Department of Ophthalmology, School of Medicine, Hacettepe University , Ankara , Turkey .
Curr Eye Res. 2014 Jun;39(6):553-60. doi: 10.3109/02713683.2013.860992. Epub 2014 Jan 8.
To derive a mathematical expression for the healthy upper eyelid (UE) contour and to use this expression to differentiate the normal UE curve from its abnormal configuration in the setting of blepharoptosis.
The study was designed as a cross-sectional study. Fifty healthy subjects (26M/24F) and 50 patients with blepharoptosis (28M/22F) with a margin-reflex distance (MRD1) of ≤2.5 mm were recruited. A polynomial interpolation was used to approximate UE curve. The polynomial coefficients were calculated from digital eyelid images of all participants using a set of operator defined points along the UE curve. Coefficients up to the fourth-order polynomial, iris area covered by the UE, iris area covered by the lower eyelid and total iris area covered by both the upper and the lower eyelids were defined using the polynomial function and used in statistical comparisons. The t-test, Mann-Whitney U test and the Spearman's correlation test were used for statistical comparisons.
The mathematical expression derived from the data of 50 healthy subjects aged 24.1 ± 2.6 years was defined as y = 22.0915 + (-1.3213)x + 0.0318x(2 )+ (-0.0005x)(3). The fifth and the consecutive coefficients were <0.00001 in all cases and were not included in the polynomial function. None of the first fourth-order coefficients of the equation were found to be significantly different in male versus female subjects. In normal subjects, the percentage of the iris area covered by upper and lower lids was 6.46 ± 5.17% and 0.66% ± 1.62%, respectively. All coefficients and mean iris area covered by the UE were significantly different between healthy and ptotic eyelids.
The healthy and abnormal eyelid contour can be defined and differentiated using a polynomial mathematical function.
推导出健康上眼睑（UE）轮廓的数学表达式，并使用该表达式来区分上睑下垂情况下正常的 UE 曲线与其异常形态。
该研究设计为一项横断面研究。共招募了 50 名健康受试者（26 名男性/24 名女性）和 50 名上睑下垂患者（28 名男性/22 名女性），他们的睑裂反射距离（MRD1）均≤2.5mm。使用多项式插值法来近似 UE 曲线。使用一组沿 UE 曲线定义的操作者标记点，从所有参与者的数字眼睑图像中计算多项式系数。使用多项式函数定义了前四阶多项式系数、UE 覆盖的虹膜面积、下眼睑覆盖的虹膜面积以及上、下眼睑总共覆盖的虹膜面积，并在统计比较中使用这些系数。使用 t 检验、Mann-Whitney U 检验和 Spearman 相关检验进行统计比较。
从 50 名年龄为 24.1±2.6 岁的健康受试者的数据中得出的数学表达式定义为 y=22.0915+(-1.3213)x+0.0318x(2)+(-0.0005x)(3)。在所有情况下，第五和后续阶数的系数均<0.00001，因此未包含在多项式函数中。方程的前四阶系数在男性和女性受试者之间均无显著差异。在正常受试者中，上、下眼睑覆盖的虹膜面积百分比分别为 6.46%±5.17%和 0.66%±1.62%。UE 覆盖的所有系数和平均虹膜面积在健康眼睑和下垂眼睑之间均有显著差异。
可以使用多项式数学函数来定义和区分健康和异常的眼睑轮廓。
