Distance of Corneal Vertex and Effective Optical Zone Margin Following Keratorefractive Lenticule Extraction in Myopic Astigmatism

Abstract

Purpose: To determine the distances from the corneal vertex to the effective optical zone margin along its major (DVO_x) and minor axes (DVO_y), to evaluate their correlation with corneal wavefront aberrations after keratorefractive lenticule extraction (KLEx) in myopic astigmatism, and to identify potential factors related to DVO_x and DVO_y.

Methods: This study included 93 eyes of 51 patients who underwent KLEx with myopic astigmatism. The decentration, area of effective optical zone and the DVO_x and DVO_y on tangential topography difference map were measured. Induced corneal aberrations were obtained before and six months after surgery. Piecewise regression analysis was used to determine the relationship between the magnitudes of DVO_x and DVO_y and induced corneal aberrations. The Pearson correlation test was used to identify potential factors related to DVO_x and DVO_y.

Results: The mean DVO_x was 2.68 ± 0.24 mm, and the mean DVO_y was 2.31 ± 0.22 mm. The Pearson correlation coefficients were higher for induced horizontal and vertical coma, coma, trefoil, higher-order aberrations with DVO, compared to those with decentration or area alone. The DVO_x and DVO_y were inversely correlated with the correction of sphere, spherical equivalent, and percent tissue altered. Subgroup analysis revealed that induced corneal aberrations were significantly greater in subgroups with DVO_x < 2.316 mm and DVO_y < 2.183 mm, except for trefoil.

Conclusions: By integrating both EOZ area and decentration, DVO_x and DVO_y provide a more comprehensive assessment of surgically induced corneal aberrations in KLEx surgery, establishing them as crucial evaluation parameters for optimizing surgical planning and enhancing visual outcomes by identifying potential causes of suboptimal results.

Translational Relevance: DVO exhibited a stronger association with corneal aberrations in KLEx surgery, compared to either decentration or area. DVO_x and DVO_y can serve as new evaluation parameters to optimize customized surgical plan and enhance visual outcomes.

Introduction

Keratorefractive lenticule extraction (KLEx) is a corneal refractive surgery assisted by femtosecond laser, proven to have safe, effective, and predictive outcomes.^1,2 The removal of the corneal lenticule alters the curvature and optical zone of the cornea, thereby enhancing visual acuity and overall quality of vision.³ However, KLEx exhibited an undercorrection ranging from 11% to 16% per diopter in astigmatism correction.^4,5 KLEx surgery may lead to a reduction of corneal visual quality, often manifesting as starbursts, glare, focusing challenges, and halos.^6,7 In high myopic astigmatism, the symptoms were seen in around 50% to 70% of patients.⁷ 

It has been established that the effective optical zone (EOZ) and decentration are closely correlated with the postoperative visual quality.^3,8,9 Therefore determination of the EOZ and decentration is clinically significant. However, the correlation of EOZ and decentration on visual quality is inverse, and a larger optical zone may enhance tolerance to decentration.¹⁰ Moreover, the EOZ displayed an oval shape in correcting myopic astigmatism, becoming more pronounced with increasing degrees of astigmatism,^11,12 which may enhance tolerance to decentration along the major axis of the oval EOZ. Therefore the EOZ and decentration need to be analyzed simultaneously, which could benefit the customization of the surgical plan and algorisms and subsequently improve the postoperative visual quality for patients with myopic astigmatism. 

In current study, we suggest new evaluation parameters, the distance from corneal vertex to EOZ edge along its major (DVO_x) and minor axes (DVO_y), which integrated the impact of decentration and EOZ following KLEx in myopic astigmatism. Our aim was to determine DVO_x and DVO_y and their correlation with corneal wavefront aberrations following KLEx in myopic astigmatism, and identify potential factors related to DVO_x and DVO_y. 

Patients and Methods

Ethics Approval

Consistent with the tenets of the Declaration of Helsinki, this retrospective study was approved by the Ethics Committee of Hainan Eye Hospital at Zhongshan Ophthalmic Center (Sun Yat-Sen University, China) (ethics acceptance number: 2023-041-01). The study was performed after informed consent was obtained from all patients. 

