Characteristics of corneal Q value and its related factors in cataract patients before operation

Background: To determine corneal Q value and its related factors in cataract patients. Methods: A retrospective study was conducted in the First Affiliated Hospital of Soochow University, Suzhou, China. In all, this study enrolled 121 eligible eyes of 121 cataract patients. The corneal Q values of anterior and posterior surfaces were measured in central 3.0, 4.0, 5.0 and 6.0 mm zone using the Sirius System. Age and gender were recorded. Cataract was diagnosed using slit-lamp examination. Results: The average Q value of the anterior surface in 3.0, 4.0, 5.0 and 6.0 mm zone were 0.09±0.42, 0.02±0.27, -0.04±0.20 and -0.11±0.17, respectively. The average Q value of the posterior surface in 3.0, 4.0, 5.0 and 6.0 mm zone were 0.02±0.81, -0.28±0.56, -0.37±0.43, -0.41±0.30, respectively. The Q values of the anterior surface at 6.0 mm zone and the posterior surface in 3.0, 4.0, 5.0 and 6.0 mm zone were statistically significant (p<0.05) across different age groups. The Q values of the posterior surfaces in 3.0, 4.0, 5.0 and 6.0 mm zone were statistically significant (p<0.05) between the male and the female groups. The Q values of the anterior surface in the 6.0 mm zone were positively correlated with Z40 cornea (Pearson correlation =0.796, p<0.001), Z40 CF (Pearson correlation =0.840, p<0.001), Z33,-3 CF (Pearson correlation =0.236, p=0.009) and total corneal higher-order aberrations (HOAs) (Pearson correlation =0.305, p<0.001); While the Q values of the posterior surface in the 6.0 mm zone were negatively correlated with Z31,-1 cornea (Pearson correlation =-0.212, p=0.019), Z33,-3


Background
The cornea is the most significant refractive component in the eye, contributing a major share of around 70% of the refractive power. Previous researches demonstrated that the cornea could be described as a quadric surface having asphericity on the surface [1][2][3].
The radial variation from the center towards the periphery of the quadric surface determines the Q value, the quantified aspherical degree indicator. The Q value, being the crucial parameter of the mathematical cornea model, is reflective of the shape of the cornea and its optical properties [4,5], which includes the aberration distribution, the spherical aberration, the refractive power, and others. Today, the corneal Q value along with its distribution properties have garnered the focus of attention of the relevant studies, besides the manner in which the optical properties are impacted in the eye [6][7][8][9].
Alongside the popularization and application of aberration theory in ophthalmology, the influence of corneal Q values on spherical aberrations following corneal refractive surgery and intraocular refractive surgery is garnering an increasing amount of attention from ophthalmologists. Corneal Q values provide an essential reference for personalized corneal refractive surgery and aspheric intraocular lens (IOL) implantation. Although corneal Q values in elderly populations are essential factors in the design of IOL procedures and for the treatment of refractive errors [10,11], few formal studies have been conducted to evaluate its relevance for cataract patients.
The Q values of different corneal surface areas are disparate, and a single value does not accurately reflect the shape of the cornea [12]. It is crucial to examine the Q values of different ranges to improve the visual acuity of cataract patients following aspheric IOL implantation. Many different factors affect corneal Q values. Previous studies have focused on the relationships between Q values and age, refractive errors [13],refractive statuses [14], and spherical aberrations [15], while studies concerning Q values and other high-order aberrations (HOAs) of the cornea are limited at present. This study aims to determine the characteristics of the corneal Q value and its correlations with corneal HOAs in cataract patients, which provide a theoretical basis for treating the errors in refraction and designing IOLs.

