post and A_apexant were significantly higher, whereas CCT, A_apexpost, A_mctpost, V_total, VOL_AAP, VOL_PAP and VOL_MCT were lower in the DS group than in the control group (p < 0.05). D_apexpost did not differ between the groups (p > 0.05). This study demonstrates that corneas of the subjects with DS are different and more aberrated than those of normal age- and sex-matched non-DS controls. Anterior corneal apex appears to be displaced in DS even with normal topography, while posterior apex seems stable although topography is abnormal. These findings may help to modify our approach in the diagnosis of keratopathy in subjects with DS.

Relationship between Corneal Morphogeometrical Properties and Biomechanical Parameters Derived from Dynamic Bidirectional Air Applanation Measurement Procedure in Keratoconus

The morphogeometric analysis of the corneal structure has become a clinically relevant diagnostic procedure in keratoconus (KC) as well as the in vivo evaluation of the corneal biomechanical properties. However, the relationship between these two types of metrics is still not well understood. The current study investigated the relationship of corneal morphogeometry and volume with two biomechanical parameters: corneal hysteresis (CH) and corneal resistance factor (CRF), both provided by an Ocular Response Analyzer (Reichert). It included 109 eyes from 109 patients (aged between 18 and 69 years) with a diagnosis of keratoconus (KC) who underwent a complete eye examination including a comprehensive corneal topographic analysis with the Sirius system (CSO). With the topographic information obtained, a morphogeometric and volumetric analysis was performed, defining different variables of clinical use. CH and CRF were found to be correlated with these variables, but this correlation was highly influenced by corneal thickness. This suggests that the mechanical properties of KC cornea contribute only in a partial and limited manner to these biomechanical parameters, being mostly influenced by morphogeometry under normal intraocular pressure levels. This would explain the limitation of CH and CRF as diagnostic tools for the detection of incipient cases of KC.

Morphogeometric analysis for characterization of keratoconus considering the spatial localization and projection of apex and minimum corneal thickness point

This work evaluates changes in new morphogeometric indices developed considering the position of anterior and posterior corneal apex and minimum corneal thickness (MCT) point in keratoconus. This prospective comparative study included 440 eyes of 440 patients (age, 7-99 years): control (124 eyes) and keratoconus (KC) groups (316 eyes). Tomographic information (Sirius®, Costruzione Strumenti Oftalmici, Italy) was treated with SolidWorks v2013, creating the following morphogeometric parameters: geometric axis-apex line angle (GA-AP), geometric axis-MCT line angle (GA-MCT, apex line-MCT line angle (AP-MCT), and distances between apex and MCT points on the anterior (anterior AP-MCTd) and posterior corneal surface (posterior AP-MCTd). Statistically significant higher values of GA-AP, GA-MCT, AP-MCT and anterior AP-MCTd were found in the keratoconus group (p ≤ 0.001). Moderate significant correlations of corneal aberrations (r ≥ 0.587, p < 0.001) and corneal thickness parameters (r ≤ -0.414, p < 0.001) with GA-AP and AP-MCT were found. Anterior asphericity was found to be significantly correlated with anterior and posterior AP-MCTd (r ≥ 0.430, p < 0.001). Likewise, GA-AP and AP-MCT showed a good diagnostic ability for the detection of keratoconus, with optimal cutoff values of 9.61° (sensitivity 85.5%, specificity 80.3%) and 18.08° (sensitivity 80.5%, specificity 78.7%), respectively. These new morphogeometric indices allow a clinical characterization of the 3-D structural alteration occurring in keratoconus, with less coincidence in the spatial projection of the apex and MCT points of both corneal surfaces. Future studies should confirm the potential impact on the precision of these indices of the variability of posterior corneal surface measurements obtained with Scheimpflug imaging technology.

Alió del Barrio J, Cavas F, Alió JL. Changes in the 3D Corneal Structure and Morphogeometric Properties in Keratoconus after Corneal Collagen Crosslinking

Keratoconus is an ectatic disorder that is presently considered one of the most prevalent reasons for keratoplasty. Corneal collagen crosslinking (CXL) is the only proven treatment option available that is capable of halting the progression of the disease by stabilizing the cone in 90% of cases, and by also reducing refractive error and maximal keratometry. This study assesses, by means of a 3D morphogeometric analysis procedure developed by our research team, the corneal structure changes that occur immediately after CXL treatment and during a 6 month follow-up period. A total of 19 eyes from 19 patients diagnosed with keratoconus who underwent CXL were included, and several variables derived from the morphogeometric analysis were calculated and evaluated for the pre-operative, 3 month postoperative, and 6 month postoperative states. Significant reductions were detected in central corneal thickness and corneal spherical-like root mean square (RMS) 3 months after surgery, with non-significant regression of the effect afterward. Significant reductions in the total corneal area/volume were found, with some levels of regression after 6 months in certain volumetric parameters. In conclusion, the eyes with higher values for morphogeometric parameters—posterior apex deviation (PAD), anterior minimum thickness point deviation (AMTPD), and posterior minimum thickness point deviation (PMTPD)—seemed more likely to undergo aberrometric improvement as a result of CXL surgery.