Patients Examinations

Patients who visited the Hainan Eye Hospital from August 2022 to October 2023 were enrolled in this study if they met the following inclusion criteria: (1) preoperative manifest spheres of −0.50D to −10.00D, manifest cylinders of −0.25D to −5.00D; (2) stable refraction for more than one year; (3) age > 18 years. Exclusion criteria were active ocular disease, corneal opacities, suspicious keratoconus, suspicious glaucoma, cataract, uveitis, history of ocular trauma or surgery, and systemic diseases. 

All enrolled patients underwent the following clinical examinations preoperatively and at six months after surgery: uncorrected distance visual acuity (UCVA), corrected distance visual acuity (CDVA), manifest refraction, cycloplegic refraction, corneal tomography (Pentacam AXL; Oculus Optikgeräte GmbH, Wetzlar, Germany), and corneal aberrations (Pentacam AXL). Corneal aberrations were analyzed for a standardized diameter of 6.0 mm. 

Surgical Technique

All KLEx standard procedure were performed using the VisuMax femtosecond laser (Carl Zeiss Meditec AG, Jena, Germany) with parameters as follows: cut energy of 140 nJ; programed optical zone of 6.5 mm and a transition zone of 0.1 mm for astigmatism; cap thickness of 120 µm; cap diameter of 7.5 mm; incision width of 2 mm; incision position at 140°. The detail surgical procedure has been described by Taneri et al.¹³ 

EOZ Area and Decentration Measurements

EOZ was measured based on tangential curvature difference map, the comparison of preoperative and six months postoperative anterior tangential curvature map of the same patient in Pentacam. To minimize measurement errors, we ensured precise head positioning and accurate target fixation, using the pupil center as a reference point during both preoperative and postoperative examinations. Image J software V 2.1.0 was used to recognize the boundary and calculate the area of EOZ automatically, where the tangential curvature difference was zero and shown in green.^14,15 For details, (1) Image was imported and the scale was set according to the plotting scale in each image (Fig. 1A); (2) Image was adjusted using “Color Threshold,” the parameters as follows: hue pass, 102 to 233; saturation pass, 0 to 255; brightness pass, 10 to 255; thresholding method, default; threshold color, white; color space, HSB; (3) Wand tool was used to outline the boundary automatically; (4) Area was measured and Fit Ellipse function was used to measure the center(x, y), angle (θ), major (2a) and minor axes (2b) of the best fitted ellipse of each EOZ (Fig. 1B); (5) The corneal vertex coordinates (x₁, y₁) were measured. The EOZ center (x, y), and corneal vertex (x₁, y₁) were defined by Image J's automatically generated coordinate system for the imported image. Therefore, the difference of (x − x₁) was the horizontal decentered displacement “m”, (y₁ − y) was the vertical decentered displacement “n.” \(\sqrt {{{{( {x - {{x}_1}} )}}^2} + {{{( {{{y}_1} - y} )}}^2}} \ \) was the total decentered displacement. 

Figure 1.

 

Evaluating the effective optical zone after KLEx. (A) Original representation of the tangential corneal curvature difference map. (B) Image adjusted with “Color Threshold” in ImageJ software, clearly delineating the borderline of the effective optical zone. (C) The fitting ellipse and its major and minor axes in the effective optical zone, marked by a yellow line on the tangential curvature difference map.

Distance of Corneal Vertex and EOZ

For clarity and computational efficiency, two coordinate systems were defined, with the best fitted ellipse center of EOZ as the origin O(0,  0). (1) Xy-coordinate system: The x and y axes represented horizontal and vertical decentration, respectively. The corneal vertex was located at (m, n) as it is horizontally and vertically displaced by m and n from the EOZ center (Fig. 2A). (2) St-coordinate system: The s and t axes corresponded to the major and minor axes of the best-fit ellipse of EOZ, respectively (Figs. 2B, 2C). The corneal vertex coordinates (p, q) in the st-system were derived from the xy-system coordinates (m, n) through the following calculation: p = |OH| + |HE| = nsin (θ) + mcos (θ), q = |HB| − |GB| = ncos (θ) − msin (θ) (θ represents the angle of the best-fit ellipse for the EOZ, measured using ImageJ software) (Fig. 2B). The distance of corneal vertex and the border of EOZ were defined as DVO_x and DVO_y, which is the distance from corneal vertex to the best fitting ellipse of EOZ along its major and minor axes. Considering the best fitted ellipse EOZ to be elliptical in shape, with its major axis denoted by 2a and minor axis denoted by 2b, its equation is:  

