The Distribution of IOL Center and Its Relationship with Internal Ocular Objective Visual Quality in Cataract Patients

Background: To investigate the distribution of the center of the intraocular lens (IOL) after phacoemulsication, and to assess the correlation between the center of IOL and preoperative angle kappa, angle alpha, and objective internal visual quality, respectively, in cataract patients with monofocal and bifocal IOLs implantation. Methods: Prospective cross-section cases series. One hundred and thirty-seven eyes of 107 patients who underwent phacoemulsication were included. Preoperative angle kappa and alpha, postoperative internal ocular aberrations, internal objective visual quality, and the center of IOL relative to the visual axis (CIV) was evaluated using iTrace system. Independent sample t-tests and Pearson correlations were performed. Results: Locations of CIV were scattered in all directions centered on corneal light reection for both C-Loop designed IOL and plate-haptic designed IOL. No correlations were found between CIV and preoperative angle kappa and alpha in both magnitude and orientation. No correlations were found between CIV and postoperative internal ocular aberrations (astigmatism, coma, and trefoil). In the bifocal IOLs group, the CIV was negatively correlated to the internal Strehl ratio at 3mm; however, it was not correlated to the Strehl ratio at 5mm. The magnitude of CIV was positively correlated to the length of the optic axis. Conclusions: CIV was not predictable according to angle kappa and alpha before cataract surgery. CIV was not related to internal ocular aberration, but large CIV may lead to light scattering due to steps between diffractive rings in patients with small pupil sizes. The magnitude of CIV may be greater in cataract patients with longer optic axis. Trial registration: retrospectively registered.

(astigmatism, coma, and trefoil). In the bifocal IOLs group, the CIV was negatively correlated to the internal Strehl ratio at 3mm; however, it was not correlated to the Strehl ratio at 5mm. The magnitude of CIV was positively correlated to the length of the optic axis.
Conclusions: CIV was not predictable according to angle kappa and alpha before cataract surgery. CIV was not related to internal ocular aberration, but large CIV may lead to light scattering due to steps between diffractive rings in patients with small pupil sizes. The magnitude of CIV may be greater in cataract patients with longer optic axis.
Trial registration: retrospectively registered.

Background
Premium intraocular lens (IOL) decentration, which can result in signi cant visual disturbances, is one of the main reasons of patient dissatisfaction. A well-centered IOL is crucial for good visual quality because the light path (the line between the xation target and the fovea) has to pass thought the center of the multifocal IOL (mIOL). Otherwise, patients may experience unpleasant photic phenomena. 1,2 These phenomena are common causes of dissatisfaction in patients with mIOLs implantation, even when uncorrected visual acuity is excellent. 3 In patients with a large angle kappa, functional IOL decentration can happen if the fovea-centric ray does not pass though IOL center, 1 and induces aberrations, glare and halo. [4][5][6] However, it was also found that many patients with a large angle kappa were asymptomatic. 1 Angle alpha, which is de ned as the intersection of the visual axis with the optic axis, is believed to represent the center of the capsular bag. A recent study showed that the location of IOL was correlated to angle alpha. 7 It has been proposed that angle kappa and alpha should be considered during preoperative assessment for mIOLs implantation to better predict outcomes. [8][9][10] Are there any potential factors that impact the center of IOL in patients who were considered good candidates for premium IOL implantation after passing strict and adequate preoperative assessment? Is IOL center predictable during preoperative assessment in cataract patients? Does a well-centered mIOLs, which has been con rmed during surgery and follow-up visit, lead to good visual outcome? We know little about how angle kappa and alpha impact the visual quality after mIOLs implantation. The aim of this study was therefore to look into the relationship among the center of IOL, angle kappa and angle alpha, and check the correlation between the center of IOL and internal ocular aberrations and objective visual quality.

Patients
In this cross-sectional cases series study, patients who had been scheduled for cataract surgery from December 2018 to December 2019 were included. All patients were subjected to phacoemulsi cation surgery and were divided into two groups depending on the type of IOL. Inclusion criteria were as follows: 1) patients' preoperative lens opacity grading greater than C2N2P0 according to Lens Opacity Classi cation System III, 2) corneal astigmatism less than 0.75 diopter, 3) no history of ocular disease other than cataract, 4) no previous ocular surgery, 5) no intraoperative and postoperative complications. Exclusion criteria included poor cooperation during examination, inability to obtain data due to severe lens opacity preoperatively, notable IOL decentration or tilt under slit lamp evaluation during the follow-up, and patients lost to follow-up.