Measurement
Corneal topography measurement was repeated three times for each of 121 patients' eye using Sirius (Sirius, CSO Inc, Florence, Italy) system. Data were analyzed for the full topographic map measurements in central 3.0, 4.0, 5.0 and 6.0 mm zone. The same qualified doctors examined the subjects, the focus was on eliminating examiner bias.
During analysis, the corneal reflex rings were clear and the tear film rupture was not disturbed. The Q values in central 3.0, 4.0, 5.0 and 6.0 mm zone were calculated by the Sirius system. The distribution of the Q values of both the anterior and posterior surfaces with large diameters (6.0 mm zone), the analysis of the correlation between the HOAs and Q values, along with the mean corneal Q values (mean±SD) having varying diameters on the anterior and posterior surfaces were included in the results. The HOAs in pupillary areas of 6.0 mm analyzed included the root mean square (RMS) values of primary spherical aberration (Z4 0 ), primary coma aberration (Z3 1,-1 ), primary trefoil aberration (Z3 3,-3 ) of the total cornea, corneal front surface, and corneal back surface and total corneal HOAs. The statistical analysis was conducted using high centrality, high repeatability, and high quality aberration values. A classification of the device signal according to the composite index of the keratoscopic and Scheimpflug images with fixation states, described high quality. The high-quality images with the coverage of Scheimpflug tomographic images over 98% were used for analysis. The anterior and posterior difference of elevation <5 mm and the difference of the tangential anterior corneal curvature <0.5D explained high repeatability. A percentage based signal of the device, according to a keratoscopic image of >90% described high centrality. However, grouping was ignored by the evaluators.

Statistical analysis
The SPSS software (version 25.0) was used for data analyses. The average Q value (mean ±SD) for varying diameters was determined using descriptive statistics. Variance analysis (One-way ANOVA) was used to compare the Q values for different diameters. Kruskal-Wallis H test was used to compare the Q values for three age groups. T-test was performed to compare Q values between the male and female groups. Pearson's correlation was used to explore the relationship between corneal Q values and HOAs. We considered a p-value of <0.05 to be statistically significant.

Subject's age distribution
In a range of 38-92 years, 67.44±10.66 years was the average age. 5.79% of the subjects belonged to the group aged 38 to 50 years, 51.24% belonged to the 50-70 years group, while 42.97% of the study population was accounted for by persons aged 70 years and above. In this study around 94.21% of the population was composed of persons aged 50 years and above, the period which was considered to be most prone to develop senile cataract. Corneal Q values for different age groups Figure 3 and Table 2 summarize the distribution of the Q values at various stages of age.

Corneal Q values
The study participants were divided into three groups according to their ages: 38-49 years old; 50-69 years old; and ≥70 years old. The one-way ANOVA analysis results indicate that anterior corneal surface Q values of the ≥70 years old group (in 6.0 mm zone) were significantly higher than those of the 38-49 years old group; posterior corneal surface Q values (in 4.0 mm and 5.0mm zone) of the ≥70 years old group were significantly lower than those of the 50-69 years old group; and the posterior corneal surface Q values (in 6.0mm zone) of the ≥70 years old group were significantly lower than those of the 38-49 years old and 50-69 years old groups. It was quite evident that with an increasing age the Q value of the anterior surface of the cornea also increased. Nevertheless, as indicated in Figure 3, with an increase in the age, the posterior surface Q value seemed to decrease.

Corneal Q values for male and female groups
The mean Q values (mean±SD) at varying diameters for both the female and male groups were determined as indicated in Table 3 However, no correlation was found to exist between the Q values of the anterior surface (in 6.0 mm zone) and total corneal primary coma aberration (Z3 1,-1 cornea); total corneal primary trefoil aberration (Z3 3,-3 cornea); primary coma aberration of the corneal front surface (Z3 1,-1 CF); primary coma aberration of the corneal back surface (Z3 1,-1 CB); primary trefoil aberration of the corneal back surface (Z3 3,-3 CB); or primary spherical aberration of the corneal back surface (Z4 0 CB). Similarly, no significant correlation was found to exist between the Q values of the posterior surface (in 6.0 mm zone) and total corneal primary spherical aberration (Z4 0 cornea); primary coma aberration of the corneal front surface (Z3 1,-1 CF); primary spherical aberration of the corneal front surface (Z4 0 CF); or primary trefoil aberration of the corneal back surface (Z3 3,-3 CB) (Table S1).