\begin{eqnarray*}&& \frac{{{{s}^2}}}{{{{a}^2}}} + \frac{{{{t}^2}}}{{{{b}^2}}} = 1, | {QF} | = a\sqrt {1 - \frac{{{{q}^2}}}{{{{b}^2}}}} ,\ \ | {PE} | = b\sqrt {1 - \frac{{{{p}^2}}}{{{{a}^2}}}} ,\\ && {\textit{DVO}_x} = | {QC} | = | {QF} | - | {FC} | = a\sqrt {1 - \frac{{{{q}^2}}}{{{{b}^2}}}} - p \\ && =a\sqrt {\!1 \,{-}\, \frac{{{{{( {n\cos ( \theta ) - m\sin ( \theta )} )}}^2}}}{{{{b}^2}}}} \,{-}\, ( {n\sin ( \theta ) {+} m\cos ( \theta )} ),\\ && {\textit{DVO}_y} = | {PC} | = | {PE} | {-} | {CE} | = b\sqrt {1 {-} \frac{{{{p}^2}}}{{{{a}^2}}}} {-} q = b\\ && \times\sqrt {1 \!-\! \frac{{{{{( {n\sin ( \theta ) + m\cos ( \theta )} )}}^2}}} {{{{a}^2}}}} - ( {n\cos ( \theta ) - m\sin ( \theta )} ) \end{eqnarray*}

(a, b and θ are known variables associated with EOZ, whereas m and n are known variables associated with decentration) (Fig. 2C). 

Figure 2.

 

Illustration of the method for calculating DVO. (A) A schematic depiction of the xy-coordinate system, wherein the corneal vertex is located at point C (m, n), displaced horizontally by “m” and vertically by “n” from the origin of the EOZ. (B) The xy-coordinate system was transformed to the st-coordinate system, using the major and minor axes of the best-fit ellipse of the EOZ as s and t axes. (C) Definition of the distances from the corneal vertex to the margin of the EOZ along its major (DVO_x) and minor axes (DVO_y).

Statistical Analysis

All data were analyzed by SPSS (version 26.0; SPSS, Inc.). Data normality was tested using the Kolmogorov-Smirnov test. The Pearson test was used for correlation analysis. Piecewise regression models were used to identify the breakpoints where slope changes abruptly and to estimate level and trend of induced corneal aberrations for individuals with DVO_x and DVO_y values above and below these breakpoints. A generalized estimating equation model was used to adjust for potential correlations between two eyes. Statistically significant was defined as a P value <0.05. 

Results

Patient Characteristics

In this retrospective study, 93 eyes of 51 patients met the inclusion criteria and were enrolled in this study. All these patients had myopic astigmatism. The preoperative and surgical parameters are shown in Table 1. 

Table 1.

 

Preoperative and Surgical Parameters of the Enrolled Patients

 

Postoperative Visual and Refractive Outcomes

Six months after the surgery, the safety index (postoperative CDVA/ preoperative CDVA) was 1.15 ± 0.11, and the efficacy index (postoperative uncorrected distance visual acuity/preoperative CDVA) was 1.10 ± 0.13. The refractive outcomes were good, as summarized in Figure 3. No complications were observed during and after surgery. 

Figure 3.

 

Visual and refractive outcomes preoperative and six months after KLEx. (A) Cumulative six-month postoperative uncorrected distance visual acuity (UDVA) and preoperative CDVA. (B) Discrepancy between postoperative UDVA and preoperative CDVA in Snellen lines. (C) Postoperative shifts in CDVA measured in Snellen lines. (D) Comparison of attempted and achieved changes in SE refraction six months after surgery. (E) The accuracy of the SE to the intended target. (F) The distribution of cylinders before and six months after surgery.

EOZ, Decentration, and DVO

The postoperative EOZ area was 23.34 ± 2.86 mm², the major axis was 5.79 ± 0.43 mm, and the minor axis was 5.12 ± 0.31 mm. The angle of the fit ellipse was positively correlated with the axes of preoperative astigmatism (r = 0.920, P < 0.001). 

