Dynamic distribution of angle kappa and its biomechanical relationships in population who are suitable for excimer laser refractive surgery

Background To explore the dynamic distribution of pupil size and center,the eccentricity distribution of angle kappa, and its correlation with other biomechanics about suitable for excimer laser refractive surgery. Methods Randomly selected 225 patients (407 eyes) who underwent femtosecond laser combined with excimer laser in situkeratomileusis,preoperative use of Wavelight Allegro Topolyzer Corneal Topography ( Wavelight Laser Technologies AG, Erlangen, Germany ) to measure the pupil size and center position, the German Wavelight EX500 excimer Laser (500Hz) records the deviation between the pupil center and the coaxially sighted corneal light reex when the patient is supine. Results and the coaxially sighted corneal light 0.102 0.30 coaxially sighted light is the side of the center (34%).Under the dark light condition, the the was: the of the eye -0.152 ± with statistical to the temporal the had no statistical change The WTW was positively correlated with ( r P <0.001).The SE and centroid shift was negative correlated ( r - 0.002).


Background
The ideal excimer laser ablation centration should be completely overlapped with the visual axis,in corneal refractive surgery [1] .If the pupil positioning tracking scan does not take into account the adjustment of the angle kappa, the actual corneal cutting area is not consistent with the ideal cutting area, which will cause "surgical origin" eccentric cutting. Therefore, it is particularly important to adjust the angle kappa during surgery [2] .However,the visual axis is so di cult to determine that the eye tracking system usually locates and tracks the center of the pupil in actual surgery.Because the pupil center is different from the visual axis,it has become a consensus among corneal refractive surgeons to adjust the laser ablation centration from the pupil center to the visual axis, compensate for the offset effect of angle kappa, and reduce higher-order aberrations after surgery [3,4] .
The coaxially sighted corneal light re ex piont is the corneal entry point of the visual axis [5] .Studies have shown that coaxially sighted corneal light re ex piont is the ideal ablation centration point, because coaxially sighted corneal light re ex piont is the closest point to the visual axis and is not affected by changes of pupil size and center position, with an average of 0.02 mm [6] .Therefore, the angle kappa can be understood as P-Dist [7] .However, the angle kappa is not a xed value, and changes with the dynamic change of the pupil center position [8,9] .That is why it is necessary to further explore the dynamic changes of the pupil size and center position suitable for excimer laser surgery, P-Dist and its correlation with other biomechanics.The related research at home and abroad hasn't been reported.
This study analyzes the P-Dist, and researches its correlation with other biomechanics to explore the dynamic changes of pupil size and center position suitable for excimer laser surgery.It provides a reference for the surgical solution design about how to optimize the femtosecond laser combined with excimer laser in situ keratomileusisin with the angle kappa compensation in accordance with the optical characteristics of individual human eyes. Excimer laser cutting was carried out using the wavefront optimized cutting procedure of the German Wavelight FS200 (200 KHz) femtosecond laser and the Wavelight EX500 excimer Laser (500 Hz), with the target refraction set to 0 D and no residual refraction.Surgical steps:Routine preoperative preparations,disinfection of operative eye,open eyes by eyelid opener, take the supine position;ask the patient to look at the upper indicator lamp before lifting the ap after making the corneal ap. The patient can see the re ective point of the corneal vertex (coaxially sighted corneal light re ex point) and red re ection (visual axis center). By adjusting the illuminance to keep the pupil size to match the preoperative examination, the Wavelight EX500 excimer laser system's x and y-axis eye-tracking adjustment program is started to make the two re ection points coincide. The reference system displays the corneal horizontal and vertical adjustments, and records the P-Dist when the patient is in the supine position.

Statistical Methods
All statistical analysis were performed using SPSS software(version19.0,SPSS,Inc.).The data of each group were tested for normality and homogeneity of variance. When pairwise comparison was performed, LSD-t test was used. Paired t test was used for right and left eyes.The biomechanical correlation was analyzed by Pearson correlation.when P < 0.05,it was considered statistically signi cant.

