运用正切曲率半径分析角膜前表面的Q值规律

A study of anterior corneal asphericity Q for tangential curvature

目的运用正切曲率半径探讨人眼角膜前表面360°子午线Q值规律性。方法中度近视无散光中国青年55人,采集Orbscan-Ⅱ角膜地形图上360条子午线、距角膜顶点0.3mm为间隔的点的前表面曲率值。建立以角膜顶点为原点的笛卡儿空间三维坐标,绕Z轴旋转坐标,形成新的三维空间坐标系。采集正切图的前表面曲率,代入方程376/F=4/(a12)[(a12)/4+(1+a2)y2]3/2,各解出一套二次曲线公式x2=a2z2+a1z(前表面截痕),确定各切面偏心率Q值及截痕特性,并统计比较其差异性,从各子午线的截痕的曲线特征归纳角膜前表面曲面空间形态的数学表达式。结果55人0°和180°子午线上的平均Q值分别为-0.211±0.22和-0.138±0.20,90°和270°子午线上的平均Q值分别为0.243±0.28和0.224±0.24。水平子午线的Q值趋向于-1,垂直子午线趋向于0。比较两种方法计算出来Q值的差异性,结果示在水平方向上的Q值没有差异性(P>0.05),在垂直方向上的Q值有差异性(P<0.01)。结论本研究分析了运用正切曲率半径值建立人眼前表面角膜数学模型的科学性,显示角膜前表面水平子午线方向非球面性趋向于长椭圆,垂直子午线方向非球面性趋向于扁椭圆,说明人眼角膜的非球面性特性主要由水平子午线实现。

Objective To explore a mathematical model to evaluate the asphericity of the anterior cornea in myopic adults. Methods The tangential curvature of the anterior cornea was measured every 0.3 mm from the apex in 360 meridians by an Orbscan-Ⅱ topographer. Cartesian coordinates were established with the origin at the apex of the cornea and its horizontal, vertical and optical axes were defined as axes X, Y and Z, respectively. Then every point was located. The coordinate was circumrotated to establish new coordinates to relocate the data from points in the oblique meridians. The mathematical formulas of the meridian sections of the anterior surface were analyzed as： anterior surface： 376/F=4/a1^2[a1^2/4＋（1＋a2）y^2]^3/2. Asphericity Q in 360 meridians could be calculated. This is the curvature coefficient for the corneal function of aspherieity. Results Asphericity Q in the horizontal meridian of 55 people was -0.211±0.22 and -0.138±0.20. Asphcrieity Q in the vertical meridian of 55 people was 0.243±0.28 and 0.224±0.24. The aspherieity Q in horizontal meridians was approximately -1. The aspherieity Q in vertical meridians was approximately 0. There were significant differences in aspherieity Q in the vertical meridians when the two methods were compared （P〈0.01）. There was no significant difference in asphericity Q in the horizontal meridians when the two methods were compared （P〉0.01）, which originate from the tangential curvature and axis curvature. Conclusion This paper reported a new method using tangential curvature to establish a mathematical model of the anterior cornea and an analysis of the regularity of the distribution of the asphericity Q. The curvature in the horizontal meridians is a prolate ellipse. The curvature in the vertical meridians is an oblate ellipse. The curvature of the horizontal meridians is important for anterior corneal asphericity.