Discussion
The cornea is the first surface of light gateway to the retina along with the tear film, representing two-thirds of the dioptric power of the human eye, making it the most important refractive element [16].The anterior surface of the cornea can be mathematically described into conic sections. The parameter most used to describe how the curvature of a parabola differs from the curve of a circle is the asphericity (Q value).
The Q value characterizes the change on cornea curvature from the center to the periphery. When Q = 0, it represents a circle, but if -1<Q<0 or Q>0, it represents a prolate or oblate ellipse, respectively. If Q = -1, the curve defines a parabola while a hyperbole is defined when Q<-1 [16,17]. The literature reported negative Q values ranging between -0.01 and -0.80 for a normal cornea, which indicates that cornea usually flattens toward the periphery and can be better fitted to a prolate ellipse shape [12,18].  [21].This substantial difference with our study and the earlier studies could have been possible due to the impact of various factors like the subject age and race, sample sizes, and the differences in testing equipment.
The anterior and posterior corneal surfaces were separately calibrated using the Sirius system in the study. The same instrument had been used by various other studies as we had used [22][23][24][25][26][27], while some other studies had utilized varying methods, like: Pentacam HR system [9], TMS-I mapping system [28]and The EyeSys corneal topography [6]. Sirius Scheimpflug-Placido tomographers are routinely employed in research and clinical use, and preceding studies that measured anterior segment parameters have demonstrated the system's high degree of repeatability and reproducibility [29,30]. The system's repeatability is akin to that reported for the Pentacam tomographers [31]. Datapoints such as simulated K, corneal power, the distance between the corneal endothelia, and the Q value are considered to be interchangeable between these two instruments [32].
Regarding the study of Q values across different ages, Dubbleman et al. [33]investigated corneal asphericity in 114 cases (aged between 18-65 years old), finding that the Q values increased with age. Age-related changes in corneal thickness and asphericity are believed to be due to the increase in the number of patients with corneal arcus senilis with age.
Guirao et al. [34]examined changes in corneal curvature across three groups, namely young people (between 20-30 years old), middle-aged people (between 40-50 years old) and elderly people (between 60-70 years old), finding that corneal asphericity progressed and became increasingly circular (from oblate to round) with age. In our study, the average age of the subjects comprising of 94.21% in the age group above 50 years was 67.44 years, while the corneal Q values of the anterior surface with a zone under 6.0 mm was found to be much higher in the group with an age above 70 years than in the group ranging from 38-49 years, which is consistent with the previous study conducted by A correlation between sex and the Q values was aptly established in our study. Carney [35], Scholz [36], Dubbelman [33] and Chan [8] arrived at similar conclusions. For the anterior surface in our study the female group was found to have a smaller Q value than the male group. However, for the posterior surface the opposite was found to be true along with certain difference in the statistics. Sex was found to be an irrelevant factor for the corneal Q values in the studies conducted by Fuller [6] and Cheung [19], which may be attributed to the difference in the subject's race and different measuring instruments.
Corneal aspheric properties influence visual acuity. Wavefront aberration refers to the optical path difference between wavefront and ideal wavefront (from the perspective of wave optics) at each point on the imaging plane of the eye. The most relevant aberrations are total HOAs, spherical aberration, coma aberration, and trefoil aberration, which are the primary causes of glare, halos, and decreased nighttime vision in patients following cataract surgery or corneal refractive surgery [37,38].Different corneal shapes produce different degrees of spherical aberration. The corneal Q value is a morphological parameter representing the geometric shape of the cornea, whereas corneal aberration (e.g., spherical aberration) describes the optical quality of the cornea and is representative of the degree of corneal optical error. However, few studies have investigated the correlation between corneal aspheric morphology and HOAs. Philip et al. [39]examined corneal morphology and its influence on HOAs using a theoretical model. It