Positions of Ocular Geometrical and Visual Axes in Brazilian, Chinese and Italian Populations

Investigation of How Corneal Densitometry Artefacts Affect the Imaging of Normal and Keratoconic Corneas

PURPOSE

To investigate corneal densitometry artefacts found in Pentacam Scheimpflug scans and their potential effect on assessing keratoconic (KC) corneas compared to normal (N) corneas.

METHODS

The current study utilises Pentacam data of 458 N eyes, aged 35.6 ± 15.8 (range 10-87), referred to as the "N group", and 314 KC eyes, aged 31.6 ± 10.8 (range 10-72), referred to as the "KC group", where densitometry data were extracted and analysed via a custom-built MATLAB code. Radial summations of the densitometry were calculated at diameters ranging from 0.5 mm to 5.0 mm. The minimum normalised radial summation of densitometry (NRSD) value and angle were determined at each diameter and then linked. KC cone locations and areas of pathology were determined, and a comparison between N and KC groups was carried out both within the averaged area of pathology and over the corneal surface.

RESULTS

Joining minimum NRSD trajectory points marked a clear distortion line pointing to the nasal-superior direction at 65° from the nasal meridian. The findings were found to be independent of eye laterality or ocular condition. Consistency was detected in the right and left eyes among both the N and KC groups. The location of the KC cone centre and the area of pathology were determined, and the densitometry output was compared both within the area of pathology and over the whole cornea. When the average densitometry was compared between N and KC eyes within the KC area of pathology, the N group recorded a 16.37 ± 3.15 normalised grey-scale unit (NGSU), and the KC group recorded 17.74 ± 3.4 NGSU (p = 0.0001). However, when the whole cornea was considered, the N group recorded 16.71 ± 5.5 NGSU, and the KC group recorded 15.72 ± 3.98 NGSU (p = 0.0467). A weak correlation was found between the Bad D index and NGSU when the whole measured cornea was considered (R = -0.01); however, a better correlation was recorded within the KC area of pathology (R = 0.21).

CONCLUSIONS

Nasal-superior artefacts are observed in the densitometry Pentacam maps, and analysis shows no significant differences in their appearance between N or KC corneas. When analysing KC corneas, it was found that the cone positions are mostly on the temporal-inferior side of the cornea, opposite to the densitometry artefact NRSD trajectory. The analysis suggests that the corneal densitometry artefacts do not interfere with the KC area of pathology as it reaches its extreme in the opposite direction; therefore, weighting the densitometry map to increase the contribution of the inferior-temporal cornea and decreasing that of the superior-nasal area would improve the classification or identification of KC if densitometry is to be used as a KC metric.

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.

A Comparative Analysis of the Camera-like Eyes of Jumping Spiders and Humans

Among invertebrates, jumping spiders are one of the few groups whose representatives have camera-like eyes, and the only group whose representatives have fovea. The latter is present in the camera-like eyes of representatives of some groups of vertebrates, including humans. Based on the literature data, a comparative analysis of the camera-like eyes of jumping spiders and humans was carried out, in the course of which the similarities and differences in the properties and functions of their basic components were identified. The presented data are necessary for the formation of knowledge about jumping spiders as model animals for studying the functioning of the visual system.

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.

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

Purpose: To investigate the effectiveness of flipping left corneas topography and analysethem quantitively along with fellow right corneas based on the assumption that they are mirror images of each other. Methods: The study involved scanning both eyes of 177 healthy participants (aged 35.3 ± 15.8) and 75 keratoconic participants (aged 33.9 ± 17.8). Clinical tomography data were collected for both eyes using the Pentacam HR and processed by a fully automated custom-built MATLAB code. For every case, the right eye was used as a datum fixed surface while the left cornea was flipped around in the superior–inferior direction. In this position, the root-mean-squared difference (RMS) between the flipped left cornea and the right cornea was initially determined for both the anterior and posterior corneal surfaces. Next, the iterative closest point transformation algorithm was applied on the three-dimensional flipped cornea to allow the flipped left corneal anterior surface to translate and rotate, minimising the difference between it and the right corneal anterior surface. Then, the RMS differences were recalculated and compared. Results: A comparison of the dioptric powers showed a significant difference between the RMS of both the flipped left eyes and the right eyes in the healthy and the KC groups (p < 0.001). The RMS of the surfaces of the flipped left corneas and the right corneas was 0.6 ± 0.4 D among the healthy group and 4.1 ± 2.3 among the KC group. After transforming the flipped left corneas, the RMS was recorded as 0.5 ± 0.3 D and 2.4 ± 2 D among the healthy and KC groups, respectively. Conclusions: Although fellow eyes are highly related in their clinical parameters, they should be treated with care when one eye topography is flipped and processed with the other eye topography in an optic-related research analysis where translation might be needed. In KC, an asymmetric disease, it was observed that a portion of the asymmetry was due to a corneal apex shift interfering with the image acquisition. Therefore, transforming the flipped left eyes by rotation and translation results in a fairer comparison between the fellow KC corneas.

