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.

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.

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 (Dapexant/Dapexpost) and minimum thickness points (Dmctant/Dmctpost) from corneal vertex, areas of the anterior and posterior surfaces (Aant/Apost), sagittal area passing through the anterior and posterior corneal apices (Aapexant/Aapexpost) and minimum thickness point (Amctpost) and corneal volume of the complete cornea (Vtotal). RESULTS: Age, gender, spherical equivalent refraction, CCT and Vtotal 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). Dapexant, Aant, Apost and Aapexant showed higher values in the DS group than in the non-DS KC group, whereas Dapexpost 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.].

Optical Impact of Corneal Clearance in Healthy Eyes Fitted with Scleral Contact Lenses: A Pilot Study.

This pilot study was conducted to evaluate the effect on refraction and optical quality of the increase in the corneal clearance after fitting a specific model of scleral contact lens (ScCL) in healthy subjects. A total of 15 eyes from 15 subjects were enrolled in the study, with evaluation of refraction, ocular aberrations and central corneal clearance with the same model of ScCL (ICD Toric, Paragon Vision Science, Gilbert, AZ, USA), but using 3 different sagittal heights: 4200, 4500 and 4800 µm. Mean values of corneal clearance for each ScCL fitted were 418.1 ± 112.1, 706.5 ± 120.3 and 989.9 ± 117.0 µm, respectively. Significant changes were detected in the spherical equivalent and high-order aberrations, especially coma and spherical aberration, when fitting ScCLs of increasing sagittal heights compared to the pre-fitting values. In conclusion, the increase in central corneal clearance when fitting ScCLs affects refraction, leading to a more myopic refractive error, and inducing an increase in different ocular HOAs. This should be considered when fitting ScCLs, especially multifocal designs.

Corneal stromal thickness changes after myopic laser corneal refractive surgery.

PURPOSE: To evaluate the postoperative behavior of the central corneal stromal thickness after myopic femto-laser-assisted in-situ keratomileusis (LASIK) and small-incision lenticule extraction (SMILE) by using combined anterior segment optical coherence tomography and a Placido disk topographer and to compare the accuracy of both laser machines in predicting the real stromal change. SETTING: Vissum Miranza, Alicante, Spain. STUDY DESIGN: Prospective, observational, comparative study. METHODS: The VisuMax 500 kHz femtosecond laser (FS) and the Amaris 750 excimer laser were used for the correction of myopia with or without myopic astigmatism. Central and paracentral stromal thicknesses (ST) and 6.0 mm corneal aberrometry were obtained with the MS39 topographer. Laser-predicted stromal consumption was recorded (maximum lenticule thickness for SMILE and central ablation depth for LASIK). Visual and refractive outcomes were also evaluated. Total follow-up was 6 months. RESULTS: 77 LASIK eyes were matched with 77 SMILE eyes. Mean preoperative spherical equivalent (SE) was -3.92 ± 1.67 diopters (D) for LASIK and -4.02 ± 1.63 D for SMILE (P = .356). After LASIK, ST parameters showed significant rethickening between months 1 and 3 (+4.38 µm for central ST; P < .001), remaining stable thereafter. After SMILE, all ST parameters remained stable from month 1. Stromal ablation prediction was higher for SMILE compared with LASIK for all SE ranges, although postoperatively such differences were significant only for ametropias ≤4 D. At 6 months, mean SMILE laser prediction error was -13.21 ± 7.00 µm, whereas LASIK prediction showed better accuracy (+0.92 ± 8.16 µm; P < .001). CONCLUSIONS: The accuracy of the Amaris 750 excimer laser in predicting the stromal consumption after LASIK was better than the VisuMax FS laser for SMILE. Although SMILE ST remained stable from month 1, after LASIK, mild stromal rethickening was observed up to the third month.

Feasibility Analysis of Bolted Joints with Composite Fibre-Reinforced Thermoplastics.

The use of composite materials has shown steady growth in recent years due to their excellent specific mechanical properties and the possibility to reduce the weight of vehicles without impairing their safety and comfort. Continuous fibre-reinforced thermoplastic composites (CFRTP) show dynamic, acoustic, and damping properties far superior to steel and can be recycled and repaired. Their excellent properties make CFRTP good candidates for anti-vibration and shock absorbing components, however, out-of-plane mechanical properties hinder the anchoring to the vehicle's body by means of bolted connections. The results obtained in this study show how the maximum torque that can be applied without cracks or breakage phenomena is lower than in standard steel joints. Although the preload's value is admissible, this one is reduced over time due to relaxation phenomena associated with the viscoelastic behaviour of thermoplastic matrix. The results obtained can be improved with the integration of metal inserts in connections' areas. In this study, a case study of a gear mount replacing the steel core with CFRTP reinforced with inserts is carried out. The results show a reduction above 50% in weight, opening the possibility of lighter structures in the automotive sector.