Preoperative and Postoperative Assessment
Preoperative assessment was taken within 2 days before surgery and postoperative assessment was taken at a 3 month follow-up visit. All patients underwent a full ophthalmologic examination, including slit-lamp examination for both anterior and posterior segments of the eye, uncorrected distance and near visual acuity, best corrected distance and near visual acuity, intraocular pressure (IOP), OCT (Heidelberg engineering, Germany), and optical biometry (Lenstar LS 900, HAAG-STREIT, USA). Visual quality and ocular aberration were determined by iTrace (Tracey Technologies, Houston, TX, USA).

IOL Selection
Three models of aspherical monofocal IOLs were used in group 1. The difference between those three models of IOLs was the ability of correcting spherical aberration. The spherical aberrations of ZCB00, 509MP and 409MP are − 0.27 µm, -0.18 µm and 0 µm, respectively. Two models of bifocal IOLs were used in group 2. The spherical aberrations of ZMB00 and 809MP are − 0.27 µm and − 0.18 µm, respectively. During preoperative examination, the corneal spherical aberration at 6 mm was measured by iTrace, and the model of IOLs was decided with the goal to remove as much of corneal spherical aberration as possible.

Surgical Procedure
The same experienced surgeon (Ting Ma) performed all the operations under topical anesthesia (Benoxil 0.4% solution, 3 times, Santen) using a standard technique of phacoemulsi cation. A 2.4 mm clear corneal incision was made with a diamond knife at the 135°axis and an auxiliary incision was made at 45°axis. All IOLs were implanted into the capsule bag, and the whole circumference of the IOL optical zone was covered by the anterior capsule. Antibiotic (Cravit 0.5%, Santen), NASIDs (Pranopulin, Senju), and arti cial tears (Hycosan, 0.1%, Eusan) were used for 4 weeks by all patients postoperatively. All operations were successful and there were no intraoperative complications.

Evaluation indicators
Angle alpha, angle kappa, internal ocular aberrations, internal modulation transfer function (MTF) and Strehl ratio of all participants were measured using iTrace aberrometer by an experienced technician (Xin Gu) before and after the surgery.
Angle kappa and alpha were measured under scotopic condition. After that, the patient's pupil was dilated to more than 6.5 mm using tropicamide (Mydrin-P, Santen) to obtain internal ocular aberrations, internal MTF and Strehl ratio for both 3 mm and 5 mm scanning zones. The iTrace system uses optical ray-tracing technology and measures the point spread function (PSF) of the eye with its retinal spot detection. Three measurements of each eye were captured, and the best scan (the image with the best quality peaks for individual points) was chosen for the nal analysis. The center of the cornea and pupil relative to corneal light re ection were presented in magnitude and orientation. Root-mean-square (RMS) terms of total higher-order aberrations (HOAs) of internal eye and individual aberrations (astigmatism, coma, and trefoil) of internal eye were evaluated. The MTF curves due to higher order aberrations and Strehl ratio were evaluated for the internal eye.

Center of IOL
The distance and orientation of the center of IOL relative to the visual axis (CIV), was determined using iTrace by the same technician (Xin Gu) at the time of the last follow-up (3 months). The patient's pupil was dilated to more than 6.5 mm so the entire optical zone of the IOL could be observed. A radial ruler was used to show the edge of the optical zone, and the center of the IOL was determined at the same time. The distance and orientation relative to the visual axis were calculated. See Fig. 1 for details.

Statistical Analysis
The mean and standard deviation of angle kappa, angle alpha, CIV, aberrations, MTF and Strehl ratio were calculated. Mean values were used for population analysis. Student paired t tests were performed to test for signi cant differences in the visual acuity, IOP pre-and postoperatively. Independent sample t tests were performed to test for signi cant differences in the magnitude and the orientation of CIV, angle kappa and angle alpha. Pearson correlations were performed for correlation analysis. A P value less than 0.05 was regarded as statistically signi cant. All statistics were calculated using SPSS 17.0. The datasets used for analysis during the current study are available from the corresponding author on reasonable request.

