Artefact-free topography based scleral-asymmetry

FEA-Based Stress-Strain Barometers as Forecasters for Corneal Refractive Power Change in Orthokeratology

PURPOSE

To improve the effectivity of patient-specific finite element analysis (FEA) to predict refractive power change (RPC) in rigid Ortho-K contact lens fitting. Novel eyelid boundary detection is introduced to the FEA model to better model the effects of the lid on lens performance, and stress and strain outcomes are investigated to identify the most effective FEA components to use in modelling.

METHODS

The current study utilises fully anonymised records of 249 eyes, 132 right eyes, and 117 left eyes from subjects aged 14.1 ± 4.0 years on average (range 9 to 38 years), which were selected for secondary analysis processing. A set of custom-built MATLAB codes was built to automate the process from reading Medmont E300 height and distance files to processing and displaying FEA stress and strain outcomes. Measurements from before and after contact lens wear were handled to obtain the corneal surface change in shape and power. Tangential refractive power maps were constructed from which changes in refractive power pre- and post-Ortho-K wear were determined as the refractive power change (RPC). A total of 249 patient-specific FEA with innovative eyelid boundary detection and 3D construction analyses were automatically built and run for every anterior eye and lens combination while the lens was located in its clinically detected position. Maps of four stress components: contact pressure, Mises stress, pressure, and maximum principal stress were created in addition to maximum principal logarithmic strain maps. Stress and strain components were compared to the clinical RPC maps using the two-dimensional (2D) normalised cross-correlation and structural similarity (SSIM) index measure.

RESULTS

On the one hand, the maximum principal logarithmic strain recorded the highest moderate 2D cross-correlation area of 8.6 ± 10.3%, and contact pressure recorded the lowest area of 6.6 ± 9%. Mises stress recorded the second highest moderate 2D cross-correlation area with 8.3 ± 10.4%. On the other hand, when the SSIM index was used to compare the areas that were most similar to the clinical RPC, maximum principal stress was the most similar, with an average strong similarity percentage area of 26.5 ± 3.3%, and contact pressure was the least strong similarity area of 10.3 ± 7.3%. Regarding the moderate similarity areas, all components were recorded at around 34.4% similarity area except the contact pressure, which was down to 32.7 ± 5.8%.

CONCLUSIONS

FEA is an increasingly effective tool in being able to predict the refractive outcome of Ortho-K treatment. Its accuracy depends on identifying which clinical and modelling metrics contribute to the most accurate prediction of RPC with minimal ocular complications. In terms of clinical metrics, age, Intra-ocular pressure (IOP), central corneal thickness (CCT), surface topography, lens decentration and the 3D eyelid effect are all important for effective modelling. In terms of FEA components, maximum principal stress was found to be the best FEA barometer that can be used to predict the performance of Ortho-K lenses. In contrast, contact pressure provided the worst stress performance. In terms of strain, the maximum principal logarithmic strain was an effective strain barometer.

Typical localised element-specific finite element anterior eye model

Purpose

The study presents an averaged anterior eye geometry model combined with a localised material model that is straightforward, appropriate and amenable for implementation in finite element (FE) modelling.

Methods

Both right and left eye profile data of 118 subjects (63 females and 55 males) aged 22-67 years (38.5 ± 7.6) were used to build an averaged geometry model. Parametric representation of the averaged geometry model was achieved through two polynomials dividing the eye into three smoothly connected volumes. This study utilised the collagen microstructure x-ray data of 6 ex-vivo healthy human eyes, 3 right eyes and 3 left eyes in pairs from 3 donors, 1 male and 2 females aged between 60 and 80 years, to build a localised element-specific material model for the eye.

Results

Fitting the cornea and the posterior sclera sections to a 5th-order Zernike polynomial resulted in 21 coefficients. The averaged anterior eye geometry model recorded a limbus tangent angle of 37° at a radius of 6.6 mm from the corneal apex. In terms of material models, the difference between the stresses generated in the inflation simulation up to 15 mmHg in the ring-segmented material model and localised element-specific material model were significantly different (p < 0.001) with the ring-segmented material model recording average Von-Mises stress 0.0168 ± 0.0046 MPa and the localised element-specific material model recording average Von-Mises stress 0.0144 ± 0.0025 MPa.

