The Efficiency of Using Mirror Imaged Topography in Fellow Eyes Analyses of Pentacam HR Data

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.

Limitations of Reconstructing Pentacam Rabbit Corneal Tomography by Zernike Polynomials

The study aims to investigate the likelihood of Zernike polynomial being used for reconstructing rabbit corneal surfaces as scanned by the Pentacam segment tomographer, and hence evaluate the accuracy of corneal power maps calculated from such Zernike fitted surfaces. The study utilised a data set of both eyes of 21 rabbits using a reverse engineering approach for deductive reasoning. Pentacam raw elevation data were fitted to Zernike polynomials of orders 2 to 20. The surface fitting process to Zernike polynomials was carried out using randomly selected 80% of the corneal surface data points, and the root means squared fitting error (RMS) was determined for the other 20% of the surface data following the Pareto principle. The process was carried out for both the anterior and posterior surfaces of the corneal surfaces that were measured via Pentacam scans. Raw elevation data and the fitted corneal surfaces were then used to determine corneal axial and tangential curvature maps. For reconstructed surfaces calculated using the Zernike fitted surfaces, the mean and standard deviation of the error incurred by the fitting were calculated. For power maps computed using the raw elevation data, different levels of discrete cosine transform (DCT) smoothing were employed to infer the smoothing level utilised by the Pentacam device. The RMS error was not significantly improved for Zernike polynomial orders above 12 and 10 when fitting the anterior and posterior surfaces of the cornea, respectively. This was noted by the statistically non-significant increase in accuracy when the order was increased beyond these values. The corneal curvature calculations suggest that a smoothing process is employed in the corneal curvature maps outputted by the Pentacam device; however, the exact smoothing method is unknown. Additionally, the results suggest that fitting corneal surfaces to high-order Zernike polynomials will incur a clinical error in the calculation of axial and tangential corneal curvature of at least 0.16 ± 01 D and 0.36 ± 0.02 D, respectively. Rabbit corneal anterior and posterior surfaces scanned via the Pentacam were optimally fitted to orders 12 and 10 Zernike polynomials. This is essential to get stable values of high-order aberrations that are not affected by Zernike polynomial fittings, such as comas for Intracorneal Ring Segments (ICRS) adjustments or spherical aberration for pre-cataract operations. Smoothing was necessary to replicate the corneal curvature maps outputted by the Pentacam tomographer, and fitting corneal surfaces to Zernike polynomials introduces errors in the calculation of both the axial and tangential corneal curvatures.

Influence of eye tilt on corneal densitometry

PURPOSE

To investigate whether Pentacam densitometry readings are affected by corneal tilt.

METHODS

In a prospective study, the right eyes of 86 healthy participants aged 42.8 ± 20.0 years (range 18-79 years) were imaged using Scheimpflug tomography. Elevation maps were exported to calculate corneal tilt using custom-made software, and densitometry readings were acquired directly from the corneal densitometry analysis add-on to the standard software Oculus Pentacam HR. Simple mediation analysis was applied to study age as a confounding factor in the correlation between corneal tilt and corneal densitometry.

RESULTS

Corneal tilt and corneal densitometry are not independent from one another because age is significantly correlated with both corneal tilt (r = 0.50, p < 0.001) and corneal densitometry (r = 0.91, p < 0.001). Only 3.8% of the correlation between tilt and densitometry operates directly, while the remaining 96.2% depends on age.

CONCLUSIONS

Corneal tilt plays a role in corneal densitometry readings, even though the interaction is strongly influenced by age. Age is a well-known factor in densitometry readings that should be taken into consideration when interpreting Scheimpflug densitometry.

Interocular Symmetry Analysis of Corneal Elevation Using the Fellow Eye as the Reference Surface and Machine Learning

Unilateral corneal indices and topography maps are routinely used in practice, however, although there is consensus that fellow-eye asymmetry can be clinically significant, symmetry studies are limited to local curvature and single-point thickness or elevation measures. To improve our current practices, there is a need to devise algorithms for generating symmetry colormaps, study and categorize their patterns, and develop reference ranges for new global discriminative indices for identifying abnormal corneas. In this work, we test the feasibility of using the fellow eye as the reference surface for studying elevation symmetry throughout the entire corneal surface using 9230 raw Pentacam files from a population-based cohort of 4613 middle-aged adults. The 140 × 140 matrix of anterior elevation data in these files were handled with Python to subtract matrices, create color-coded maps, and engineer features for machine learning. The most common pattern was a monochrome circle (“flat”) denoting excellent mirror symmetry. Other discernible patterns were named “tilt”, “cone”, and “four-leaf”. Clustering was done with different combinations of features and various algorithms using Waikato Environment for Knowledge Analysis (WEKA). Our proposed approach can identify cases that may appear normal in each eye individually but need further testing. This work will be enhanced by including data of posterior elevation, thickness, and common diagnostic indices.