Results
One hundred and forty-seven eyes from 113 patients underwent phacoemulsi cation, 4 patients did not return for the follow-up examination after surgery, and 2 patients did not cooperate (poor xation) during examination. At the end of this study, data of 137 eyes (77 right eyes and 60 left eyes) from 107 patients were included. Ninety-one eyes of 74 patients (30 male and 44 female) were implanted with monofocal IOLs, and 46 eyes (24 right eyes and 22 left eyes) of 33 patients (13 male and 20 female) were implanted with bifocal IOLs. The mean age was 67.38 ± 12.16 (range 20 to 86 years) in the monofocal group and 66.06 ± 9.55(range 37 to 83 years) in the bifocal group. In the monofocal group, 43 eyes were implanted with one-piece plate-haptic lenses and 48 eyes were implanted with one-piece C-Loop haptic lenses. In the bifocal group, 36 eyes were implanted with one-piece plate-haptic lenses and 10 eyes were implanted with one-piece C-Loop haptic lenses. In the monofocal group, preoperative uncorrected distance visual acuity (UDVA) was signi cantly lower than postoperative UDVA (0.84 ± 0.39 versus 0.17 ± 0.11 Mean ± SD, logMAR, t = 12.890, P = 0.000), and preoperative corrected distance visual acuity (CDVA) was signi cantly lower than postoperative CDVA (0.54 ± 0.33 versus 0.07 ± 0.09, Mean ± SD, logMAR, t = 14.383, P = 0.000). In the bifocal group, preoperative UDVA was 0.75 ± 0.48, which was signi cantly lower than postoperative UDVA (0.15 ± 0.19, Mean ± SD, logMAR, t = 6.460, P = 0.000), and preoperative CDVA 0.44 ± 0.39,Mean ± SD, logMAR was signi cantly lower than postoperative CDVA (0.10 ± 0.24, Mean ± SD, logMAR, t = 3.426, P = 0.002). Postoperative uncorrected near visual acuity (UNVA) was 0.20 ± 0.20 (Mean ± SD, logMAR) in the bifocal group. Table 1 shows the ocular bio-metric data. *: Only the magnitude of angle kappa and alpha is shown in the table In group 1, magnitudes of preoperative angles kappa and alpha were signi cantly different from the magnitude of CIV; and no correlations were found between CIV and the magnitudes of preoperative angles kappa and alpha. There were signi cant differences between the orientation of CIV and orientations of preoperative angles kappa and alpha; and no correlations were found ( Table 2). The distributions of CIV, angle kappa and angle alpha of all 91 eyes of Group 1 were graphed in polar coordinate diagrams in Fig. 2. Locations of angle kappa and alpha were distributed mostly on the temporal side of the corneal light re ection, while angle alpha clustered along the horizontal line. The location of IOL centers showed a broader distribution. For Group 1, the distribution of CIV of two different designed IOL is shown in Fig. 3.
No signi cant differences were found between plate-haptic IOL and C-Loop haptic IOL for CIV in both magnitude and orientation (Table 3). There were no signi cant differences between males and females or right eyes and left eyes for CIV in magnitude and orientation (Table 3). Age did not correlate with CIV magnitude and orientation (r=-0.005, P = 0.096, r=-0.006, P = 0.952, respectively). The length of the optic axis positively correlated with CIV in magnitude (r = 0.236, P = 0.028), while no correlation was found between the length of the optic axis and CIV in orientation (r=-0.139, P = 0.200).  The correlation between CIV and internal individual ocular aberrations, internal total HOA, internal MTF due to HOA, and internal Strehl ratio were determined. In Group 1, there was no correlation between the magnitude of CIV and astigmatism

