Smith George, Atchison David A, Iskander D Robert, Jones Catherine E, Pope James M
Department of Optometry and Vision Sciences, University of Melbourne, Parkville, Victoria, Australia.
Vision Res. 2009 Oct;49(20):2442-52. doi: 10.1016/j.visres.2009.07.014. Epub 2009 Aug 6.
We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7-82years. The two-conic-surface model (7mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.
我们开发了用于拟合晶状体形状的正交最小二乘法技术，并使用自助法来确定与五个不同模型的估计顶点曲率半径和非球面度相关的不确定性。研究了三个现有模型，其中一个模型在前表面和后表面使用两个独立的二次曲线，另外两个全晶状体模型分别基于调制双曲余弦函数和广义二次曲线函数。提出了两个新模型，一个使用两个相互依赖的二次曲线，另一个是基于多项式的全晶状体模型。这些模型用于描述20个年龄在7至82岁的人晶状体的体外形状数据集。对于该数据集，双二次曲面模型（区域直径7mm）和相互依赖表面模型的优值函数明显低于其他三个模型，这表明它们很可能比其他模型能更好地描述较宽年龄范围内的人晶状体形状（尽管双二次曲面模型无法描述晶状体赤道区域）。在一些模型之间，关于曲率半径和表面非球面度的估计存在相当大的差异。在五个考虑的模型中，双曲余弦模型和新的基于多项式的全晶状体模型在确定曲率半径和表面非球面度方面具有最佳精度。大多数模型发现，随着年龄增长，前表面曲率半径显著增加，而后表面曲率半径没有显著变化。大多数模型发现非球面度分布广泛，但通常为正值且与年龄无显著相关性。由于相互依赖表面模型的优值函数低于三个全晶状体模型，因此进一步开发一个准确描述所有年龄段人晶状体完整形状的模型仍有空间。结果突出了选择合适的晶状体形状模型仍存在的持续困难。