Conclusions

The study illustrates an averaged geometry model of the anterior human eye that is easy to generate through two parametric equations. This model is combined with a localised material model that can be used either parametrically through a Zernike fitted polynomial or non-parametrically as a function of the azimuth angle and the elevation angle of the eye globe. Both averaged geometry and localised material models were built in a way that makes them easy to implement in FE analysis without additional computation cost compared to the limbal discontinuity so-called idealised eye geometry model or ring-segmented material model.

Performance of Zernike polynomials in reconstructing raw-elevation data captured by Pentacam HR, Medmont E300 and Eye Surface Profiler

PURPOSE

To investigate the capability of Zernike polynomials fitting to reconstruct corneal surfaces as measured by Pentacam HR tomographer, Medmont E300 Placido-disc and Eye Surface Profiler (ESP).

METHODS

The study utilised a collection of clinical data of 527 participants. Pentacam HR raw elevation data of 660 eyes (430 healthy and 230 keratoconic) were fitted to Zernike polynomials of order 2 to 20. Same analyses were carried out on 158 eyes scanned by Medmont E300 Placido-disc and 236 eyes were scanned by ESP for comparison purposes. The Zernike polynomial ​fitting was carried out using a random 80% of each individual eye surface's data up to a corneal radius of 5 mm and the root means squared fitting error (RMS) was calculated for the unused 20% portion of the surface data. The process was carried out for the anterior and posterior surfaces of the corneal measurements of the Pentacam HR and the anterior surfaces only with the ESP and the Medmont E300 measurements.

RESULTS

Statistical significances in reduction of RMS were noticed up to order 14 among healthy participants (p < 0.0001 for right eyes, p = 0.0051 for left eyes) and up to order 12 (p < 0.0001 for right eyes, p = 0.0002 for left eyes) in anterior surfaces measured by the Pentacam. Among keratoconic eyes, statical significance was noticed up to order 12 in both eyes (p < 0.0001 for right eyes, p = 0.0003 for left eyes). The Pentacam posterior corneal data, both right and left, healthy and keratotic eyes recorded significance (p < 0.0001) in reduction of RMS up to order 10 with same RMS values of 0.0003 mm with zero standard deviation. RMS of fitting Zernike polynomials to Medmont data up to order 20 showed a consistent reduction in RMS with the increase of the fitting order with no rise at high fitting orders. Minimum RMS = 0.0047 ± 0.0021 mm, 0.0046 ± 0.0019 mm for right and left eyes respectively were recorded at order 20 and were more than 15 times the minimum RMS of the Pentacam. RMS of fitting Zernike polynomials to ESP data also showed a consistent reduction in RMS with the increase of the fitting order with no sign of any rise at high fitting orders. Similar to the Medmont, minimum RMS of 0.0005 ± 0.0003 mm, 0.0006 ± 0.0003 mm was recorded at order 20 for right and left eyes respectively and was 2 times the minimum RMS of the Pentacam for right eyes and 1.7 times the minimum RMS of the Pentacam for left eyes.

CONCLUSIONS

Orders 12 and 10 Zernike polynomials almost perfectly matched the raw-elevation data collected from Pentacam for anterior and posterior surfaces, respectively for either healthy or keratoconic corneas. The Zernike fitting could not perfectly match the data collected from Medmont E300 and ESP.