Discussion
Angle alpha is de ned as the angular distance between optic and visual axes and was rst measured by Tscherning using an ophthalmophakometer. 11 It can indicate the distance between the center of the capsular and visual axis because theoretically the optic axis passes through the center of curvature of each surface -the anterior and posterior corneal surfaces, as well as anterior and posterior crystalline lens surfaces in the system of the eye. A recent study showed that the location of IOL is correlated to angle alpha. 7 We investigated the correlation between the CIV and preoperative angle alpha for both magnitude and orientation, but no correlations were found. CIV showed a diffuse distribution (Fig. 2). Plotting the center of IOL relative to the corneal light re ection showed wide scattering without a discernible pattern (Fig. 2G-I), whereas the values for angle alpha fell on a narrow horizontal line on the temporal sides of corneal light re ection (Fig. 2D-F). This nding suggests that decentration of IOL relative to visual axis may not be related to a larger angle alpha. Further studies need to be done for the relationship between large angle alpha and visual quality.
Angle kappa is the intersection of the visual axis and the pupillary axis. 12 It can be measured by the distance from the pupil center to a point that is very close to the visual axis, such as the corneal vertex or corneal light re ection. 12 In previous studies, it has been found that poor satisfaction after multifocal lens implantation may be related to large angle kappa. 1, 13 Qi Y et al reported that with preoperative angle kappa greater than 0.5 mm, visual quality decreased in patients implanted with trifocal diffractive IOLs. 5 The association between angle kappa and bad visual quality is unclear. Prakash G et al proposed the concept of functional IOL decentration, indicating that the light passes through paracentral IOL rings or through the edge of the IOL rings even when the IOL seems to be well-centered in the capsular bag in those eyes with greater angle kappa. 1 In this study, we found no correlation between the CIV and angle kappa in magnitude and orientation. The distribution of angle kappa in both eyes was similar to CIV. However, when the left eyes and right eye were checked separately, locations of angle kappa distributed mostly to the temporal side of corneal light re ection, while the center of IOL were scattered in all directions relative to the corneal light re ection (Fig. 2). Similar distributions of CIV were found in both C-Loop designed IOLs and plate-haptic designed IOL (Fig. 3). These ndings indicate that the postoperative location of an IOL maybe affected by factors such as the size of capsular bag, asymmetric zonular weakness, or uneven capsular contraction rather than angles kappa and alpha.
The PSF, which in an optical system represents the intensity distribution of light from a point-like object projected onto the retina, indicates the extent of the blurring of vision. Calculating the maximum intensity of this observed retina image and dividing it by the maximum intensity of a diffraction-limited ideal optic system yields the Strehl ratio. 14 Aberrations are not the only factor contributing to the PSF, but diffraction, scatter, and phase shift are also important. In this study, the correlation analysis showed that astigmatism, coma, trefoil and HOA from internal eye were not correlated with the magnitude of CIV in both monofocal IOL group and bifocal IOL group. It should be pointed out that the magnitude of CIV was 0.02 to 0.85 mm and 0.06 to 0.48 mm in monofocal and bifocal group, respectively. This may not be large enough to induce large internal aberrations. However, the Strehl ratio of the internal eye was negatively correlated to the magnitude of CIV at 3 mm pupil size in the bifocal IOL group. This indicates that a small decentration of a bifocal IOL may affect visual quality compared to a monofocal IOL, and larger CIV may reduce visual quality by reasons other than aberrations, such as scatter or phase shift. No correlation was found between the magnitude of CIV and the Strehl ratio of internal eye at 5 mm in patients with bifocal IOLs. The reasons maybe that the main factors contribute to visual quality become more complicated due to a larger pupil size and the impact of CIV on visual quality is reduced. Hence, when the magnitude of CIV is large and the pupil size is small, even a relatively minor decentration may cause the light to pass through other diffractive rings rather than the central optical region of the mIOL.
Neither gender nor age were signi cantly correlated to the magnitude and the orientation of the center of the IOL. However, the length of the optic axis positively correlated with the center of IOL in magnitude, which indicates that the location of the IOL may be more variable in patients with longer optical axis than in normal patients.

Conclusion
In summary, the center of IOL relative to the visual axis was not related to angle kappa and angle alpha. A large CIV may be a risk factor for unpleasant visual phenomena in patients with small pupil sizes. Although our study showed that in cataract patients the magnitude of angle kappa does change after the cataract surgery, 15

Consent for publication
The consent for publication have been obtained.

Availability of data and materials
The datasets generated and analysed during the current study are not publicly available due to the privacy but are available from the corresponding author on reasonable request.

Competing interests
The authors declare that they have no competing interests.