Distribution of angle alpha and angle kappa offsets among adult candidates for cataract surgery

Advances in cataract and refractive surgery have raised patient expectations for complete refractive correction and optimal visual outcomes. Patients opting for modern intraocular lens (IOL)-based refractive surgery, including multifocal IOLs, extended depth of focus (EDOF) IOLs, and high-power toric IOLs, may experience postoperative glare, haloes, and other photic phenomena [1‐3].

Angle alpha and angle kappa, representing misalignments between the eye’s axes, may be linked to these phenomena, potentially impacting visual quality [4‐7]. Research suggests that a significant angle kappa correlates with increased glare and halo effects following multifocal IOL implantation [5]. Additionally, the magnitude of angle kappa offset has been associated with visual outcomes, including modulation transfer function cutoff, following trifocal diffractive IOL implantation [8]. In a study focusing on two aspheric IOLs, higher alpha angles were linked to elevated higher-order aberrations (HOAs) across all pupil sizes, and an increase in angle kappa was associated with decreased vision quality, as evidenced by a reduced Strehl ratio and increased internal HOAs [9]. Similarly, larger horizontal angle kappa and alpha were associated with greater horizontal decentration, while a deeper anterior chamber depth and larger vertical angle kappa predicted increased vertical decentration [10].

Accurate centration is crucial for successful laser refractive surgery. A decentered ablation can lead to postoperative glare, irregular astigmatic error, and reduced best spectacle-corrected visual acuity (BCVA). While pupil-centered laser ablation generally yields optimal refractive outcomes, it can pose challenges for individuals with high angle kappa values, potentially causing a significant discrepancy between the laser-ablated zone and the visual axis, resulting in less-than-optimal refractive results [11‐14].

Currently, there is limited understanding regarding the global distribution of angle alpha and angle kappa and their relationship with other ocular biometric parameters. Swept-source optical coherence tomography (ssOCT) devices, such as the IOLMaster 700 (Carl Zeiss Meditec, AG, Germany), now offer measurement of these angles' offset magnitudes alongside other ocular biometric parameters [15]. This study aimed to characterize the distributions of angle alpha and angle kappa offset magnitudes, along with their associated ocular biometric parameters, in a large population of adult candidates for cataract surgery.

This cross-sectional retrospective study adhered to the tenets of the Declaration of Helsinki and received institutional review board approval. Patient consent was waived due to the retrospective de-identified nature of the study.

A total of 8,119 eyes of 4,781 candidates for cataract surgery were included in this study, out of 18,171 records from the IOLMaster 700. The patients included 2,536 (53.0%) females, the mean age of the entire study was 70.7 ± 12.9 years (median 72.0 years; range 18–99 years; Table 1), and there were 4,051 (49.9%) right eyes.

There is paucity of literature on the potential role and measurements of angles alpha and kappa offset magnitude in cataract and refractive surgery, among populations worldwide. In this study, those values were measured with the IOLMaster 700 device in a large population of cataract surgery candidates.

In our study,there was no variation in angle alpha offset magnitude between the right and left eyes, in contrast to a significant variation in angle kappa offset magnitudes (Table 1 and Fig. 2). Since demographic and conventional ocular biometric parameters, including AL, Kmean, ACD, and LT, were similar between right and left eyes, this variation appears to represent a real difference and not a confounder effect. The variance in angle kappa offset magnitude could be further seen when stratified for gender and quadrants. Eye dominance, which was not measured in this study, may also be related to this finding, as demonstrated elsewhere [20]. Recently Mahr et al. collected angle alpha offset magnitudes of both right and left eyes but did not compare their offset magnitudes [21]. Instead, they found a positive correlation between right and left eyes.

AL-related differences in angle alpha were demonstrated and found to be higher in short eyes and very long eyes (Table 4). There were also gender-related differences in the offset magnitude of angle alpha, with an average larger one found in females (Table 6). Gender-related differences have been examined by others as well. Meng et al. [16] demonstrated gender-related difference in angle alpha offset magnitude in a Chinese population, but it is not clear whether angle alpha offset magnitude was greater in males or females due to ambiguity between their text and the related statistics. In contrast, Wang et al. [22] observed no significant gender-specific differences, a result that could be attributable to the relatively small sample size in their study (n = 81 eyes). Similar to angle alpha offset magnitude, AL-related differences in angle kappa offset magnitude were demonstrated and found to be higher in short eyes and very long eyes (Table 4). In contrast to angle alpha offset magnitude, no gender-related differences in the offset magnitude of angle kappa were demonstrated (Table 6), as reported by Meng et al. [16] and Wang et al. [22].

In the present study, the highest offset magnitudes of both angles were observed in short eyes, with a nonlinear trend of a gradual decrease in both angles’ offset magnitudes as AL increased, towards a nadir. In addition, there was a significant positive correlation of the offset magnitudes of angle alpha and angle kappa with each other. Similar findings were demonstrated by Basmak et al. [23] and by Meng et al. [16] Our findings make it clearer that the hyperopic patient is especially prone to high angle alpha and angle kappa offset magnitudes, which makes them especially challenging with laser-assisted in situ keratomileusis (LASIK), and probably with IOLs as well, even with EDOF type lenses.