Effect of Corneal Tilt on the Determination of Asphericity

Purpose: To quantify the effect of levelling the corneal surface around the optical axis on the calculated values of corneal asphericity when conic and biconic models are used to fit the anterior corneal surface. Methods: This cross-sectional study starts with a mathematical simulation proving the concept of the effect that the eye's tilt has on the corneal asphericity calculation. Spherical, conic and biconic models are considered and compared. Further, corneal asphericity is analysed in the eyes of 177 healthy participants aged 35.4 ± 15.2. The optical axis was determined using an optimization procedure via the Levenberg-Marquardt nonlinear least-squares algorithm, before fitting the corneal surface to spherical, conic and biconic models. The influence of pupil size (aperture radii of 1.5, 3.0, 4.0 and 5.0 mm) on corneal radius and asphericity was also analysed. Results: In computer simulations, eye tilt caused an increase in the apical radii of the surface with the increase of the tilt angle in both positive and negative directions and aperture radii in all models. Fitting the cornea to spherical models did not show a significant difference between the raw-measured corneal surfaces and the levelled surfaces for right and left eyes. When the conic models were fitted to the cornea, changes in the radii of the cornea among the raw-measured corneal surfaces' data and levelled data were not significant; however, significant differences were recorded in the asphericity of the anterior surfaces at radii of aperture 1.5 mm (p < 0.01). With the biconic model, the posterior surfaces recorded significant asphericity differences at aperture radii of 1.5 mm, 3 mm, 4 mm and 5 mm (p = 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively) in the nasal temporal direction of right eyes and left eyes (p < 0.01, p < 0.01, p < 0.01 & p < 0.01, respectively). In the superior-inferior direction, significant changes were only noticed at aperture radii of 1.5 mm for both right and left eyes (p = 0.05, p < 0.01). Conclusions: Estimation of human corneal asphericity from topography or tomography data using conic and biconic models of corneas are affected by eyes' natural tilt. In contrast, the apical radii of the cornea are less affected. Using corneal asphericity in certain applications such as fitting contact lenses, corneal implant design, planning for refractive surgery and mathematical modelling when a geometrical centre of the eye is needed should be implemented with caution.

Repeatability of Anterior Eye Surface Topography Parameters from an Anterior Eye Surface Profilometer

SIGNIFICANCE

Anterior eye shape measurements are important for clinical contact lens fitting. The detailed assessment of measurement repeatability using the Eye Surface Profiler (ESP; Eaglet Eye B.V., AP Houten, the Netherlands) allows for more reliable interpretation of eye surface topography measurements.

PURPOSE

This study aimed to determine the repeatability of the ESP for anterior central corneal power and anterior eye surface height measurements.

METHODS

A Badal optometer was mounted on the ESP to provide an external fixation target with appropriate accommodation control and refractive correction. Forty-five healthy young adults underwent two sessions of anterior eye measurements, separated by 20 minutes, using the ESP. In each session, three consecutive scans were captured. Sagittal height data were obtained from 8-mm central cornea and from 8- to 14-mm diameter (encompassing the corneal periphery and anterior sclera). Anterior corneal powers were determined from the central cornea. Intersessional and intrasessional repeatability values were determined as coefficients of repeatability and root mean square error differences.

RESULTS

Sagittal height intersessional coefficients of repeatability for central nasal (5 μm) and central temporal (7 μm) were better than peripheral nasal (24 μm) and peripheral temporal (21 μm) regions. Sagittal height intrasessional coefficients of repeatability were 9, 8, 28, and 31 μm for central nasal, central temporal, peripheral nasal, and peripheral temporal regions, respectively. Intersessional coefficients of repeatability of mean sphere, 90/180° (J0) astigmatism, and oblique (J45) astigmatism were 0.67, 0.22, and 0.13 D, respectively, with corresponding intrasessional coefficients of repeatability of 1.27, 0.21, and 0.27 D.

CONCLUSIONS

The modified measuring procedure for the ESP used in this study provides highly repeatable sagittal height measurements in the central cornea but is less repeatable in the corneal periphery and scleral region. Results of the current study can be considered when using ESP in the interpretation of anterior eye surface shape measurements and in contact lens fitting and design.

