近视成年国人角膜的形态及数学模型研究

Measurement of corneal shape and its use in mathematical models of adult Chinese myopic eyes

目的 研究近视成年国人角膜的前、后表面形态并建立其数学模型.方法 数字模拟研究.用OrbscanⅡZ采集494只近视眼角膜前、后表面的地形图数据,计算得到角膜前、后表面各特定点三维坐标值（X值、Y值、Z值）并且导入统计学软件SAS 8.01,用非线性回归法拟合判断单眼角膜前、后表面形态并分析其相关因素.以1.00 D为梯度将角膜前表面屈光力为40.00～47.00 D的眼分为7组,随机选择每一组90％的眼,以非线性回归法拟合每一组角膜前、后表面的通用数学方程;根据通用数学方程预测每一组剩余10％的眼的角膜前、后表面各特定点的Z轴坐标值,将预测和实测的各Z轴坐标值用SPSS软件进行相关性检验,判断拟合方程的质量.结果 近视成年国人角膜前表面均为椭球面,后表面93.9％为椭球面,5.1％为椭圆抛物面,1.0％为双叶双曲面.计算得到7组角膜前、后表面共14个数学模型.角膜前、后表面所有Z轴坐标的预测值与实测值的相关系数r均＞0.99（P＜0.01）.结论 近视成年国人角膜的前表面和绝大多数后表面均为椭球面；运用合理的分组和非线性回归拟合,可建立较为精确的近视成年国人角膜的数学模型.

Objective To investigate the shapes of corneal anterior and posterior surfaces and use these shapes in mathematical models of the myopic eyes of adult Chinese.Methods This was a numerical Simulation.Four hundred ninety-four corneal topographies of myopic patients were measured with an Orbscan Ⅱ Z.The specified points of the X-,Y-,Z-axis coordinate values of the anterior and posterior corneal surfaces were calculated from the Orbscan Ⅱ Z data and imported for modeling using SAS 8.01.Ninety percents of the eyes were randomly selected from each group for modeling.The anterior and posterior corneal surface shapes were fitted using SAS 8.01 statistical software by a non-linear regression method using the relevant parameters of the corneal surface data.Front corneal refractive powers from 40.00 D to 47.00 D were divided into 7 groups based on 1.00 D intervals.The Z coordinate values of the remaining 10% of the eyes from each group were predicted based on the mathematical models.The predicted results and the actual values were compared using correlations.Results An ellipsoid was found to fit all corneal anterior surfaces and 93.9% of the posterior surfaces of myopic adults.The corneal posterior surfaces were parabaloid in 5.1% of the cases and were hyperbolic in 1.0%.Fourteen mathematical models were demonstrated to fit the anterior and posterior corneal surface data.The correlation coefficient for the Z-axis coordinates of the predicted results and the actual values was r〉0.99 （P〈0.01）.Conclusion An ellipsoid is found to fit all corneal anterior surfaces and a majority of the posterior surfaces in myopic adults.Precise anterior and posterior corneal surface mathematical models could be established by reasonable groupings and a non-linear regression method.