Discussion
Although angle kappa compensation combined with personalized femtosecond laser combined with excimer laser in situ keratomileusis has a good theoretical basis, there is still a signi cant gap between the actual and ideal visual quality [10] .Factors in uencing angle kappa include axial length, ACD and corneal curvature radius,but the proportion of each factor has not been con rmed [11,12] .Moreover, the size and central position of the pupil in corneal refractive surgery cannot be ignored.In order to ensure the accuracy of surgical positioning, it is necessary to ensure the matching with the preoperative pupil size and position, iris texture recognition, corneal limbus recognition [13,14] .
At present, the target of non-interference pupil center-corneal re ex line-of-sight tracking technology based on image processing is the pupil center of the operated eye, and the direction of the visual axis is estimated by calculating the vector between the pupil center and corneal re ex [15] .The laser cutting area is mostly centered on the coaxially sighted corneal light re ex point [16] . If the positions of the two are different, the locked pupil center needs to be adjusted accordingly [17] . The centrifugation used is a xed value, but the ideal centrifugation should also change with the dynamic changes of the pupil.Therefore, according to the pupil size, center position and dynamic change of angle kappa of the patients who are suitable for excimer laser surgery, obtained the individualized pupil center displacement curve. During the operation, the pupil dynamics were monitored to adjust the angle kappa and calibrate the ablation centration in real time to ensure that each scanning-spot excimer lase was in the correct position [18] .
In this study, the average shift distribution between the center of the cornea and the center of the pupil was 0.322 ± 0.194 mm (range: 0.005 to 0.956 mm), and 64% of the eyes were ≤ 0.40 mm. We also measured P-Dist during the operation, and showed that the average P-Dist = 0.225 mm, the minimum 0.010 mm and the maximum 0.580 mm, 80% of the eyes is ≤ 0.30 mm, and the coaxially sighted corneal light re ex point is mainly biased which is Upper temporal side of the pupil center (34%).The angle kappa is not a xed value,which will change under different conditions [19] .In uenced by factors such as intraoperative illumination, surgical stimulation, eye type, emotional tension, and accommodation convergence caused by close gaze indicator lights, the dynamic changes of pupil size and central position can be caused [20,21] .Theoretically, when the size and the center of pupil continuously change during surgery, the angle kappa also changes signi cantly [7,22] .Therefore, we speculate that there is difference in diopter and visual quality after different angle kappa compensation percentage.
The results of this study indicate that the positions of the pupils' center of the left and right eyes were signi cantly different in low light conditions. The X axis of the left eye is -0.046 ± 0.091 mm, and the X axis of the right eye is -0.152 ± 0.084 mm. The right eye deviated from the left eye to the temporal side by 0.106 ± 0.095 mm under dark light.The Measured Centroid Shift of the left eye is 0.127 ± 0.103 mm, and that of the right eye is 0.176 ± 0.139 mm, with statistical difference.We speculate that the majority of the population is right-handed, and the head deviates to the right side when working in close range. Due to the inconsistent gaze target distance, the left eye needs more accommodation force to achieve the same state as the right eye (the right eye is closer), causing smaller pupils, shallower anterior chambers and larger angle kappa relative to the right eye.
The changes in the pupil center positions of the left and right eyes guide us the left eye should adjust a larger proportion of angle kappa when positioning in excimer laser surgery. Because the angle kappa offset of the left eye is greater than that of the right eye.If positioned at the center of the cornea, the right eye can appropriately adjust the ablation centration at a position slightly within 0.152 mm from the corneal center to the temporal side to nd the ablation centration point which is most closest to the visual axis [23] .To avoid the reduction of postoperative retinal imaging quality caused by unnecessary eccentric ablation [24,25] .
Our results also show a positive correlation between lateral WTW and pupil diameter change. The related results have not been reported at home and abroad.This conclusion guides us to treat patients with large cornea during the operation to ruduce the dynamic changes in pupil size whit a darker environment as much as possible in order to improve the e ciency of pupil matching [26] .There is no correlation between the SE and the change of pupil diameter, but there is a negative correlation between the SE and Measured Centroid Shift.It has been reported in the literature that the refractive state has a signi cant correlation with the angle kappa, which is consistent with the results of this study [15] .Therefore, We speculate that the dynamic change of pupil center of Measured Centroid Shift is small for people with high myopia.Therefore, it can be understood that the dynamic change of angle kappa is correspondingly reduced, and the e ciency of pupil matching is higher. It is suggested that the proportion of compensating angle kappa vector is higher during operation.
This study rstly explored the offset distribution between the pupil center and the corneal co-re ective point, and its correlation with other biomechanical factors such as the eyeball.It further con rms the importance of accurately locating the position of the ablation centration and the necessity to reasonably adjust the angle kappa vector ratio under different myopia degrees and eye type.This study also has limitations,the insu cient samples and the individual variability may affect the results.The relationship between angle kappa compensation and visual quality needs to be further studied. The digital relationship between various individualized cutting modes still needs further exploration.

Conclusions
The pupil of the left eye becomes smaller, the anterior chamber becomes shallower, and the angle kappa increases relative to the right eye.In patients with large WTW, a darker light environment is maintained during the operation to improve the e ciency of pupil matching.The dynamic change of angle kappa in high myopia population is small.This study further con rmed the importance of accurately locating ablation centration and the necessity of rationally adjusting angle kappa ratio according to different myopia degrees and eye types.
Abbreviations ACD: Anterior chamber depth (from endothelium); Std. Error: Standard error of the estimate; SE: Spherical equivalent; P-Dist:the distance(eccentricity) between the pupil center and the coaxially sighted corneal light re ex point ; WTW: White-to-white corneal diameter the corneal transverse diameter .

Declarations
Ethics approval and consent to participate The study protocol was approved by the Ethics Institutional Review Board of the A liated Hospital of Yanbian University ( No.2020032) and informed consent was obtained from all participants before enrollment.

Consent for publication
Applicable.
Availability of data and materials The data will not be made public in order to protect the participant's identity.

Competing interests
The authors declare that they have no competing interests.  Figure 1