Corneoscleral Topography Measured with Fourier-based Profilometry and Scheimpflug Imaging

SIGNIFICANCE

Precise measurement of corneoscleral topography makes a valuable contribution to the understanding of anterior eye anatomy and supports the fitting process of contact lenses. Sagittal height data, determined by newer noninvasive techniques, are particularly useful for initial scleral lens selection.

PURPOSE

The purpose of this study was to investigate the agreement and repeatability of Fourier-based profilometry and Scheimpflug imaging, in the measurement of sagittal height and toricity of the corneoscleral region.

METHODS

Minimal (Minsag), maximal (Maxsag) sagittal height, toricity (Maxsag - Minsag), and the maximum possible measurement zone diameter of 38 subjects were compared using the Eye Surface Profiler (ESP; Eagle Eye, Houten, the Netherlands) and the corneoscleral profile module of the Pentacam (Oculus, Wetzlar, Germany) at two different sessions. Correlations between the instruments were analyzed using the Pearson coefficient. Differences between sessions and instruments were analyzed using Bland-Altman and paired t tests.

RESULTS

For an equal chord length, the measurement with Pentacam was significantly greater for Minsag (344 μm; 95% confidence interval [CI], 322 to 364 μm; P < .001) and significantly greater for Maxsag (280 μm; 95% CI, 256 to 305 μm; P < .001), but significantly smaller for toricity (-63 μm; 95% CI, -95 to -31 μm; P < .001). Maximum possible measurement zone diameter with ESP (16.4 ± 1.3 mm) was significantly greater than with Pentacam (14.8 ± 1.1 mm) (P < .001). Repeated measurements from session 1 and session 2 were not significantly different for Pentacam and ESP (P = .74 and P = .64, respectively). The 95% CIs around differences indicate good repeatability for Pentacam (mean difference, -0.9 μm; 95% CI, -6.7 to 4.8 μm) and ESP (4.6 μm; -22.4 to 31.6).

CONCLUSIONS

Although both instruments deliver useful data especially for the fitting of scleral and soft contact lenses, the sagittal height and the toricity measurements cannot be considered as interchangeable.

CLEAR - Scleral lenses

Scleral lenses were the first type of contact lens, developed in the late nineteenth century to restore vision and protect the ocular surface. With the advent of rigid corneal lenses in the middle of the twentieth century and soft lenses in the 1970's, the use of scleral lenses diminished; in recent times there has been a resurgence in their use driven by advances in manufacturing and ocular imaging technology. Scleral lenses are often the only viable form of contact lens wear across a range of clinical indications and can potentially delay the need for corneal surgery. This report provides a brief historical review of scleral lenses and a detailed account of contemporary scleral lens practice including common indications and recommended terminology. Recent research on ocular surface shape is presented, in addition to a comprehensive account of modern scleral lens fitting and on-eye evaluation. A range of optical and physiological challenges associated with scleral lenses are presented, including options for the clinical management of a range of ocular conditions. Future applications which take advantage of the stability of scleral lenses are also discussed. In summary, this report presents evidence-based recommendations to optimise patient outcomes in modern scleral lens practice.

Fibril density reduction in keratoconic corneas

This study aims to estimate the reduction in collagen fibril density within the central 6 mm radius of keratoconic corneas through the processing of microstructure and videokeratography data. Collagen fibril distribution maps and topography maps were obtained for seven keratoconic and six healthy corneas, and topographic features were assessed to detect and calculate the area of the cone in each keratoconic eye. The reduction in collagen fibril density within the cone area was estimated with reference to the same region in the characteristic collagen fibril maps of healthy corneas. Together with minimum thickness and mean central corneal refractive power, the cone area was correlated with the reduction in the cone collagen fibrils. For the corneas considered, the mean area of keratoconic cones was 3.30 ± 1.90 mm². Compared with healthy corneas, fibril density in the cones of keratoconic corneas was lower by as much as 35%, and the mean reduction was 17 ± 10%. A linear approximation was developed to relate the magnitude of reduction to the refractive power, minimum corneal thickness and cone area (R² = 0.95, p < 0.001). Outside the cone area, there was no significant difference between fibril arrangement in healthy and keratoconic corneas. The presented method can predict the mean fibril density in the keratoconic eye's cone area. The technique can be applied in microstructure-based finite-element models of the eye to regulate its stiffness level and the stiffness distribution within the areas affected by keratoconus.