The decentration was 0.35 ± 0.16 mm, the absolute of X-axis of decentration was 0.21 ± 0.15 mm, the absolute of Y-axis of decentration was 0.24 ± 0.15 mm. The DVO_x was 2.68 ± 0.24 mm, and the DVO_y was 2.31 ± 0.22 mm. 

Corneal Aberrations

Preoperative corneal spherical aberration was 0.19 ± 0.08 µm, horizontal coma was 0.01 ± 0.15 µm, vertical coma was −0.04 ± 0.21 µm, coma was 0.17 ± 0.08 µm, trefoil was 0.09 ± 0.05 µm, total higher-order aberrations (HOAs) was 0.40 ± 0.11 µm, and lower-order aberrations (LOAs) was 1.83 ± 0.76 µm. After surgery, absolute values for most corneal aberrations increased significantly (spherical aberration for P = 0.001, trefoil for P = 0.005, LOAs for P = 0.009, coma, vertical coma and total HOAs for P < 0.001). Changes in horizontal coma was not statistically significant. At six months after surgery, the induced corneal spherical aberration was 0.05 ± 0.15 µm, horizontal coma was 0.06 ± 0.25 µm, vertical coma was −0.50 ± 0.25 µm, coma was 0.28 ± 0.22 µm, trefoil was 0.28 ± 0.10 µm, total HOAs was 0.41 ± 0.28 µm, and LOAs was 0.25 ± 0.91 µm. 

The correlations between the decentration, EOZ area, DVO_x, DVO_y, and the induced corneal aberrations after surgery were shown in Table 2. The Pearson correlation coefficients for horizontal coma, trefoil with DVO_x, and for trefoil and HOAs with DVO_y, were higher than those for decentration or area. The correlation between spherical aberration and DVO_x was comparable to that of the EOZ area (Table 2). Because DVO_x and DVO_y exhibit stronger correlations with specific types of corneal aberrations, DVO was used to represent the overall correlation of DVO_x and DVO_y with aberrations in Figure 4. The heatmap (Fig. 4) demonstrated that DVO uniquely correlated with all induced corneal aberrations and exhibited a stronger association with induced horizontal coma, vertical coma, total coma, and HOAs in patients with high astigmatism. The correlation of DVO with induced corneal aberrations was more pronounced in patients with moderate to high astigmatism compared to those with low astigmatism. 

Table 2.

 

Correlation Between Induced Corneal Aberrations and Decentration, EOZ Area, DVO_x and DVO_y

 

Figure 4.

 

Correlation between induced corneal aberrations and decentration, EOZ area and DVO in different degrees of astigmatism. The heatmap was colored by the absolute value of the correlation coefficient. The correlation strength increased from purple to red. HA, high astigmatism; MA, middle astigmatism; LA, low astigmatism.

Correlation and Regression Analyses

The relationship between DVO and the surgical parameters was summarized in Table 3. The DVO_x and DVO_y were inversely correlated with the correction of sphere, spherical equivalent and percent tissue altered (PTA). The DVO_x was positively correlated with the absolute value of corrected cylinders. Neither DVO_x nor DVO_y was correlated with preoperative pupillary offset (including x-axis and y-axis). Both DVO_x and DVO_y were positively correlated with area and negatively correlated with decentration. 

Table 3.

 

Correlation Between the DVO and Possible Influencing Factors

 

Subgroup Analysis

Piecewise linear regression analysis revealed estimated breakpoints at 2.316 mm for DVO_x and induced coma, 2.651 mm for total HOAs, along with a breakpoint at 2.183 mm for DVO_y and induced spherical aberration. Although no distinct breakpoints were identified for DVO_x with induced spherical aberration or DVO_y with either induced coma or total HOAs as shown in Figure 5, a clear trend was observed: the smaller the DVO_x, the higher the induced spherical aberration; the smaller the DVO_y, the higher the induced coma and total HOAs. To investigate the DVO and preoperative and postoperative characteristics and induced corneal aberrations relationship further, we performed subgroup analysis based on lower breakpoints, DVO_x < 2.316 mm (n = 9) versus DVO_x ≥ 2.316 mm (n = 84), and for DVO_y < 2.183 mm (n = 24) versus DVO_y ≥ 2.183 mm (n = 69) (Table 4, Table 5). The sphere, spherical equivalent (SE), ablation depth, PTA and decentration were significantly higher, while the EOZ area was significantly smaller in groups with DVO_x < 2.316 mm and DVO_y < 2.183 mm groups. These groups also showed significantly greater absolute values of induced corneal spherical aberration, horizontal coma, vertical coma, coma, and total HOAs. Additionally, postoperative SE was significantly lower and the absolute values of induced LOAs was significantly higher in the DVO_x <2.316 mm group. 

