Liu Lei, Marsh-Tootle Wendy, Harb Elise N, Hou Wei, Zhang Qinghua, Anderson Heather A, Norton Thomas T, Weise Katherine K, Gwiazda Jane E, Hyman Leslie
School of Optometry, University of Alabama at Birmingham, Birmingham, USA.
School of Optometry, University of California at Berkeley, Berkeley, USA.
Ophthalmic Physiol Opt. 2016 Nov;36(6):615-631. doi: 10.1111/opo.12321.
High-quality optical coherence tomography (OCT) macular scans make it possible to distinguish a range of normal and diseased states by characterising foveal pit shape. Existing mathematical models lack the flexibility to capture all known pit variations and thus characterise the pit with limited accuracy. This study aimed to develop a new model that provides a more robust characterisation of individual foveal pit variations.
A Sloped Piecemeal Gaussian (SPG) model, consisting of a linear combination of a tilted line and a piecemeal Gaussian function (two halves of a Gaussian connected by a separate straight line), was developed to fit retinal thickness data with the flexibility to characterise different degrees of pit asymmetry and pit bottom flatness. It fitted the raw pit data between the two rims of the fovea to improve accuracy. The model was tested on 3488 macular scans from both eyes of 581 young adults (376 myopes and 206 non-myopes, mean (S.D.) age 21.9 (1.4) years). Estimates for retinal thickness, wall height and slope, pit depth and width were derived from the best-fitting model curve. Ten variations of Gaussian and Difference of Gaussian models were fitted to the same scans and compared with the SPG model for goodness of fit (by Root mean square error, RMSE), model complexity (by the Bayesian Information Criteria) and model fidelity.
The SPG model produced excellent goodness of fit (mean RMSE = 4.25 and 3.89 μm; 95% CI: 4.20, 4.30 and 3.86, 3.93 for fitting horizontal and vertical profiles respectively). The SPG model showed pit asymmetry, with average nasal walls 17.6 (11.6) μm higher and 0.96 (0.61) steeper than temporal walls and average superior walls 7.0 (12.2) μm higher and 0.41 (0.65) steeper than the inferior walls. The SPG model also revealed a continuum of human foveal shapes, from round bottoms to extended flat bottoms (up to 563 μm). 49.1% of foveal profiles were best fitted with a flat bottom >30 μm wide. Compared with the other tested models, the SPG was the preferred model overall based on the Bayesian Information Criteria.
The SPG is a new parsimonious mathematical model that improves upon other models by accounting for wall asymmetry and flat pit bottoms, providing an excellent fit and more faithful characterisation of typical foveal pit shapes and their known variations. This new model may be helpful in distinguishing normal foveal shape variations by refractive status as well by other characteristics such as sex, ethnicity and age.
高质量的光学相干断层扫描（OCT）黄斑扫描能够通过对中央凹坑形状进行特征化来区分一系列正常和患病状态。现有的数学模型缺乏灵活性，无法捕捉所有已知的凹坑变化，因此对凹坑的特征化精度有限。本研究旨在开发一种新模型，以更稳健地描述个体中央凹坑的变化。
开发了一种倾斜分段高斯（SPG）模型，该模型由一条倾斜线和一个分段高斯函数（由一条单独的直线连接的高斯函数的两半）的线性组合组成，用于拟合视网膜厚度数据，具有描述不同程度的凹坑不对称性和凹坑底部平坦度的灵活性。它拟合了中央凹两个边缘之间的原始凹坑数据，以提高准确性。该模型在581名年轻成年人（376名近视者和206名非近视者，平均（标准差）年龄21.9（1.4）岁）双眼的3488次黄斑扫描上进行了测试。从最佳拟合模型曲线中得出视网膜厚度、壁高和斜率、凹坑深度和宽度的估计值。将高斯模型和高斯差分模型的十种变体拟合到相同的扫描数据上，并与SPG模型进行拟合优度（通过均方根误差，RMSE）、模型复杂性（通过贝叶斯信息准则）和模型保真度的比较。
SPG模型具有出色的拟合优度（水平和垂直剖面拟合的平均RMSE分别为4.25和3.89μm；95%置信区间：4.20，4.30和3.86，3.93）。SPG模型显示出凹坑不对称性，平均鼻侧壁比颞侧壁高17.6（11.6）μm，陡0.96（0.61），平均上壁比下壁高7.0（12.2）μm，陡0.41（0.65）。SPG模型还揭示了人类中央凹形状的连续性，从圆形底部到扩展的平坦底部（长达563μm）。49.1%的中央凹剖面最适合底部宽度>30μm的平坦底部。与其他测试模型相比，基于贝叶斯信息准则，SPG总体上是首选模型。
SPG是一种新的简约数学模型，通过考虑壁不对称性和平坦的凹坑底部，在其他模型的基础上进行了改进，能够出色地拟合并更忠实地描述典型的中央凹坑形状及其已知变化。这种新模型可能有助于根据屈光状态以及性别、种族和年龄等其他特征来区分正常的中央凹形状变化。