Compressive behaviour of soft contact lenses and its effect on refractive power on the eye and handling off the eye

PURPOSE

To investigate the stress-strain behaviour of 9 soft contact lens materials, that are commonly used in the market, under uniaxial compression loading.

METHODS

Seven types of hydrogel and two types of silicone-hydrogel soft contact lens materials were hydrated in phosphate-buffered saline (PBS) solution then subjected to uniaxial compression loads. The load rate was set to 16.0 N/min starting with two consecutive initial 5.0 N loading cycles followed by three relaxation periods of 4.0 min within which there were two more 5.0 N loading cycles and eventually, a full loading cycle that stopped at a load of 49.0 N. The load and contraction data obtained experimentally were analysed to derive the stress-strain behaviour. Finite Element (FE) analysis was then utilised to evaluate the performance of soft contact lenses on the human eye and handling lenses off the eye.

RESULTS

Unlike tensile tests, all tested materials showed nonlinear behaviour when tested under compression. When fitted to first-order Ogden hyperelastic model, parameter μ was found to be varying in the range 0.12 to 0.74 MPa and material parameter α was found to be varying in the range 8.2 to 20.326 among the nine tested materials. Compression modulus of elasticity was 2.2 times higher than the tensile modulus of elasticity on average. FE simulation with nonlinear Ogden constitutive model showed a limited change (8%~12%) in the optical performance when compared to other material models, however, it predicted higher stress when the lens was simulated under bending during off-eye handling.

CONCLUSIONS

Compression tests revealed slightly nonlinear behaviour when materials were strained under compression stress down to 15% ~ 30% of their nominal heights. Considering the physiological compression loading range of 8 mmHg, secant moduli of elasticity were 1.5% to 6.9% higher than the tension moduli of elasticity depending on the material. Tensile-based moduli of elasticity could be used in FE analysis as a step towards simulating the optical performance of soft contact lenses on-eye. However, nonlinear compression-based material models are recommended for FE analysis of soft contact lenses when lens-handling is investigated off-eye.

Which feature influences on-eye power change of soft toric contact lenses: Design or corneal shape?

PURPOSE

This study investigates how both the peripheral zone design and corneal shape affect the behaviour of soft contact lenses on-eye.

METHODS

In this study, soft contact lenses of varying nominal cylindrical powers and peripheral zone designs-a single-prism gravity-based stabilised lens (G1P), two-prism blink-based stabilised lens (B2P) and four-prism blink-based stabilised lens (B4P)-were generated as finite element models. The on-eye simulation results were analysed to identify the impact of each peripheral zone design (Each with different volume ratios) on the effective power change (EPC) when worn by a subject. Topographies of three eyes of varying average simulated anterior corneal curvature (flat, average & steep) were used in this study.

RESULTS

The volume of the lens's peripheral zone as a ratio of the total lens volume (Vp) recorded very weak correlations with the effective power change (EPC) among the three investigated designs when they were fitted to the flat eye (R = -0.19, -0.15 & -0.22 respectively), moderate correlations with the average eye (R = 0.42, 0.43 & 0.43 respectively) and strong correlations with the steep eye (R = 0.91, 0.9 & 0.9 respectively). No significant differences were noticed among the three investigated designs and none of the cylindrical lenses designed with axis 90° recorded EPC values outside the acceptance criteria range (ACR) of ±0.25 D. No significant differences in EPC were recorded among the three designs G1P, B2P and B4P (p>0.6) when they were designed with three axes at 90°, 45° and 0°. Moving the toric lens axis away from 90° dragged the EPC to the negative side and most of the investigated lenses with axes at 45° and 0° recorded EPCs outside the ±0.25D range.