Figure 5.

 

Piecewise linear regression analysis of induced corneal aberrations with DVO_x and DVO_y. Piecewise linear regression analysis was conducted on induced spherical aberration (A, D), induced coma (B, E), and total HOAs (C, F) with DVO_x and DVO_y. The breakpoints were 2.316 mm and 2.651 mm for DVO_x with induced coma and total HOAs, and 2.183 mm for DVO_y with induced spherical aberration. The figure on the left showed a steep slope, whereas the figure on the right was smoothed.

Table 4.

 

Subgroup Analysis of Characteristics According to Degree of DVO_x and DVO_y

 

Table 5.

 

Subgroup Analysis of Induced Corneal Aberrations According to Degree of DVO_x and DVO_y

 

Discussion

In this study, we introduced the DVO_x and DVO_y, the distance from corneal vertex to the margin of EOZ along its major and minor axes, as new postoperative evaluation parameters that combine the effects of EOZ area and decentration and provide more reasonable information on postoperative corneal aberrations. In our study, the safety index and efficacy index were 1.15 ± 0.11 and 1.10 ± 0.13, respectively. These results indicate that KLEx is generally safe and effective for myopia and myopic astigmatism, in accordance with previous studies.^16,17 

The EOZ was defined as the region that achieves the intended correction, providing effective visual quality with minimal wavefront aberrations in the cornea.¹⁸ Additionally, the EOZ exhibited an oval shape in myopic astigmatism.¹¹ Previous studies had introduced various methods to evaluate EOZ, which were based on corneal topography, the ray-tracing approach, and HOAs.^19–21 Manual delineation of color margins on corneal topography or tomography maps was widely used in clinical and research settings due to its simplicity. According to Qian et al.,²² the EOZ was defined as the largest ring diameter for which the difference between the mean ring power and the power of the pupil center does not exceed 1.50 diopters on the corneal power map of Pentacam. Hou et al.¹⁵ confirmed the EOZ as the average value of the diameters that were manually measured from 6 different corneal meridians at 30° intervals based on the tangential curvature difference map of Pentacam HR. However, the reliability of manual assessments in previous studies may be compromised by variability between examiners. Additionally, relying solely on a one-dimensional parameter of EOZ may be inadequate for assessing the postoperative oval shaped EOZ in myopic astigmatism. Techniques based on HOAs and ray-tracing approaches provide more data but were also more complex, calculation intensive, and less commonly used. Camellin et al.²³ transferred corneal wavefront aberrations to an equivalent defocus and analyzed the diameter with a change of 0.25 D in the RMS. Using a ray-tracing program within C-scan corneal topography, both Wachler et al.²⁴ and Nepomuceno et al.²⁵ traced rays to determine the minimum aperture required for visual quality to surpass the 20/32 threshold. However, methods that impose restrictions on optical zone size may compromise the accuracy of other parameters, such as underestimating decentration. In summary, there was no standard method to evaluate EOZ, and the simplicity and accuracy of assessments were hard to be satisfied simultaneously.¹⁹ 

In this study, Image J software was used to define the EOZ as the corneal tangential curvature change of “0 D” based on the color threshold in the difference map, which refers to the borderline of the green and blue colors, and the fitted ellipse was used in measuring the oval area, center, major and minor axes of the EOZ in myopic astigmatism automatically. To our knowledge, this method was first proposed in studies, making the EOZ measurement accurate, simple, and convenient. Additionally, it offered multiple-dimensional parameters of EOZ in myopic astigmatism. 