was found that fourth-order aberration (especially spherical aberration) varied alongside corneal asphericity. Kiely et al. [40] studied corneal morphology and its influence on corneal aberration, finding that the degree of corneal aberration varied alongside corneal asphericity and the radius of the corneal apex curvature. Calossi [17] analyzed the relationship between asphericity and the degree of spherical aberration of the anterior corneal surface. It was found that, as long as the corneal refractive index and the pupil diameter remained constant, flatter corneal surfaces from the center to the periphery (negative Q value) equated to lesser degrees of spherical aberration, and steeper corneal surfaces from the center to the periphery (positive Q value) equated to greater degrees of spherical aberration. Our results indicated that both the anterior and posterior surfaces of the cornea correlate significantly with the degree of spherical aberration of the corresponding ranges. That is to say that, alongside higher Q values, the degree of spherical aberration increases accordingly, which is consistent with previous studies [17.39,40]. Furthermore, this finding reflects the morphological characteristics of the cornea in optical imaging.
Coma and trefoil were both third-order aberrations, which reflected the asymmetry of refractive characteristics of the eye and were the representation of irregularity, inclination, eccentricity, and other symmetry of the eye. The depth of the focus gets enhanced by the aberration of the vertical coma [41].Theoretically, coma is correctable, however, technically, it is much difficult to conduct a surgical correction under the circumstances. In certain cases Trefoil becomes unmanageable and surgery may worsen the situation. Related studies have indicated that spherical and coma aberration is associated with decreased visual acuity and contrast sensitivity in healthy people [42]. In this study, a positive correlation was found to exist between Q values and the degree of trefoil aberration of the front corneal surface, while a negative correlation exists between Q values and total coma aberration, coma aberration of the corneal back surface, total trefoil aberration, and trefoil aberration of the front corneal surface. These findings suggest that preoperative evaluation of corneal Q values before cataract surgery is hugely significant to the postoperative recovery of visual function and enhancing patients' visual acuity.
The primary feature of this study is that the corneal Q values for 3.0, 4.0, 5.0 and 6.0 mm zone were tallied separately. It was found that the Q value relates to aperture size and that the average values vary statistically across different diameters. This conclusion is hugely significant for product design relating to corneal shapes (e.g., contact lenses), and designers should adjust their design parameters according to different diameters.
Meanwhile, according to the mathematical model, the Q value affects the degree of aberration and refractive power distribution of the cornea, thus providing a reference for the design of products related to corneal optical properties and parameters, such as IOLs.
The Q values of the posterior corneal surface were also examined in this study. Although In conclusion, the purpose of this research was to study the factors related to the corneal Q values in cataract patients. We found that there were great individual differences in Q values. The Q values were found to have a correlation with HOAs, sex, and age. Further studies with regards to the optical properties of the human eye shall be able to access the results as ready reference, besides they could be helpful in improving the designing of the

Declarations
Ethics approval and consent to participate The study was performed in accordance with the Declaration of Helsinki and approved by the ethics committee board of the First Affiliated Hospital of Soochow University. The patients provided written informed consent for their participation in the study. A copy of the written consent is available for review by the editor of this journal.

Consent for publication
Written informed consent was obtained for publication of this manuscript and any accompanying images. A copy of the written consent is available for review by the editor of this journal.

Availability of data and materials
All data have been shared in the Figures and Tables.

Competing interests
All authors declare that they have no competing interests.  Note: "*" means compared with 3.0 mm diameter p < 0.05; "**" means compared with 4.0 mm diameter p < 0.05; "***" means compared with 5.0 mm diameter p < 0.05.  Figure 1 Corneal Q value distribution of the anterior surface.