中文摘要：

目的探讨国人个体角膜数学模型的二次曲线方程模式及初步结果。方法建立角膜顶点为原点的笛卡儿空间三维坐标，绕z轴旋转坐标，建立新的三维空间坐标系，并明确新旧坐标的转换关系；采集ORBSCANⅡ角膜地形图系统测量的角膜顶点、0°、30°、60°、90°、120°、150°、180°、210°、240°、270°、300°、330°子午线上距角膜顶点分别为1．0、1．5、2．0、2．5、3．0、3．5、4．0、4．5mm处点的前、后表面曲率和角膜厚度值d0，代人一套方程组，解出二次曲线公式x^2=a2x^2＋a1x（前表面截痕）、^2=a1（z-d0）^2＋a2（z—d0）（后表面截痕，d0为中央角膜厚度），确定各切面截痕特性及偏心率Q值；从各子午线的截痕的曲线特征归纳角膜前、后表面曲面空间形态的数学表达式。结果角膜前、后表面各子午线截痕的数学表达式均为椭圆二次曲线轨迹。角膜前、后表面曲面符合椭球二次曲面数学表达式。结论本研究报告了二次曲线公式的人眼角膜前、后表面数学模型新表达式；本小样本正常国人角膜前后表面各子午线截痕均符合椭圆二次曲线的形态特征，角膜前、后表面的曲面空间形态均为椭球面。

英文摘要：

Objective To explore the method on the conic equation to establish the mathematical model of the adult cornea and its preliminary result. Methods The curvature of anterior cornea and of posterior cornea, the corneal thickness of the points in the distance of 1.0, 1.5, 2. 0, 2. 5, 3.0, 3.5, 4. 0, 4. 5ram away from the apex in the meridians of 0~, 30~, 60~, 90~, 120~, 150~, 180~, 210~, 240~, 270~, 300~, 330~meridians were collected from the Orbscan II topography. Cartesian coordinate was established with the origin at the apex of cornea and its horizontal, vertical and optical axes were defined as axis of X, Y and Z respectively. Then every point was located. The coordinate was circumrotated to establish a new coordinates to relocate the data of the points at the oblique meridians. The mathematical formulas of the meridians sections of the anterior and posterior surface were analyzed as： anterior surface ：x^2 = a1z^2 ＋ a2z, posterior surface ：x^2 = a1 （z -d0 ）^2 ＋ a2 （z -d0 ） （do is the corneal thickness）. And the asphericity Q could be deduced. The mathematical formulas of the anterior and the posterior cornea surface as ： anterior surface ： x^2/a^2 ＋ y^2/b^2 ＋ （z-c）^2/c^2=1, posterior surface ：x^2/a^2 ＋ y^2/b^2 ＋（z-c-d0）^2/c^2 =1.Results The mathematical models of the meridian section of the anterior and posterior surface of the cornea show conic formula as ellipse. The mathematical formulas of the anterior and the posterior cornea surface show conic surfaces. Conclusions The paper reported a new method in conic formula to establish the mathematical model of the normal cornea. The shape of the meridians sections of the anterior and posterior surface of cornea are ellipse. The shape of the anterior and the posterior corneal surface are both ellipsoid.