Comparative evaluation of methods for obtaining the stress-free geometry of keratoconus corneas with different levels of severity

A biomechanical model that simulates the physiological pressure load on the cornea without considering the stresses in vivo will result in an overstress or underestimation of the stress field and incorrect deformation of the corneal structure. Therefore, it is essential to propose numerical models that consider the stress-free geometry of the cornea. In this study, the Displacement and Pre-stress methods were compared to obtain the stress-free geometry (S-FG) and the physiological estimated geometry (P-EG), based on the patient-specific geometric behavior and the computational time required to reach each geometry. The same shape and contour conditions were considered in the models obtained from both methods for each of the pathological scenarios analyzed. Both methods behaved differently to obtain the free geometry, and this difference increased with the severity grade of the disease. However, they behaved in a similar way to reach the physiological estimated geometry. The Displacement method required a lower computational cost to reach the free geometry, with both methods presenting a similar computational cost to obtain the physiological geometry. The stress-free geometries obtained by both methods allowed to characterize the existing biomechanical decompensation during the progression of the diseases. In conclusion, the calculation of the stress-free corneal geometry associated to the clinically measured intraocular pressure with the Displacement and Prestress Methods in keratoconus eyes allows the development of accurate and useable models in clinical practice in real time. This displacement method shows some benefits in terms of computational cost.

Study of the Influence of Boundary Conditions on Corneal Deformation Based on the Finite Element Method of a Corneal Biomechanics Model

Implementing in silico corneal biomechanical models for surgery applications can be boosted by developing patient-specific finite element models adapted to clinical requirements and optimized to reduce computational times. This research proposes a novel corneal multizone-based finite element model with octants and circumferential zones of clinical interest for material definition. The proposed model was applied to four patient-specific physiological geometries of keratoconus-affected corneas. Free-stress geometries were calculated by two iterative methods, the displacements and prestress methods, and the influence of two boundary conditions: embedded and pivoting. The results showed that the displacements, stress and strain fields differed for the stress-free geometry but were similar and strongly depended on the boundary conditions for the estimated physiological geometry when considering both iterative methods. The comparison between the embedded and pivoting boundary conditions showed bigger differences in the posterior limbus zone, which remained closer in the central zone. The computational calculation times for the stress-free geometries were evaluated. The results revealed that the computational time was prolonged with disease severity, and the displacements method was faster in all the analyzed cases. Computational times can be reduced with multicore parallel calculation, which offers the possibility of applying patient-specific finite element models in clinical applications.

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.

Corneal Epithelium Thickness and Refractive Changes After Myopic Laser Corneal Refractive Surgery

PURPOSE

To evaluate the postoperative changes in corneal epithelium thickness and refractive power after femtosecond laser-assisted laser in situ keratomileusis (LASIK) and small incision lenticule extraction (SMILE) for myopia correction using anterior segment optical coherence tomography (OCT) with an integrated Placido disc topographer.

METHODS

The VisuMax 500-kHz femtosecond laser (Carl Zeiss Meditec AG) and Amaris 750 excimer laser (SCHWIND eye-tech-solutions) were used. Central, paracentral, and 6-mm epithelial thickness values were obtained, and the change in the value of epithelial thickness was calculated. Changes in the refractive power of the epithelium were also evaluated. The repeatability of this new measurement was also analyzed using the intraclass correlation (ICC). The total follow-up period was 6 months.

RESULTS

A total of 77 LASIK eyes were matched with 77 SMILE eyes. Mean spherical equivalent was -3.92 ± 1.67 diopters (D) for LASIK versus -4.02 ± 1.63 D for SMILE (P = .356). Epithelial thickness parameters significantly and equally thickened in both types of surgery. The change in the value of epithelial thickness was positively correlated with spherical aberration. Analysis of the refractive power of the corneal epithelial layer (ICC > 0.70) showed a tendency for the postoperative myopization of the refractive component of this layer (-0.11 D for SMILE and -0.53 D for LASIK at 3 mm) and an increase in its cylinder and aberrometry. Increasing postoperative spherical aberration and epithelial thickness increased myopization of the epithelial refractive sphere (P < .05).

CONCLUSIONS

Corneal epithelium thickens similarly after LASIK and SMILE, being slightly higher after SMILE. This correlates with the induced spherical aberration. Corneal epithelium thickening induces myopization of its refractive power, which accounts for a slight regression of the net refractive power change on the treated cornea. [J Refract Surg. 2022;38(9):602-608.].

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.

