论文部分内容阅读
目的本文试以数学方法归纳分析角膜地形图内的光学数据,初步推算验证正常人眼角膜的椭球形态的数学表达。方法对每位研究对象进行OrbscanⅡ角膜地形图系统检测,采集角膜顶点和0°、30°、60°、90°、120°、150°、180°、210°、240°、270°、300°、330°子午线上距角膜顶点分别为1.5、2.5、3.5、4.5mm处点的角膜前表面、后表面的曲率半径及角膜厚度的数据,用三维坐标和椭圆二次曲线方程分别推算角膜前、后表面的空间数学表达式及其形状系数;并验证由较平坦子午线到较陡峭子午线角膜曲率分布Toric光学面特性。结果本研究样本显示的正常人角膜空间形态的数学表达式为,角膜前表面的椭球方程式x2/8.0532+y2/7.9732+(z-8.226)2/8.2262=1,角膜后表面椭球方程式x2/6.8362+y2/6.7452+(z-8.080)2/7.5272=1;角膜前表面形状系数陡峭子午线e2=1-(15.61z-y2)/z2,平坦子午线e2=1-(15.61z-x2)/z2,角膜后表面形状系数陡峭子午线e2=1-[12.254(z-0.553)-y2]/(z-0.553)2,平坦子午线e2=1-[12.254(z-0.553)-x2]/(z-0.553)2;斜轴子午线角膜曲率分布符合正弦规律F′=Fa+(Fb-Fa).Sin2α。结论正常人角膜前后表面的空间形态基本符合椭球面,而且角膜曲率具有从平坦子午线向陡峭子午线正弦相关的变化规律。(中华眼科杂志,2006,42992-997)
Objective This paper attempts to mathematical analysis of the optical data within the corneal topography, preliminary projections verify the normal human cornea oval spherical morphology of the mathematical expression. Methods The Orbscan Ⅱ corneal topography system was detected in each subject. The corneal vertexes were collected at 0 °, 30 °, 60 °, 90 °, 120 °, 150 °, 180 °, 210 °, 240 °, 270 °, 300 ° , 330 ° meridian from the corneal apex at 1.5,2.5,3.5,4.5mm point of the anterior corneal surface, the radius of curvature of the posterior surface and corneal thickness data, respectively, using three-dimensional coordinates and elliptic conic equations were estimated corneal anterior, The mathematical expression of the back surface and the shape coefficient of the surface; and verify the Toric optical characteristics of the corneal curvature distribution from the relatively flat meridian to the steeper meridian. Results The mathematical expression of normal human corneal spatial morphology showed in this study is that the ellipsoid equation x2 / 8.0532 + y2 / 7.9732 + (z-8.226) 2 / 8.2262 = 1 of the anterior corneal surface, the posterior corneal surface ellipsoid equation x2 /6.8362+y2/6.7452+(z-8.080)2/7.5272=1; steep meridian e2 = 1- (15.61z-y2) / z2, e2 = 1- (15.61z-x2) / z2, corneal topography coefficient steep meridian e2 = 1- [12.254 (z-0.553) -y2] / (z- 0.553) 2, flat meridian e2 = 1- [12.254 (z- 0.553) -x2] / z-0.553) 2; The skew axis meridian corneal curvature distribution accord with the sine law F ’= Fa + (Fb-Fa) .Sin2α. Conclusions The spatial morphology of corneal anterior and posterior surface of normal people is basically consistent with ellipsoid, and the corneal curvature has a sinusoidal correlation with the change from flat meridian to steep meridian. (Chinese Journal of Ophthalmology, 2006,42992-997)