Anterior and posterior ratio of corneal surface areas: A novel index for detecting early stage keratoconus

Purpose

To evaluate the diagnostic ability of the ratio of anterior and posterior corneal surface areas (As/Ps) comparing with other keratoconus screening indices in distinguishing forme fruste keratoconus (FFKC) from normal eyes.

Methods

In this comparative study, 13 eyes of 13 patients with FFKC, 29 eyes of 29 patients with keratoconus (KC) and 88 eyes of 88 patients with normal subjects were involved.

The As/Ps measured by the anterior segment optical coherence tomography (AS-OCT) and other indices measured by AS-OCT and rotating Scheimpflug–based corneal tomography were evaluated. The area under receiver-operating-characteristics (AU-ROC) was calculated to assess the diagnostic ability in discriminating FFKC from normal eyes.

Results

The As/Ps, the Belin/Ambrosio display enhanced ectasia total derivation value (BAD-D) and posterior and anterior elevation values showed the AU-ROC 0.9 or more in differentiating FFKC from normal eyes (0.980, 0.951, 0.924 and 0.903, respectively). The sensitivity and specificity were 0.92 and 0.96 for the As/Ps, 1.00 and 0.90 for BAD-D, 0.85 and 0.86 for posterior elevation value, and 0.85 and 0.96 for anterior elevation value, respectively.

Conclusions

Among the several indices for keratoconus screening which we evaluated, the As/Ps obtained by AS-OCT had the large AU-ROC with high sensitivity and specificity in detecting FFKC, which was comparable with BAD-D obtained by rotating Scheimpflug–based corneal tomography. The As/Ps may provide information for improving the diagnostic accuracy of KC, even in the initial stage of the disease.

A Machine-Learning Model Based on Morphogeometric Parameters for RETICS Disease Classification and GUI Development

This work pursues two objectives: defining a new concept of risk probability associated with suffering early-stage keratoconus, classifying disease severity according to the RETICS (Thematic Network for Co-Operative Research in Health) scale. It recruited 169 individuals, 62 healthy and 107 keratoconus diseased, grouped according to the RETICS classification: 44 grade I; 18 grade II; 15 grade III; 15 grade IV; 15 grade V. Different demographic, optical, pachymetric and eometrical parameters were measured. The collected data were used for training two machine-learning models: a multivariate logistic regression model for early keratoconus detection and an ordinal logistic regression model for RETICS grade assessments. The early keratoconus detection model showed very good sensitivity, specificity and area under ROC curve, with around 95% for training and 85% for validation. The variables that made the most significant contributions were gender, coma-like, central thickness, high-order aberrations and temporal thickness. The RETICS grade assessment also showed high-performance figures, albeit lower, with a global accuracy of 0.698 and a 95% confidence interval of 0.623–0.766. The most significant variables were CDVA, central thickness and temporal thickness. The developed web application allows the fast, objective and quantitative assessment of keratoconus in early diagnosis and RETICS grading terms.

Assessment of the Association between In Vivo Corneal Morphogeometrical Changes and Keratoconus Eyes with Severe Visual Limitation

Assessing changes suffered by the cornea as keratoconus progresses has proven to be vital for this disease diagnosis and treatment. This study determines the corneal biometric profile in eyes considered as affected by keratoconus (KC) showing severe visual limitation, by means of in vivo 3D modelling techniques. This observational case series study evaluated new objective indices in 50 healthy and 30 KC corneas, following a validated protocol created by our research group, which has been previously used for diagnosis and characterization of KC in asymptomatic (preclinical) and mild visually impaired eyes. Results show a statistically significant reduction of corneal volume and an increase of total corneal area in the severe KC group, being anterior and posterior corneal surfaces minimum thickness points the best correlated parameters, although with no discrimination between groups. Receiving operator curves were used to determine sensitivity and specificity of selected indices, being anterior and posterior apex deviations the ones which reached the highest area under the curve, both with very high sensitivity (96.7% and 90%, respectively) and specificity (94.0% and 99.9%, respectively). The results suggest that once severe visual loss appears, anterior corneal topography should be considered for a more accurate diagnosis of clinical KC, being anterior apex deviation the key metric discriminant. This study can be a useful tool for KC classification, helping doctors in diagnosing severe cases of the disease, and can help to characterize corneal changes that appear when severe KC is developed and how they relate with vision deterioration.