Dynamic Moduli of Polybutylene Terephthalate Glass Fiber Reinforced in High-Temperature Environments

The aim of this work was to show the evolution over time of the dynamic moduli in components made of Polybutylene Terephthalate reinforced with glass fiber when they are held to temperatures close to the glass transition temperature over time. For this purpose, PBT samples reinforced with short, glass fibers of Ultradur^® material with 0%, 20%, and 50% in weight content were tested. Dynamic moduli showed an increment with glass fiber content showing a nonlinear behavior with the temperature. The evolution of storage modulus was depicted by means of a modified law of mixtures with an effectiveness factor depending on temperature and fiber content, whereas the evolution over time was obtained with a time-temperature transformation generated with the TTS Data Analysis software of TA-instruments for a given temperature. Storage modulus showed a linear relationship with glass fiber content when components were held to temperatures near to their respective glass transition temperature, obtained from the maximum of loss modulus curve with temperature. In summary, the value and evolution of dynamic moduli of PBT samples improved with glass fiber content, allowing us to increase the durability of components when they are submitted to high-temperature environments.

Subclinical keratoconus detection with three-dimensional (3-D) morphogeometric and volumetric analysis

PURPOSE

To assess the efficacy of morphogeometric and volumetric characterization of the cornea based on three-dimensional (3-D) modelling in diagnosis of subclinical keratoconus (KC).

METHODS

Cross-sectional study. Ninety-three eyes with subclinical KC with a best spectacle-corrected distance visual acuity ≥20/20 (grade zero KC according to the RETICS classification) and 109 control eyes were included. Computer-based 3-D corneal morphogeometric model was generated using raw topographic data. Distance-, area- and volume-based parameters were used for statistical analysis. Distance parameters included deviation of anterior (D_apexant )/posterior (D_apexpost ) apices and minimum thickness points (D_mctant , D_mctpost ) from corneal vertex, and D_apexant -D_apexpost difference. Areal variables were derived from anterior (A_ant ) and posterior (A_post ) corneal surfaces, sagittal plane passing through corneal apices (A_apexant , A_apexpost ) and thinnest point (A_mctant , A_mctpost ). Total corneal volume (V_total ) and volumetric distribution (with 0.1mm steps) centred to thinnest corneal point (VOL_mct ) and anterior (VOL_aap )/posterior (VOL_pap ) apices comprised the volume-based parameters.

RESULTS

In the subclinical KC group, all D values, D_apexant -D_apexpost difference, A_ant , A_post and A_apexant values were higher (p < 0.001), while A_apexpost , A_mctpost , V_total , VOL_mct , VOL_aap and VOL_pap values were lower when compared to the control group (p < 0.001). Regression analysis-based formula correctly classified 96.8% of the eyes with subclinical KC and 94.5% of the normal ones (p < 0.0001).

CONCLUSIONS

Eyes with subclinical KC seem to represent asymmetrically displaced anterior and posterior corneal apex, corneal thinning and volume loss. 3-D morphogeometric and volumetric parameters and differentiation formula can be incorporated into topography software to detect subclinical KC with high sensitivity and specificity in clinical practice.

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.

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.

An angle-supported foldable phakic intraocular lens for correction of myopia: A five-year follow-up

OBJECTIVE

To evaluate the efficacy and safety of an angle-supported foldable phakic intraocular lens (pIOL) for the correction of moderate to high myopia after 5 years follow-up.

METHODS

Prospective and retrospective, observational, longitudinal, non-randomised consecutive series of cases conducted on a total of 100 eyes of 67 patients with moderate to high myopia implanted with an Acrysof Cachet pIOL (Alcon Laboratories Inc.) with the aim of minimising the refractive error. The ages ranged between 18 to 60years. Uncorrected distance visual acuity (UDVA), manifest refraction, corrected distance visual acuity (CDVA), endothelial cells density, pIOL position, intraocular pressure, and complications were recorded preoperatively and during the 5 year follow-up.

RESULTS

Five years after implantation, the mean manifest spherical equivalent refraction reduced significantly from -11.62±3.35 dioptres (D) to -0.33±0.85D. UDVA was 20/20 or better in 5 of 25 cases (20%), and 20/40 or better in 22 cases (88%). CDVA was 20/20 or better in 17 cases (68%), and 20/32 or better in 23 cases (92%) of eyes. The residual refractive error was within ±0.50D of emmetropia in 12 cases (48%), and within ±1.00D in 19 cases (76%). Mean endothelial cell loss at 5 years was 11.8% central, and 13.7% peripheral. Mean endothelium-pIOL distance was 2.11±0.18mm, and mean pIOL-crystalline distance was 0.88±0.20mm.

CONCLUSIONS

This angle supported pIOL provided a favourable refractive correction and predictability, as well as acceptable safety in patients with moderate to high myopia. Although endothelial cell density decreased over 5years, the results are within the range reported in previous studies with other pIOLs.