Anterior corneal asphericity calculated by the tangential radius of curvature

Influence of different parameters on the corneal asphericity (Q value) assessed with progress in biomedical optics and imaging - A review

The corneal eye diseases such as Keratoconus cause weakening of the cornea, with this disease the cornea can change in shape. This condition affects between 1 in 3,000 to 1 in 10,000 people. The main reason for the development of such conditions is unknown and can have significant impacts. Over the last decade, with advancements in computerized corneal topography assessments, researchers have increasingly expressed interest in corneal topography for research as well as clinical activities. Up till now, several aspheric numerical models have been developed as well as proposed to define the complex shape of the cornea. A commonly used term for characterizing the asphericity in an eye is the Q value, a common indicator of the aspherical degree of the cornea. It is one of the critical parameters in the mathematical description model of the cornea as it represents the cornea's shape and the eye's characteristics. Due to the utmost importance of this Q value of the cornea, a couple of studies have attempted to explore this parameter and its distribution, merely in terms of its influence on the human eye's optical properties. The corneal Q value is an important factor that needs to be determined to treat for any refractive errors as corneal degeneration are disease that can lead to potential problems with the structure of the cornea. This study aims to highlight the need to understand Q value of the cornea as this can essentially assist with personalising corneal refractive surgeries and implantation of intraocular lenses. Therefore, the relevance of corneal Q value must be studied in association with different patients, especially ones who have been diagnosed with cataracts, brain tumours, or even COVID-19. To address this issue, this paper first carries out a literature review on the optics of the cornea, the relevance of corneal Q value in ophthalmic practice and studies corneal degenerations and its causes. Thereafter, a detailed review of several noteworthy relevant research studies examining the Q value of the cornea is performed. To do so, an elaborate database is created, which presents a list of different research works examined in this study and provides key evidence derived from these studies. This includes listing details on the age, gender, ethnicity of the eyes assessed, the control variables, the technology used in the study, and even more. The database also delivers important findings and conclusions noted in each study assessed. Next, this paper analyses and discusses the magnitude of corneal Q value in various scenarios and the influence of different parameters on corneal Q value. To design visual optical products as well as to enhance the understanding of the optical properties of an eye, future studies could consider the database and work presented in this study as useful references. In addition, the work can be used to make informed decisions in clinical practice for designing visual optical products as well as to enhance the understanding of the optical properties of an Eye.

Comprehensive Assessment of Posterior Corneal Asphericity Change Calculated by Tangential Radius of Curvature After FS-LASIK and SMILE

PURPOSE

To evaluate changes in posterior corneal asphericity (ΔQ) using the tangential radius of curvature after femtosecond laser-assisted in situ keratomileusis (FS-LASIK) and small incision lenticule extraction (SMILE) procedures.

METHODS

One hundred twenty right eyes of myopic patients who underwent either FS-LASIK or SMILE procedures were analyzed using Sirius 3D corneal topography for assessment. The tangential radius was employed to calculate both preoperative and postoperative posterior corneal Q-values across each semimeridian. After both surgical interventions, the ΔQ value variations across the 360° semimeridional regions of the posterior corneal surface were compared.

RESULTS

A marked postoperative increase in the posterior corneal Q-value was documented. No significant differences were noted between the postoperative Q-values or ΔQ-values of the two surgical approaches. Among patients with moderate myopia, postoperative Q-value exhibited considerably lower increases and ΔQ-value significantly smaller than their counterparts with high myopia. Moreover, the fluctuation in ΔQ across semimeridional regions was less evident in patients with moderate myopia than in those with high myopia. Notably, the degree of ΔQ fluctuation across semimeridional regions was similar between both surgical categories. These data offer insights into variations in the posterior corneal surface after refractive surgeries depending on the degree of myopia, illuminating their clinical relevance.

CONCLUSIONS

Both FS-LASIK and SMILE introduce notable changes to posterior corneal asphericity among patients with different myopia intensities. Furthermore, the influence on the asphericity across the entire posterior surface is similarly distributed between FS-LASIK and SMILE techniques. [J Refract Surg. 2024;40(3):e133-e141.].

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.

Comparative Change in Anterior Corneal Asphericity After FS-LASIK and SMILE

PURPOSE

To evaluate changes in anterior corneal asphericity (ΔQ) by calculating tangential radius (r_t) after femtosecond laser-assisted in situ keratomileusis (FS-LASIK) and small incision lenticule extraction (SMILE).

METHODS

Sirius corneal topography (Costruzione Strumenti Oftalmici) was used to evaluate 120 right eyes from patients with moderate and high myopia who had previously undergone FS-LASIK and SMILE. The preoperative and postoperative tangential radii obtained in reference to various semi-meridional regions and radii zones were compared. Variation in ΔQ values in semi-meridional regions across 360 degrees of the anterior surface after FS-LASIK and SMILE were compared.

RESULTS

The tangential radii in the 1.2- and 1.8-mm radii zones were lower in patients who underwent SMILE compared to those who underwent FS-LASIK. The tangential radii in the 2.4- and 3-mm zones were higher in patients who underwent SMILE compared to those who underwent FS-LASIK. In both the moderate and high myopia groups, postoperative Q-values and ΔQ-values were lower in patients who had undergone SMILE than in patients who had undergone FS-LASIK. Postoperative Q-values and ΔQ-values were lower in the moderate myopia group than in the high myopia group for FS-LASIK and SMILE. The magnitude of variation in ΔQ as a function of semi-meridional region was lower in patients who had undergone SMILE than in patients who had undergone FS-LASIK.