Keratoconic eyes with stable corneal tomography could benefit more from custom intraocular lens design than normal eyes

We investigated whether eyes with keratoconic corneal tomography pattern could benefit more from aberration correction with custom intraocular lenses (IOLs) than normal cataractous eyes despite the effect of misalignment on the correction of aberrations. Custom IOLs (cIOLs) were calculated for twelve normal and twelve keratoconic eyes using personalized numerical ray tracing models. The Stiles-Crawford weighted root-mean-square spot-size (wRMS) at the virtual fovea was evaluated for cIOLs and aberration-neutral IOLs (nIOLs) in a simulated clinical study with 500 virtual IOL implantations per eye and per IOL. IOL misalignment (decentration, tilt, rotation) and pupillary ectopia (4.5 mm iris aperture) were varied upon each virtual implantation. The nIOLs achieved average wRMS of 16.4 ± 4.3 μm for normal, and 92.7 ± 34.4 μm for keratoconic eyes (mean ± standard deviation). The cIOLs reduced the average wRMS to 10.3 ± 5.8 μm for normal, and 28.5 ± 18.6 μm for keratoconic eyes. The cIOLs produced smaller wRMS than nIOLs in most virtual implantations (86.7% for normal and 99.4% for keratoconic eyes). IOL misalignment resulted in larger wRMS variations in the keratoconus group than in the normal group. Custom freeform IOL-optics-design may become a promising option for the correction of advanced aberrations in eyes with non-progressive keratoconic corneal tomography pattern.

Study and characterization of morphogeometric parameters to assist diagnosis of keratoconus

Background

In case of significant imperfections on the cornea, data acquisition is difficult and a significant level of missing data could require the interpolation of important areas of the cornea, resulting in a very ambiguous model. The development of methods to define in vivo customised geometric properties of the cornea based only on real raw data is extremely useful to diagnose and assess the progression of diseases directly related to the corneal architecture. The present work tries to improve the prognostic of corneal ectasia creating a 3D customised model of the cornea and analysing different geometric variables from this model to determine which variables or combination of them could be defined as an indicator of susceptibility to develop keratoconus.

Methods

A corneal geometric reconstruction was performed using zonal functions and retrospective Scheimpflug tomography data from 187 eyes of 187 patients. Morphology of healthy and keratoconic corneas was characterized by means of geometric variables. The performance of these variables as predictors of a new geometric marker was assessed and their correlations were analysed.

Results

The more representative variable to classify the corneal anomalies related to keratoconus was posterior apex deviation (area under receiver operating characteristic curve > 0.899; p < 0.0001). However, the strongest correlations in both healthy and pathological corneas were provided by the metrics directly related to the thickness, as deviations of the anterior/posterior minimum thickness points.

Conclusions

The presented morphogeometric approach based on the analysis and custom geometric modelling of the cornea demonstrates to be useful for the characterization and diagnosis of keratoconus disease, stating that geometrical deformation is an effective marker of the ectatic disease’s progression.

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.

Keratoconus Detection Based on a New Corneal Volumetric Analysis

There are numerous tomographic indices for the detection of keratoconus risk. When the indexes based on corneal volume are analyzed, two problems are presented: on the one hand, they are not very sensitive to the detection of incipient cases of keratoconus because they are not locally defined in the primary developmental region of the structural abnormalities; and on the other hand, they do not register the geometric decompensation driven by the asymmetry present during the disease progression. This work performed a morphogeometric modeling of the cornea by the aid of CAD tools and using raw topographic data (Sirius system, CSO, Firenze). For this method, four singular points present on the corneal surfaces were located and the following parameters based on corneal volume were calculated: VOL_mct, defined by the points of minimal thickness; VOL_aap, defined by the anterior corneal apex, and VOL_pap, defined by the posterior corneal apex. The results demonstrate that a further reduction of corneal volume in keratoconus happens and significantly progresses along the disease severity level. The combination of optical and volumetric data, that collect the sensitivity of the asymmetry generated by the disease, allows an accurate detection of incipient cases and follow up of the disease progression.