In studies on EOZ, a negative correlation was found between induced corneal aberrations and postoperative EOZ area after KLEx.^12,26 A smaller EOZ area was associated with poorer visual quality.²⁶ However, these studies only considered the impact of EOZ size on visual quality. Generally, large decentration of EOZ was associated with greater postoperative aberrations.²⁷ But the threshold for EOZ decentration varied across different studies. Lee et al.¹⁰ considered that decentered distances under 0.335 mm could result in more favorable corneal aberrations. Supporting this, a significant increase in total HOAs, coma, and spherical aberrations was observed in ablation decentrations greater than 0.30 mm, compared to decentrations less than 0.15 mm after photorefractive keratectomy.²⁷ Although, in some cases, decentrations no greater than 0.2 mm still led to severe visual symptoms, including monocular diplopia.⁸ These inconsistencies may stem from variations in EOZ sizes across different studies, resulting in different outcomes. Specifically, higher SE corrections result in smaller EOZs, reducing tolerance to decentration and leading to increased corneal wavefront aberrations. Lee et al.¹⁰ reported similar findings, indicating that treatments with a larger optical zone could enhance tolerance to decentration. Thus relying solely on conventional measures of EOZ area or decentration was insufficient for suggesting postoperative visual quality, the effects of EOZ area and decentration should be considered simultaneously. In this study, DVO was defined as the distance from corneal vertex to the margin of EOZ, enabling a comprehensive analysis of the effects of EOZ area and decentration to induced visual quality. 

Studies showed that the postoperative EOZ is smaller than the programed optical zone in most cases.^11,19,28 Furthermore, in myopic astigmatism, the EOZ exhibited an oval shape, becoming increasingly elliptical with higher astigmatism after KLEx.¹¹ In this study, we found that the angle of fitting ellipse of EOZ showed a strong correlation with the axis of astigmatic correction. Therefore we established a coordinate axis along the major and minor axes of the fitted ellipse of EOZ and defined DVO_x and DVO_y as the distances from corneal vertex to the EOZ edge along these axes. In this study, DVO_x demonstrated a stronger negative association with horizontal coma and trefoil and DVO_y with trefoil and HOAs, when comparing their correlations to increased corneal aberrations versus decentration or EOZ area alone in all patients. The correlation coefficient between spherical aberration, vertical coma and DVO was also notably high. In high astigmatism, DVO showed more pronounced correlation with induced corneal aberrations. These findings suggested that DVO_x and DVO_y were greater parameters, offering greater insight into postoperative visual quality than decentration or EOZ area do, particularly in high astigmatism. Additionally, decentration positively correlated with horizontal coma, coma, and total HOAs, EOZ area and DVO showed negative correlations. The correlation between DVO and corneal aberrations mirrored that of EOZ area but was inverse to that of decentration. This is attributable to the opposing effects of decentration and EOZ area on DVO: increased decentration reduces DVO by bringing the corneal vertex closer to the EOZ edge, while a larger EOZ area increases DVO. 

In the present study, the associations between DVO_x, DVO_y and preoperative parameters were analyzed. DVO_x and DVO_y showed a negative relationship with corrected sphere, SE and PTA. DVO_x was positively correlated with cylinder correction. Several researchers claimed that the EOZ area was larger with lower myopia,^20,26,29 and higher cylinder correction,^3,11 resembling the relationship between DVO and refractive correction. To further explore the relationship between DVO_x, DVO_y, and visual quality, piecewise regression models identified the breakpoints of DVO_x and DVO_y in the relationship with induced corneal aberrations. When DVO_x < 2.316 mm and DVO_y < 2.183 mm, the slope of induced spherical aberration for DVO_y, as well as coma and total HOAs for DVO_x, changed abruptly. Lower DVO values corresponded to higher induced corneal aberrations, larger sphere, SE, ablation depth and PTA. These findings suggested that in patients with larger decentration, acceptable visual quality can be achieved if the EOZ was large enough or the decentration was in a favorable direction, keeping the DVO below the threshold. The increased corneal tissue ablation and laser energy required to correct high myopia may lead to greater postoperative wound healing reactions, resulting in smaller EOZ areas and DVO values.²¹ A lower postoperative SE was achieved in the DVO_x < 2.316 mm group, confirming that eyes with lower DVO tend to have a less favorable outcome after surgery. The safety index was above 1 across all subgroups, suggesting overall procedural safety. This seemingly contradicts our finding that smaller DVO correlated with poorer visual quality. However, clinical observations revealed that some patients, despite achieving normal postoperative UCVA and CDVA, experienced occasional visual disturbances such as intermittent focusing difficulties, reduced clarity, and ghosting, particularly in low-light conditions. We speculate that the bright, uniform illumination of standard acuity charts may mask these subtle visual impairments, which are more pronounced under the varying lighting conditions of daily life. Therefore, although the safety index provides valuable information, additional, more informative evaluation parameters, such as DVO, are necessary for a comprehensive assessment of KLEx. However, given the small sample size of patients with smaller DVO_x or DVO_y values, further studies are needed to confirm these findings. 