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 (Dapexant/Dapexpost) and thinnest point (Dmctant/Dmctpost) from corneal vertex, anterior/posterior surface area (Aant/Apost), sagittal area passing through the anterior/posterior apex (Aapexant/Aapexpost) and thinnest point (Amctpost), total corneal volume (Vtotal) and volumetric progression for each 0.05 mm step of the radius value centred to the thinnest point (VOLMCT) and anterior/posterior apex (VOLAAP/VOLPAP) comprised the morphogeometric/volumetric parameters. In the DS group, 58.1% of the eyes presented abnormal topography. High-order and coma aberrations, asphericity, Dapexant, Aant, Apost and Aapexant were significantly higher, whereas CCT, Aapexpost, Amctpost, Vtotal, VOLAAP, VOLPAP and VOLMCT were lower in the DS group than in the control group (p < 0.05). Dapexpost 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.

Diagnostic Value of Corneal Epithelial and Stromal Thickness Distribution Profiles in Forme Fruste Keratoconus and Subclinical Keratoconus.

PURPOSE: To assess the diagnostic values of corneal epithelial and stromal thickness distribution characteristics in forme fruste keratoconus (FFKC) and subclinical keratoconus (KC). METHODS: This cross-sectional study was conducted at VISSUM Innovation and Miguel Hernandez University, Alicante, Spain. Twenty-seven eyes (27 subjects) with FFKC, 50 eyes (50 subjects) with subclinical KC with a best spectacle corrected distance visual acuity ≥20/20 (Snellen) (grade zero KC according to the Red Temática de Investigación Cooperativa en Salud classification), and 66 control eyes (66 subjects) were included. Epithelial and stromal thicknesses and epithelium/stroma (E/S) thickness ratio at center, thinnest point, 5-, and 8-mm circles obtained from the MS-39 device (CSO, Firenze, Italy) were compared among the control, FFKC, and subclinical KC groups. RESULTS: The FFKC group had thinner 8-mm superior-nasal epithelium and higher central E/S ratio compared with the control group (P < 0.05). In the subclinical KC group, the E/S ratios in the 5-mm temporal and superior zones were higher than those in the control group (P < 0.05). The FFKC and subclinical KC groups had thinner stroma compared with the control group (P < 0.05). A two-parameter formula correctly classified 94% of the eyes with subclinical KC and 98.5% of the normals, whereas another three-parameter model had 75% sensitivity and 94.3% specificity for discriminating FFKC from normals. CONCLUSIONS: This study identified different epithelial distributional and behavioral patterns in eyes with FFKC and subclinical KC. Eyes with FFKC seem to have increased central E/S ratio and asymmetric superior-nasal epithelial thinning, whereas keratometric and volumetric alterations seem to be more prominent in subclinical KC.

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 (Dapexant) and posterior (Dapexpost) apex and minimum thickness points (Dmctant, Dmctpost), Dapexant-Dapexpost difference, total corneal volume (Vtotal), volumetric distribution (VOLAAP, VOLPAP, and VOLMCT), and percentage of relative volume increase (VOLAAPrel, VOLPAPrel, and VOLMCTrel) between 2 consecutive radii centered to anterior/posterior apex and thinnest point were evaluated. RESULTS: Dapexpost and Dapexant-Dapexpost 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 Vtotal compared with the control group (P < .05). Dapexpost, Dapexant-Dapexpost difference, and VOLMCTrel 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.

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.

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.

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 (Dapexant )/posterior (Dapexpost ) apices and minimum thickness points (Dmctant , Dmctpost ) from corneal vertex, and Dapexant -Dapexpost difference. Areal variables were derived from anterior (Aant ) and posterior (Apost ) corneal surfaces, sagittal plane passing through corneal apices (Aapexant , Aapexpost ) and thinnest point (Amctant , Amctpost ). Total corneal volume (Vtotal ) and volumetric distribution (with 0.1mm steps) centred to thinnest corneal point (VOLmct ) and anterior (VOLaap )/posterior (VOLpap ) apices comprised the volume-based parameters. RESULTS: In the subclinical KC group, all D values, Dapexant -Dapexpost difference, Aant , Apost and Aapexant values were higher (p < 0.001), while Aapexpost , Amctpost , Vtotal , VOLmct , VOLaap and VOLpap 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.