The patient population of the present study was older than that of Meng et al. [16] (70.7 ± 12.4 vs 64.6 ± 11.9 years, respectively), and demonstrated larger right eye angle alpha (0.498 ± 0.198 vs 0.45 ± 0.21 mm, respectively) and angle kappa (0.368 ± 0.205 vs 0.30 ± 0.18 mm, respectively) offset magnitudes. Left eyes were not included in Meng et al.’s study [16]. Lopes et al. [24] demonstrated significantly greater angle kappa values in right eyes in an Italian population, non-significant differences in a Brazilian population, and significantly lower values in a Chinese population. It should be noted that those values cannot be compared to ours since Lopes et al. measured angle alpha and angle kappa by means of novel computational methods and reported these results in angular units. Langenbucher et al. [25] measured each cartesian coordinate of the offsets separately while grouping the right and left eyes together. Their preoperative measurements yielded an impressively smaller mean Ix value in comparison to our study (-0.006 vs. 0.436 mm, respectively) and a larger mean Iy value (0.131 vs. 0.046 mm, respectively). Px and Py values differences were similar. We assume that reasonable explanations of this significant variation are the mixture of both right and left eyes in the same group or a different method of calculation rather than using the crude analysis output of the IOLMaster 700. Using their own technique, they have tried to predict the post-operative CWC, using preoperative measurements, but reached unreliable results.

Kim et al. examined the repeatability of measurements taken by the IOLMaster 700, including chord mu, Px, Py, and pupil diameter, and compared them with those from Scheimpflug tomography (Pentacam HR, Oculus, Germany) [26]. The IOLMaster 700 exhibited superior repeatability, while the correlation between the two devices ranged from moderate to high. In another study, Zhang et al. found good agreement in angle kappa but poor agreement in angle alpha among three systems that used different technologies: Pentacam HR (Oculus, Germany), iTrace (Tracey Technology, Houston, Texas) and the IOLMaster 700 [27]. These findings are important to consider when using these parameters.

Cataract and refractive surgery with a monovision target approach require that one eye be allocated for each target distance. The conventional monovision approach is to correct the dominant eye for distance vision [28‐30]. Kim et al. [20] demonstrated a smaller angle kappa in the dominant eye in a Korean population. In the present study, angle kappa offset magnitude was significantly greater in right eyes but, as noted earlier, we did not document eye dominance nor made a sub-group analysis of only patients with both eyes included. Further research aiming to find a relation between angle kappa’s offset magnitude and eye dominance is needed, with possible implication of its application as an objective marker to aid in choosing the eye more suitable for distance vs. near target, without the need of subjective optometric examination of eye dominance.

It is worth mentioning that Masket et al. [31], in their review of pseudophakic dysphotopsias, found an association between high positive angle kappa and high hyperopia, compatible with our findings. They noted that a high positive angle kappa and hyperopia are potentially in clinical association with negative dysphotopsias. Together with our findings, angle kappa values or offset magnitudes may be used as a cutoff when considering multifocal IOLs, as Mahr et al. [21] proposed using angle alpha alone. Indeed, the measurements norms are prone to be biometer-dependent, yet population-based baseline values can assist in eliminating the extreme values, or at least, require special attention and warning to the patients that they may be at higher risk due to pre-existing alignment issues, as part of their informed consent.

We demonstrated a strong association between angle alpha and angle kappa offset magnitudes, as well as variable associations between them and many biometric measurements. Since only several biometric devices currently report angle alpha and angle kappa offset magnitudes, reporting and analyzing these parameters and their correlations may reveal important future applications and possibly establish the necessity to assess both eyes before any ocular surgical intervention, in contrast to the current assumption of eye symmetry in these parameters. Moreover, recent studies have described a variety of relations between right and left eyes among various populations around the world [21, 24], which, in turn, can affect decision making regarding IOL-based refractive surgery as well as laser keratorefractive surgery.

The strengths of our study are our large population with a wide range of ages, and evidence to show that there is no symmetry between the right and left eyes. In addition, we measured angle alpha and angle kappa offset magnitudes of all patients with a single device, the IOLMaster 700 (a strength and a limitation simultaneously).

This study has several limitations, including its retrospective design, the inclusion of non-paired right and left eyes, and the absence of documentation regarding eye dominance. Ethnic differences that could not be addressed in this study due to its retrospective nature may warrant further exploration. Additionally, the angles are measured as offsets, and their clinical impact remains unclear. Angle lambda represents the deviation between the line of sight and the pupillary axis. Previous studies have suggested that a significant magnitude of angle lambda offset may lead to symptoms of dysphotopsia following trifocal IOL implantation [3]. However, the IOLMaster 700 does not currently assess this angle or its offset magnitude, which prevented its inclusion in our study.

In conclusion, the present study documents that the offset magnitudes of both the angle alpha and angle kappa present significant variations according to gender, eye laterality, angle location, and biometric parameters, such as AL. These values are also population-specific. Due to the importance of angle alpha and angle kappa for the satisfaction of patients after modern cataract and refractive surgery, understanding and subclassifying these angles and their offset magnitudes may improve patient selection and aid in choosing the most suitable personalized treatment options. Possible implications, such as refinement of objective identification of the dominant eye in monovision approach should be further inspected.