The present study compared the pupil barycenter configurations that can be used to calculate the kappa angle in terms of distance in patients with myopia and hyperopia. Results showed that the kappa angle distance over the pupil barycenter distance was higher in hyperopic cases than in myopic cases. In another study, higher positive kappa angle values were found in patients with hyperopia than in patients with myopia and emmetropia [4]. A difference was observed between the mean kappa angle values of the right and left eyes [4]. The kappa angles of the left eyes of patients with emmetropia tend to be slightly increased [4, 10, 11]. In our study, the mean distance of the pupil and iris barycenter origins was higher in the right eye in both myopic and hyperopic cases.
Evidence showing the importance of the kappa angle in refractive surgery, whether in laser surgery or in multifocal lens treatment, is increasing [12–15]. Generally, hyperopic eyes have a wide kappa angle, and these eyes are prone to decentralized treatment during laser ablation [16]. The mean kappa angles were 5.46° and 5.22° in the studies by Hashemi et al. [2] and Basmak et al. [4], respectively. The small difference between the angles is believed to be due to the age groups of the subjects included in the study, which was between 14 and 81 years in the study by Hashemi et al. [2] and between 20 and 40 years in the study by Basmak et al. [4]. The ages of the cases included in our study ranged from 7 to 60 years, and the mean pupil barycenter distance was 0.30 mm in our study.
In the study by Hashemi et al. [2], the mean kappa angles for patients with myopia, emmetropia, and hyperopia were 5.13°±1.50°, 5.72°±1.10°, and 5.52°±1.19°, respectively. A significant correlation was found between the refractive status of the patients and the kappa angle measurements, which was consistent with the findings of Hashemi et al. [2]. In the study by Basmak et al. [4], the values, which were obtained by with Orbscan II, were 4.51°, 5.55°, and 5.65°, respectively [4]. Qazi et al. [17] measured the preoperative kappa angles using Orbscan and reported values of 5.0° and 6.9° in myopic and hyperopic cases, respectively, with an average spherical equivalent of 3.50 D. The average kappa angles were 4.66° in myopia with refractive defects between − 3.00 and − 6.00 D and 5.45° in hyperopia with refractive defects between 2.00 and 4.00 D. In our study, the mean pupil barycenter origin kappa angle distances were 0.38 ± 0.15 and 0.21 ± 0.11 mm in hyperopia and myopia, respectively. The mean distance of the pupil barycenter originating from the kappa angle was 0.22 mm in myopia with refractive error between −3.00 and −6.00 D and 0.39 mm in hyperopia with refractive error between 2.00 and 4.00 D.
Kappa angle measurement may depend on the biometric, geometric, and optical properties of the cornea, globe, retina, crystalline lens, and anterior chamber depth. Depending on the corneal power, anterior chamber depth, and nodal point, we can expect that the optic axis and the entrance and exit of the pupil have specific localizations. Meanwhile, the visual axis also depends on the geometric and anatomical features of the fovea, nodal point, and pupil entrance. Thus, there seems to be some relationship in the geometric, optical, and biometric properties of the eye when there are changes in the kappa angle [2].
A synoptophore measures the kappa angle using the corneal reflection method, which is the most widely used method in clinical practice [5]. Basmak et al. [4] used both Orbscan II corneal topography and synoptophore to measure the basin and arc kappa angle. According to their results, the kappa angles obtained with Orbscan II were higher than those obtained with synoptophore. They also reported higher kappa angles in patients with hyperopia than those with emmetropia or myopia. Yeo et al. [18] used ultrasound biomicroscopy and corneal topography to measure the kappa angle and obtained reliable results. New instruments such as Galilei (Ziemer Ophthalmic Systems) and OPD Scan II (Nidek) are started to be used in the measurement of the kappa angle. If the kappa angle cannot be automatically and directly measured, the distance between the corneal vertex and the pupillary center (x and y Cartesian values) can be used to calculate the kappa angle [16]. The Lenstar LS 900 (Haag-Streit AG) device can be used for this purpose. Although Lenstar LS 900 does not directly measure the kappa angle [8], we can apply the Pythagorean theorem to measure the pupil barycenter distances (x and y coordinates of the pupil center; dx and dy) and determine the kappa angle distance. Likewise, we evaluated the kappa angle distance using the iris barycenter distances (x and y coordinates of the iris center; dx and dy) and compared the pupil and iris barycenter origin kappa angle distances.
In our study, the kappa angle distances were higher in hyperopic cases when calculating the kappa angle distance of both the pupil and iris barycenter origins. Although the corneal and lens thickness values were higher in the hyperopic cases included in our study, the anterior chamber depth and pupil diameter were also found to be higher in myopic cases. Meanwhile, no significant difference was observed between hyperopic and myopic cases in terms of astigmatism and white-to-white measurements.
This study had several limitations. First, patients with emmetropia were not included in this study, and second, the study was not conducted according to age groups. More objective evaluations can be made by including primarily hyperopic and myopic cases as well as emmetropic cases. If the cases are according to age groups, age-related changes in the kappa angle can also be detected.
In conclusion, the kappa angle distances are higher in hyperopic cases than in myopic cases. We believe that the calculations of the pupil barycenter originating from the kappa angle distance can be used as an alternative in the evaluation of the kappa angle.