DVO, as an integrated measure of EOZ size and decentration, shows a positive correlation with EOZ size and a negative correlation with decentration. Therefore, low DVO values are expected in three situations: (1) a small postoperative EOZ, often resulting from high SE/PTA; (2) significant decentration, typically caused by poor patient fixation, surgeon inexperience, or a large preoperative kappa angle; or (3) a combination of a slightly smaller EOZ and a mild decentration (not exceeding 0.3 mm), which, although not individually extreme, can together cause decentration that exceeds the EOZ's tolerance. To optimize surgical plans for patients with predicted low DVO values, we recommend that refractive surgeons consider the following: For scenarios 1 and 2: (a) Increase the intended optical zone while preserving sufficient corneal tissue; (b) Use experienced surgeons, especially when performing surgery on patients with high corrected SE and PTA; (c) Consider alternative surgical approaches, such as eye-tracking LASIK, if there are difficulties with fixation; and (d) Carefully assess the centration during surgery. For example, repeatedly measure the kappa angle to ensure accuracy, especially when the kappa angle is large. A kappa angle greater than 0.3 mm may indicate the need for manual adjustment of centration, and even smaller kappa angles might require correction if a low DVO is predicted. For Scenario 3, where the combined effects of EOZ and decentration could previously be overlooked, potentially misattributed to visual fatigue, refractive adaptation, or psychological factors, postoperative DVO parameters now allow for identification of the issue. Therefore, in these cases, enhanced follow-up and consideration of therapeutic intervention are recommended. In conclusion, DVO supports the customization of surgical planning to improve postoperative visual quality and offers valuable insights into potential causes of suboptimal visual quality in patients with myopic astigmatism. 

This study has several limitations. First, the relationship between DVO_x, DVO_y, and visual quality needs further investigation across different SEs and astigmatism types. Second, the potential for corneal vertex shifts following refractive surgery may introduce errors on tangential curvature difference maps. Third, the observed variability in horizontal coma correlation between eyes warrants further study. Fourth, the small sample size of patients with smaller DVO_x and DVO_y values necessitates larger studies to validate the subgroup analysis findings. Finally, considering the established differences in EOZ between KLEx and other refractive surgeries, likely because of their distinct surgical principles, and the strong correlation between DVO and EOZ size, further research is warranted to explore the applicability of DVO in these other refractive procedures. 

Conclusions

DVO_x and DVO_y were crucial new evaluation parameters and provided enhanced insights into postoperative visual quality than decentration or area after KLEx. Additionally, Image J software was initially used for measuring the EOZ after keratorefractive surgery, a method that balances convenience, accuracy, and repeatability. The current results demonstrated that larger DVO in myopic astigmatism is related to smaller induced corneal aberrations, except for trefoil. Furthermore, having DVO_x more than 2.316 mm and DVO_y more than 2.183 mm could yield more favorable outcomes in terms of spherical aberration, coma, total HOAs and LOAs. 

Acknowledgments

Supported by the National Natural Science Foundation of China (82271116), Hainan Province Clinical Medical Center, Science and Technology Planning Project of Hainan Province (ZDYF2022SHFZ326, LCYX202406), and Hainan Province Clinical Medical Center. 

Author Contributions: Conception and design, XM and XZ; administrative support, XZ; data collection, XM, HD, ZY, XC, SH, AL, XW and YL; data analysis and interpretation, XM and HH; drafting of the manuscript, XM; critical revision of the manuscript, XM and XZ. All authors read and approved the final manuscript. 

Disclosure: X. Meng, None; H. Ding, None; H. He, None; Z. Yang, None; X. Chen, None; S. Hu, None; A. Li, None; X. Wang, None; Y. Luo, None; X. Zhong None