CONCLUSIONS

In all cases, the shape of the cornea had a more dominant effect on EPC when compared to the peripheral zone design. Corneal shape influences the soft toric contact lens's on-eye power change more than the lens design.

Anterior Scleral Regional Variation between Asian and Caucasian Populations

Purpose: To evaluate the anterior scleral shape regional differences between Asian and Caucasian populations. Methods: The study included 250 Asian eyes and 235 Caucasian eyes from participants aged 22 to 67 years (38.5 ± 7.6). Three-dimensional (3D) corneo-scleral maps were acquired using a corneo-scleral topographer (Eye Surface Profiler, Eaglet Eye BV) and used to calculate sagittal height. For each 3D map, the sclera (maximum diameter of 18 mm) and cornea were separated at the limbus using an automated technique. Advanced data processing steps were applied to ensure levelled artefact-free datasets to build an average scleral shape map for each population. Results: Statistically, Asian and Caucasian sclerae are significantly different from each other in sagittal height (overall sclera, p = 0.001). The largest difference in sagittal height between groups was found in the inferior-temporal region (271 ± 203 µm, p = 0.03), whereas the smallest difference was found in the superior-temporal region (84 ± 105 µm, p = 0.17). The difference in sagittal height between Caucasian and Asian sclera increases with the distance from the limbus. Conclusions: Asian anterior sclera was found to be less elevated than Caucasian anterior sclera. However, the nasal area of the sclera is less elevated than the temporal area, independently of race. Gaining knowledge in race-related scleral topography differences could assist contact lens manufacturers in the process of lens design and practitioners during the process of contact lens fitting.

Limbus misrepresentation in parametric eye models

Purpose

To assess the axial, radial and tangential limbus position misrepresentation when parametric models are used to represent the cornea and the sclera.

Methods

This retrospective study included 135 subjects aged 22 to 65 years (36.5 mean ±9.8 STD), 71 females and 64 males. Topography measurements were taken using an Eye Surface Profiler topographer and processed by a custom-built MATLAB code. Eye surfaces were freed from edge-effect artefacts and fitted to spherical, conic and biconic models.

Results

When comparing the radial position of the limbus, average errors of -0.83±0.19mm, -0.76±0.20mm and -0.69±0.20mm were observed within the right eye population for the spherical, conic and biconic models fitted up to 5mm. For the same fitting radius, the average fitting errors were -0.86±0.23mm, -0.78±0.23mm and -0.73±0.23mm for the spherical, conic and biconic models respectively within the left eye population. For the whole cornea fit, the average errors were -0.27±0.12mm and -0.28±0.13mm for the spherical models, -0.02±0.29mm and -0.05±0.27mm for the conic models, and -0.22±0.16mm and 0.24±0.17mm for the biconic models in the right and left eye populations respectively.

Conclusions

Through the use of spherical, conic and biconic parametric modelling methods, the eye’s limbus is being mislocated. Additionally, it is evident that the magnitude of fitting error associated with the sclera may be propagating through the other components of the eye. This suggests that a corneal nonparametric model may be necessary to improve the representation of the limbus.

Anatomical and physiological considerations in scleral lens wear: Conjunctiva and sclera

While scleral lenses have been fitted using diagnostic lenses or impression moulding techniques for over a century, recent advances in anterior segment imaging such as optical coherence tomography and corneo-scleral profilometry have significantly improved the current understanding of the anatomy of the anterior eye including the morphometry of the conjunctiva, sclera, and corneo-scleral junction, as well as the ocular surface shape and elevation. These technological advances in ocular imaging along with continual improvements and innovations in scleral lens design and manufacturing have led to a global increase in scleral lens prescribing. This review provides a comprehensive overview of the conjunctiva and sclera in the context of modern scleral lens practice, including anatomical variations in healthy and diseased eyes, the physiological impact of scleral lens wear, potential fitting challenges, and current approaches to lens modifications in order to minimise lens-induced complications and adverse ocular effects. Specific topics requiring further research are also discussed.