不同屈光状态儿童角膜前表面非球面特性分析及建模

目的 运用正切曲率半径推算儿童角膜前表面Q值并分析水平区间Q值规律及不同屈光状态与Q值的关系。通过拟合计算垂直方向Q值，得出360条半子午线范围的Q值，完成全角膜前表面数学模型的建立。方法 横断面研究。通过Orbscan Ⅱ角膜地形图仪得到84例儿童右眼（12例近视、45例正视、27例远视）360条半子午线Ft值，运用线性回归方程计算各半子午线Q值，分析角膜鼻、颞侧区间Q值分布规律（配对t检验）及屈光状态对Q值的影响（单因素方差分析）。运用Matlab R2009b（矩阵实验室Matrix Laboratory）系统拟合计算其中62例儿童右眼数据（10例近视、25例正视、27例远视）得到360条半子午线Q值，并分析角膜360条半子午线Q值分布规律（配对t检验）。结果 ①进行计算的所有半子午线所得到的决定系数R2均大于或等于0.5。84眼鼻侧、颞侧区间Q值均在-1与0之间，平均值分别为：-0.42±0.16，-0.23±0.08，二者差异有统计学意义（t=-9.527，P<0.05）。鼻侧、颞侧r0平均值分别为：7.85±0.24，7.83±0.24，二者差异有统计学意义（t=3.213，P<0.05）。鼻侧和颞侧半子午线Q值与r0不存在相关性（鼻侧r=-0.077，P=0.487；颞侧r=0.001，P=0.992）。②近视组和正视组、近视组和远视组鼻侧Q平均值差异有统计学意义（F=3.907，P<0.05），颞侧各组之间均无统计学意义（F=0.204，P＞0.05）。③经过MATLAB系统进行拟合计算得到的曲线决定系数R2均大于0.9。④对48只眼进行垂直方向Q值拟合计算。拟合前后水平鼻侧方向半子午线Q值平均值分别为-0.45±0.16，-0.45±0.16，颞侧分别为-0.21±0.08，-0.20±0.10，拟合前后水平鼻、颞侧区间平均Q值t检验差异无统计学意义（鼻侧t=2.009，P>0.05；颞侧t=2.009，P>0.05）。拟合后垂直方向上方、下方半子午线Q值平均值为-0.24±0.10、-0.17±0.08。结论 ①采用线性回归以正切曲率半径推算Q值的方法结果稳定可靠。研究对象角膜前表面趋向长椭圆形（prolate），鼻侧较颞侧区间显著，水平较垂直区间显著。屈光不正对Q值影响较小。②将360条半子午线Q值通过拟合曲线计算，Q值呈双峰状分布，峰顶分别为上方及下方垂直半子午线。③拟合计算后水平方向半子午线的非球面性均较垂直方向显著，垂直方向Q值向0靠拢。④采用MATLAB系统的曲线拟合计算全角膜Q值的方法证明是稳定可靠的。解决了垂直方向半子午线Q值的计算问题，使建立全角膜前表面数字模型成为现实。

An analysis of corneal asphericity and modeling of the anterior corneal surface in children with different refractive states

Objective To calculate the Q-value of the anterior corneal surface of children by using the tangential radius of curvature； to analyze the distribution of horizontal Q-values and the relationship between Q-value and different refractions. The vertical Q-values were calculated by curve fitting， and the Q-values of the 360° semi-meridians were then obtained， to complete the mathematical model of the anterior corneal surface. Methods The Ft-values of the 360 semi-meridians from the 84 right eyes of the children （12 cases of myopia， 45 cases of hyperopia， and 27 cases of emmetropia） were calculated by Orbscan Ⅱ topography using a linear regression equation to calculate the Q-values of the semi-meridians and analyze the nasal and temporal distribution of the Q-values and the effect of refractive state. MATLAB R2009b （Matrix Laboratory） was used for curve fitting calculations of the right eye data from 62 children （10 myopes， 25 hyperopes and 27 emmetropes） to obtain Q-values of 360 semi-meridians and to analyze the distribution of the Q-values. Results ①All of the coefficients of determination （R2） were greater than or equal to 0.5. The Q-values of the nasal and temporal distributions were between 1 and 0. The mean Q-values of the nasal distribution of 84 right eyes was -0.42±0.16， and the temporal distribution was -0.23±0.08. The difference was statistically significant （t=-9.527， P<0.05）. The mean r0 of the nasal distribution of 84 right eyes was 7.85±0.24 and the temporal distribution was 7.83±0.24. The difference was statistically significant （t=3.213， P<0.05）. No statistical correlation was found between Q-values and r0 in this study （nasal distribution r=-0.077， P=0.487， temporal distribution r=0.001， P=0.992）. ②The Q values of a one-way ANOVA analysis of emmetropes， myopes and hyperopes showed that the differences between the nasal corneas of myopes and emmetropes and of myopes and hyperopes were statistically significant （P<0.05）. No significant difference was found between the emmetropes and hyperopes （P>0.05）. The differences between the temporal distributions were not statistically significant （P>0.05）. ③The coefficient of determination （R2） of the curve fitting by MATLAB was greater than 0.9.④Fitting the vertical Q-values of the 48 eyes： the mean Q-values of the nasal distribution of the semi-meridian before and after curve fitting were -0.45±0.16 and -0.45±0.16 and the temporal distributions were -0.21±0.08 and -0.20±0.10. There were no significant differences before and after curve fittings （nasal distribution， t=2.009， P>0.05， temporal distribution， t=2.009， P>0.05）. The mean vertical Q-values of the superior and inferior distributions after curve fitting were -0.24±0.10 and -0.17±0.08. Conclusion ①The method of using linear regression to calculate the Q-value of the anterior corneal surface by the tangent radius of curvature proved to be stable and reliable. Corneal asphericity was represented by a prolate ellipse and a trend toward a more prolate Q-value was found in the nasal and horizontal distributions. The Q-value had a weak correlation to ametropia. ?②The distribution of 360 semi-meridians of the Q-value calculated from the curve fits were in the form of a double hump and the two peaks were above and below the vertical semi-meridinans. ③After curve fitting calculations， the horizontal semi-meridians had more asphericity than the vertical meridians， which were more round.④The method using the Curve Fitting Toolbox of the MATLAB System to fit the Q-values proved to be stable and reliable. It solves the problem of calculating Q-values， and enables the creation of a digital model of the corneal anterior surface to become a reality