CONCLUSIONS

FS-LASIK and SMILE alter anterior corneal tangential radius and anterior corneal asphericity in patients with moderate or high myopia. SMILE is more effective than FS-LASIK in preserving normal anterior corneal asphericity. [J Refract Surg. 2021;37(3):158-165.].

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.

Group Analysis of Q Values Calculated with Tangential Radius of Curvature from Human Anterior Corneal Surface

Objective

To calculate the Q values from the human anterior corneal surface with the tangential radius of curvature and analyze its distribution characteristics in different age and refractive status groups.

Methods

Tangential power maps of the anterior cornea from Orbscan II were acquired for 201 subjects' right eyes. They were divided into groups of adults and children and then divided further into subgroups according to the refraction status. The Q values of each semimeridian were calculated by the tangential radius with a linear regression equation. The Q value distribution in both the nasal cornea and temporal cornea were analyzed.

Results

The mean temporal Q values of the emmetropia group of adults and all children's groups were significantly different from the mean nasal Q value. The mean nasal corneal Q values were more negative in children. The adult group showed differences only in the low myopia group. The mean Q value of the nasal cornea among different refractive groups of children was significantly different, and so was the temporal cornea between the adult myopia and emmetropia group.

Conclusion

The method using the tangential radius of curvature combined with linear regression to obtain anterior surface Q values for both adults and children was stable and reliable. When we analyzed the anterior corneal Q value, area division was necessary.

The analysis of corneal asphericity (Q value) and its related factors of 1,683 Chinese eyes older than 30 years

Purpose

To determine corneal Q value and its related factors in Chinese subjects older than 30 years.

Design

Cross sectional study.

Methods

1,683 participants (1,683 eyes) from the Handan Eye Study were involved, including 955 female and 728 male with average age of 53.64 years old (range from 30 to 107 years). The corneal Q values of anterior and posterior surfaces were measured at 3.0, 5.0 and 7.0mm aperture diameters using Bausch & Lomb Orbscan IIz (software version 3.12). Age, gender and refractive power were recorded.

Results

The average Q values of the anterior surface at 3.0, 5.0 and 7.0mm aperture diameters were -0.28±0.18, -0.28±0.18, and -0.29±0.18, respectively. The average Q value of the anterior surface at the 5.0mm aperture diameter was negatively correlated with age (B = -0.003, p<0.01) and the refractive power (B = -0.013, p = 0.016). The average Q values of the posterior surface at 3.0, 5.0, and 7.0mm were -0.26±0.216, -0.26±0.214, and -0.26±0.215, respectively. The average Q value of the posterior surface at the 5.0mm aperture diameter was positively correlated with age (B = 0.002, p = 0.036) and the refractive power (B = 0.016, p = 0.043).

Conclusion

The corneal Q value of the elderly Chinese subjects is different from that of previously reported European and American subjects, and the Q value appears to be correlated with age and refractive power.

Comprehensive Evaluation of Anterior Corneal Change in Asphericity Calculated by the Tangential Radius of Curvature after LASIK

To evaluate the change in the anterior corneal asphericity (ΔQ) comprehensively calculated using the tangential radius (r_t) after LASIK. Forty-two right eyes were evaluated using the Orbscan II corneal topographer. The pre- and postoperative Q-values of the flat principal semimeridians calculated by the sagittal radius were compared to those by the tangential radius. The Q-value of each semimeridian in the horizontal region was calculated by r_t. Fourier fitting was used to model the 360-semimeridional variation of Q-values and to fit the Q-values in the vertical region before and after surgery. There were significant differences in Q-values between the two methods before (P < 0.001) and after surgery (P = 0.003). A significant increase in postoperative Q-value was detected compared to preoperative Q-value (P < 0.001) calculated by r_t. The 360-semimeridional variation of the Q-values was well fitted with a third- and fourth-degree Fourier function before and after surgery. The ΔQ-value distribution presented double valley variation, with the amount of ΔQ being lowest in the near-vertical regions and highest in the near-horizontal regions. Calculating the Q-value with r_t combined with Fourier fitting, we evaluated 360 ΔQ-values' variation of semimeridians of the entire anterior corneal surface and then displayed true and complete anterior corneal shape after LASIK.

Registration of eye reflection and scene images using an aspherical eye model

This paper introduces an image registration algorithm between an eye reflection and a scene image. Although there are currently a large number of image registration algorithms, this task remains difficult due to nonlinear distortions at the eye surface and large amounts of noise, such as iris texture, eyelids, eyelashes, and their shadows. To overcome this issue, we developed an image registration method combining an aspherical eye model that simulates nonlinear distortions considering eye geometry and a two-step iterative registration strategy that obtains dense correspondence of the feature points to achieve accurate image registrations for the entire image region. We obtained a database of eye reflection and scene images featuring four subjects in indoor and outdoor scenes and compared the registration performance with different asphericity conditions. Results showed that the proposed approach can perform accurate registration with an average accuracy of 1.05 deg by using the aspherical cornea model. This work is relevant for eye image analysis in general, enabling novel applications and scenarios.