A new approach to keratoconus detection based on corneal morphogeometric analysis

Purpose

To characterize corneal structural changes in keratoconus using a new morphogeometric approach and to evaluate its potential diagnostic ability.

Methods

Comparative study including 464 eyes of 464 patients (age, 16 and 72 years) divided into two groups: control group (143 healthy eyes) and keratoconus group (321 keratoconus eyes). Topographic information (Sirius, CSO, Italy) was processed with SolidWorks v2012 and a solid model representing the geometry of each cornea was generated. The following parameters were defined: anterior (A_ant) and posterior (A_post) corneal surface areas, area of the cornea within the sagittal plane passing through the Z axis and the apex (A_apexant, A_apexpost) and minimum thickness points (A_mctant, A_mctpost) of the anterior and posterior corneal surfaces, and average distance from the Z axis to the apex (D_apexant, D_apexpost) and minimum thickness points (D_mctant, D_mctpost) of both corneal surfaces.

Results

Significant differences among control and keratoconus group were found in A_apexant, A_apexpost, A_mctant, A_mctpost, D_apexant, D_apexpost (all p<0.001), A_post (p = 0.014), and D_mctpost (p = 0.035). Significant correlations in keratoconus group were found between A_ant and A_post (r = 0.836), A_mctant and A_mctpost (r = 0.983), and D_mctant and D_mctpost (r = 0.954, all p<0.001). A logistic regression analysis revealed that the detection of keratoconus grade I (Amsler Krumeich) was related to A_post, A_tot, A_apexant, A_mctant, A_mctpost, D_apexpost, D_mctant and D_mctpost (Hosmer-Lemeshow: p>0.05, R² Nagelkerke: 0.926). The overall percentage of cases correctly classified by the model was 97.30%.

Conclusions

Our morphogeometric approach based on the analysis of the cornea as a solid is useful for the characterization and detection of keratoconus.

Smoothing Splines on Unit Ball Domains with Application to Corneal Topography

Optical coherence tomography (OCT) is a non-invasive imaging technique used to study and understand internal structures of biological tissues such as the anterior chamber of the human eye. An interesting problem is the reconstruction of the shape of the biological tissue from OCT images, that is not only a good fit of the data but also respects the smoothness properties observed in the images. A similar problem arises in Magnetic Resonance Imaging (MRI). We cast the problem as a penalized weighted least squares regression with a penalty on the magnitude of the second derivative (Laplacian) of the surface. We present a novel algorithm to construct the Kimeldorf-Wahba solution for unit ball domains. Our method unifies the ad-hoc approaches currently in the literature. Application of the theory to data from an anterior segment optical coherence tomographer is presented. A detailed comparison of the reconstructed surface using different approaches is presented.

Corneal topography in keratoconus: state of the art

The morphological characterization of the cornea using corneal topographers is a widespread clinical practice that is essential for the diagnosis of keratoconus. The current state of this non-invasive exploratory technique has evolved with the possibility of achieving a great number of measuring points of both anterior and posterior corneal surfaces, which is possible due to the development of new and advanced measurement devices. All these data are later used to extract a series of topographic valuation indices that permit to offer the most exact and reliable clinical diagnosis. This paper describes the technologies in which current corneal topographers are based on, being possible to define the main morphological characteristics that the keratoconus pathology produces on corneal surface. Finally, the main valuation indices, which are provided by the corneal topographers and used for the diagnosis of keratoconus, are also defined.

Customized Finite Element Modelling of the Human Cornea

Aim

To construct patient-specific solid models of human cornea from ocular topographer data, to increase the accuracy of the biomechanical and optical estimate of the changes in refractive power and stress caused by photorefractive keratectomy (PRK).

Method

Corneal elevation maps of five human eyes were taken with a rotating Scheimpflug camera combined with a Placido disk before and after refractive surgery. Patient-specific solid models were created and discretized in finite elements to estimate the corneal strain and stress fields in preoperative and postoperative configurations and derive the refractive parameters of the cornea.

Results

Patient-specific geometrical models of the cornea allow for the creation of personalized refractive maps at different levels of IOP. Thinned postoperative corneas show a higher stress gradient across the thickness and higher sensitivity of all geometrical and refractive parameters to the fluctuation of the IOP.

Conclusion

Patient-specific numerical models of the cornea can provide accurate quantitative information on the refractive properties of the cornea under different levels of IOP and describe the change of the stress state of the cornea due to refractive surgery (PRK). Patient-specific models can be used as indicators of feasibility before performing the surgery.