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Table1 The average radius of curvature of the lenses at different distance to lens anterior surface center（略）
Table 2 Lens surface asymmetric index in different Radius of circle（LSAI）（略）
RESULTS
The red zone of the topography above showed lens anterior surface.The radii of curvature increased from the center to the periphery.The spots where the radii of curvature were the same were connected. And the lens anterior surface flattened from the center to the periphery. The lens anterior surface topograph of the radius of curvature (Figure 2).
The radii of curvature in different directions on lens anterior surface were different.Therefore the surface was imperfectly rotational symmetric.There was difference in radii of curvature from lens anterior surface center to periphery as well. The average radii of curvature of lens anterior surface increased gradually from the center to the periphery(Table 1). To determine the correlation between the radius of curvature and the position on the lens surface from which the calculation was made,curve regression between the measurements were shown in Table 1.
Lens surface asymmetric index increased from the lens surface center to the periphery.It showed that the central zone of lens anterior surface was more rotational symmetric than the peripheral zone ( Table 2) .
The horizontal and vertical meridians of lens anterior surfaces were fit to four curves of circle,ellipse,parabola and hyperbola.The r2 values of hyperbola fit were the largest either for horizontal or vertical meridians (Table 3) .
DISCUSSION
In this study we used threecoordinate measuring system to scan the lens anterior surface.The scanning points interval was 0.2mm.The coordinate data of almost one thousand six hundred points on the lens surface were obtained.The computer model of lens anterior surface was made and its topographical features were analysed.For the points obtained from lens surface were very dense,the computer model approximated to the real surface.Any difference from different areas of the lens anterior surface could be reflected,as the points were picked from all over the surface.
The cadaver eyes were kept in balanced salt solution under 4℃ and all measurements were finished within 24 hours after eyes were enucleated.Before measurements,the cornea and iris were removed with other intraocular tissues intact.Thus the crystalline lens was still suspended by lens zonules and maintained the physiological shape. So the measurement results presented the topographical features of normal crystalline lens anterior surface.Henryk et al pointed out that the lens surface was imperfectly rotational symmetric[4]. But there was no measurement data testifying the point of view.In our experiment,we picked up points in the directions of eight meridians and measured the lens anterior surface radii of curvature at the points.Two way analysis of variance showed that there was statistical difference among eight directions.But according to the topography of lens anterior surface and the measurement data,lens surface was more rotational symmetric than corneal surface.We used LSAI to demonstrate the surface rotational symmetry.The values of LSAI increased gradually.Therefore,the lens anterior surface was more symmetric at the center,and more asymmetric in the periphery.That meant the central zone of the lens anterior surface was more regular.
Our experiment results showed that the radii of curvature of every lens anterior surface increased from the center to the periphery in all directions.The differences were statistically significant.We further analyzed the correlation between the distance to the surface center and the radii of curvature at the corresponding location.Curve regressions were performed and the correlations between the variants were the third power function.The analysis demonstrated that the radii of curvature increased acceleratively.As for what kind of curve the lens anterior surface was,researchers didnt agree with each other.Brown drew the conclusion that the lens anterior surface was elliptic[1]. Howcroft believed that it was hyperbolic[2]. And the view of Koretz was that the surface was parabolic[3]. We analysed the horizontal and vertical meridians of lens anterior surface,for the lens anterior surface was imperfectly rotational symmetric.The horizontal and vertical meridians of lens anterior surface were fit to four conic sections of circle,ellipse,parabola and hyperbola.The r2 value of circle fitting was the least among all curves.It testified again the aspheric topographical feature of lens anterior surface.The r2 value increased from circle,ellipse,parabola to hyperbola.So the lens anterior surface was typically hyperbolic.
Table 3 The r2 values of fitting lens anterior surfaces to curves（略）
P<0.01 for all
Figure 1 The location of concentric circles and meridians on the lens surface（略）
Figure 2 The lens anterior surface topograph of the radius of curvature（略）
【参考文献】
1 Brown N. The change in lens curvature with age. Exp Eye Res1974;19(2):175183
2 Howcroft MJ, Park JA. Aspheric curvature for the human lens. Vision Res 1977;17:12171223
3 Koretz JF,Handelman GH,Brown NP. Analysis of human crystalline lens curvature as a function of accommodative state and age. Vision Res 1984;24(10):11411151
4 Kasprzak. New approximation for the whole profile of the human crystalline lens. Ophthalmic Physiol Opt2000;20(1):3143
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