正视儿童角膜前表面数学模型的建立及非球面的评价  

A mathematical model of the corneal anterior surface of emmetropic children and an evaluation of asphericity

作　　者：朱乐如[1] 王波[2] 施明光[1] 

机构地区：[1]温州医学院附属第二医院眼科,温州浙江325000 [2]南京财经大学,江苏南京210046

出　　处：《眼视光学杂志》2009年第2期123-128,133,共7页Chinese Journal of Optometry & Ophthalmology

基　　金：国家自然科学基金项目(30471858)

摘　　要：目的通过二次曲线方程来描述正视儿童角膜前表面的二维空间形态,根据各子午线非球面性的变化规律推导出其三维形态的数学表达式及非球面性变化规律表达式。方法随机选取在本院进行常规体检的正常儿童77例(77只右眼),分别用Humphrey ALTAS和Orbscan-Ⅱ角膜地形图系统进行测量,并记录前表面轴向图36条子午线(从0°开始,每间隔10°取子午线至350°)上4.5mm内所有点的曲率值。通过建立三维座标系、座标轴旋转、解方程组,求得各个子午线上的二次曲线表达式及Q值。根据36条子午线Q值,求得最适二次曲面方程式及Q值变化规律的函数表达式。结果①角膜前表面各截痕的Q值介于-1～0.5之间。配对t检验显示,两种仪器各截痕Q差值在0°、10°、20°、30°、170°、180°、190°、200°、210°、220°、350°子午线差异无统计学意义。②角膜前表面的二次曲面方程为:x2/9.6982+y2/8.74912+(z-11.5124)2/11.51242=1(Orbscan-Ⅱ);x2/9.94062+y2/9.09022+(z-11.8522)211.85222=1(Humphrey ALTAS)。③角膜前表面Q值变化规律为:Q=-1+1/0.365sin12θ+1.351(Orbscan-Ⅱ);Q=-1+1/0.296sin2θ+1.344(Humphrey ALTAS)。结论①正视儿童角膜前表面各截痕形态均为椭圆形,在水平、近水平方向上为长椭圆形。②正视儿童角膜前表面为长轴在Z轴、短轴在Y轴的长椭球面。③各截痕的Q值随角度变化呈正弦规律。Objective To describe the shape of the planar space of the corneal anterior surface of children with emmetropia by using a conic section, and then to plot the changes in asphericity on 36 meridians to deduce the formulae of the three-dimensional shape of the corneal anterior surface. Methods Seventy-seven right eyes of 77 children were measured with both the Humphrey ALTAS and Orbscan-Ⅱ. The curvature of all the points on 36 meridians （per 10° from 0° to 350°）, limited to a 4.5 mm zone, was collected. A coordinate was established with the horizontal, vertical and optical axis defined as the X, Y and Z axis. A circumrotation was then made. The formulae were calculated and the Q of 36 meridians, deduced from the formulae of the anterior surface, identified the shift rule of asphericity. Results The Q of the anterior surface was between -1～0.5. There was no significant difference in Q between the two instruments for the following meridians： 0°, 10°, 20°, 30°, 170°, 180°, 190°, 200°, 210°, 220° and 350°. The formulae of the anterior surface were：x^2/9.698^2＋y^2/8.7491^2＋（z-11.5124）^2/11.5124^2=1（Orbscan-Ⅱ）;x^2/9.9406^2＋y^2/9.0902^2＋（z-11.8522）^2/11.8522^2=1（Humphrey ALTAS）.The change in Q followed the meridians：Q=-1＋1/-0.365sin^2θ＋1.351（Orbscan-Ⅱ）;Q=-1＋1/0.296sin^2θ＋1.344（Humphrey ALTAS）. Conclusion The formulae of each meridian of the corneal anterior surface are ellipses, and the asphericity of the horizontal or near-horizontal meridians are prolate ellipses. The formulae of the anterior surface are ellipsoids, with the major axis on the Z axis and the short axis on the Y axis.The Q is related to the sine of the angles.

关 键 词：角膜地形图 角膜 前表面 儿童 数字模型 

分 类 号：R772[医药卫生—眼科] R779.7[医药卫生—临床医学]