Low-Cost Eye Tracking Calibration: A Knowledge-Based Study

Subject calibration has been demonstrated to improve the accuracy in high-performance eye trackers. However, the true weight of calibration in off-the-shelf eye tracking solutions is still not addressed. In this work, a theoretical framework to measure the effects of calibration in deep learning-based gaze estimation is proposed for low-resolution systems. To this end, features extracted from the synthetic U2Eyes dataset are used in a fully connected network in order to isolate the effect of specific user’s features, such as kappa angles. Then, the impact of system calibration in a real setup employing I2Head dataset images is studied. The obtained results show accuracy improvements over 50%, probing that calibration is a key process also in low-resolution gaze estimation scenarios. Furthermore, we show that after calibration accuracy values close to those obtained by high-resolution systems, in the range of 0.7°, could be theoretically obtained if a careful selection of image features was performed, demonstrating significant room for improvement for off-the-shelf eye tracking systems.

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.

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.

Artefact-free topography based scleral-asymmetry

PURPOSE

To present a three-dimensional non-parametric method for detecting scleral asymmetry using corneoscleral topography data that are free of edge-effect artefacts.

METHODS

The study included 88 participants aged 23 to 65 years (37.7±9.7), 47 women and 41 men. The eye topography data were exported from the Eye Surface Profiler software in MATLAB binary data container format then processed by custom built MATLAB codes entirely independent from the profiler software. Scleral asymmetry was determined initially from the unprocessed topography before being determined again after removing the edge-effect noise. Topography data were levelled around the limbus, then edge-effect was eliminated using a robust statistical moving median technique. In addition to comparing raw elevation data, scleral elevation was also compared through fitting a sphere to every single scleral surface and determining the relative elevation from the best-fit sphere reference surface.

RESULTS

When considering the averaged raw topography elevation data in the scleral section of the eye at radius 8 mm, the average raw elevations of the right eyes' sclera were -1.5±1.77, -1.87±2.12, -1.36±1.82 and -1.57±1.87 mm. In the left eyes at the same radius the average raw elevations were -1.62±1.78, -1.82±2.07, -1.28±1.76 and -1.68±1.93 mm. While, when considering the average raw elevation of the sclera after removing the edge effect, the average raw elevations of the right eyes were -3.71±0.25, -4.06±0.23, -3.95±0.19 and -3.95±0.23 mm. In the left eyes at the same radius the average raw elevations were -3.71±0.19, -3.97±0.22, -3.96±0.19 and -3.96±0.18 mm in the nasal, temporal, superior and inferior sides respectively. Maximum raw elevation asymmetry in the averaged scleral raw elevation was 1.6647±0.9015 mm in right eyes and 1.0358±0.6842 mm in left eyes, both detected at -38° to the nasal side. Best-fit sphere-based relative elevation showed that sclera is more elevated in three main meridians at angles -40°, 76°, and 170° in right eyes and -40°, 76°, and 170° in left eyes, all measured from the nasal meridian. Maximum recorded relative elevation asymmetries were 0.0844±0.0355 mm and 0.068±0.0607 mm at angular positions 76° and 63.5° for right and left eyes in turn.

CONCLUSIONS

It is not possible to use corneoscleral topography data to predict the scleral shape without considering a method of removing the edge-effect from the topography data. The nasal side of the sclera is higher than the temporal side, therefore, rotationally symmetric scleral contact lenses are more likely to be translated towards the temporal side. The scleral shape is best described by levelled raw elevation rather than relative elevation.