关于人眼视力发展的非线性成长率理论

目的使用非线性成长率理论分析人眼视力发展规律。方法使用高斯光学及成像方程推导出两个参数：屈光状态改变率（M）及眼轴成长率（N），用以预测MOS（初始近视）、年龄（A^＊）及其后视力的发展情况。结果当有效焦距F=（21-22）、密码M=（2．67—2．9）（D／mm）时，此计算值符合实验平均值（2．7）。当年龄A^＊=（3，6）岁的屈光度变化已知时，我们计算其MOS预测年龄为A^＊=（7．3，21．8）岁（在不同条件下）。此值反比于M值在A=6及A=3的比值或N=N—N^＊，即非正视态及正视态的眼轴成长率之差。本理论也可用来预测在年龄A=25时的近视度，分别为D=-14及-0．49的上述两例情况，同时也能分析Lain等人的测量值（由出生到青年期的视力发展情况）。结论本理论可预测MOS、其后发展情况及其符合实验值（M）。使用成长率差值（dN）比使用L/rl比值能更准确地预测MOS。

A nonlinear growth rate theory for human eye vision development

Objective A nonlinear growth rate theory for the analysis of vision development in human eye.Methods Using gaussian optics and image equation, we derive for mulas for refractive error change rate (M=dD/dL) and axial growth rate (N=dL/dA), where dL and dA are the axial and age change. These two rates may be used to predict the myopia onset (MOS) age (A~*) and D at a predicted period under a linear approximation.Results For effective focal length F = (21-22) mm, we calculated D values and rates N at age A = (3,6), we predict A~* = (7.3, 21.8) years for D = (+3.5, +1.0) and D = (+2.5, 2.0), respectively. The A~* is shown to be inverse proportionally to the ratio of the M value at age 6 and 3, or dN=N-N~*, the difference of the axial growth rate of the ametropic and emmetropic state. We also predict the repiatction error at age 25 to be about (-14, -0.4) diopter for above example. Our calculated data may be used to analyze the measured refraction data of Lam et al for infant to youth.Conclusion It is possible to predict MOS and vision development using a growth rate theory under certain assumptions. Our calculated value of M is consistent with measured data. A better predictor for MOS shall be based on dN=N-N~* rather than the ratio of L/r1, or N alone.[