Green Moshe Noam, Bloom Jonathan Michael, Kulbersh Richard
School of Orthodontics, Unversity of Detroit Mercy, Detroit, Mich.
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass.
Am J Orthod Dentofacial Orthop. 2017 Sep;152(3):355-363. doi: 10.1016/j.ajodo.2016.12.025.
In this article, we aimed to establish an ideal definition for the craniofacial midsagittal plane (MSP) by first finding an optimal "plane of best fit" and then deriving a simple approximation for clinical use that is highly accurate.
For 60 adolescent patients, 3-dimensional coordinates of 8 central landmarks and 6 pairs of lateral landmarks were collected. Across all patients, the coplanarity of the central landmarks was compared with that of the midpoints of the lateral landmarks. The MSP of best fit was then found by minimizing the mean square distance of the 8 central landmarks to a plane. Across all patients, each possible 3-point plane was compared with the MSP of best fit with respect to both orientation and proximity.
The central landmarks were more coplanar and thus more accurate than the midpoints of the lateral pairs. The plane defined by nasion, basion, and incisive foramen was the closest to the MSP of best fit in both orientation and proximity.
The nasion-basion-incisive foramen plane should be used for skull orientation and 3-dimensional cephalometric analyses because it approximates the MSP of best fit with high accuracy, avoids the use of horizontal reference planes, avoids influence from upper and midface asymmetry, uses easily identifiable relevant landmarks, and is simple to define.
在本文中,我们旨在通过首先找到最佳“拟合平面”,然后推导出一个高度准确的、供临床使用的简单近似值,来为颅面矢状中线平面(MSP)建立一个理想的定义。
对60名青少年患者收集了8个中央标志点和6对侧方标志点的三维坐标。在所有患者中,比较中央标志点的共面性与侧方标志点中点的共面性。然后通过最小化8个中央标志点到一个平面的均方距离来找到最佳拟合的MSP。在所有患者中,将每个可能的三点平面与最佳拟合的MSP在方向和接近度方面进行比较。
中央标志点比侧方标志点的中点更共面,因此更准确。由鼻根点、颅底点和切牙孔所定义的平面在方向和接近度上都最接近最佳拟合的MSP。
鼻根点-颅底点-切牙孔平面应用于颅骨定向和三维头影测量分析,因为它高精度地近似最佳拟合的MSP,避免使用水平参考平面,避免上颌和中面部不对称的影响,使用易于识别的相关标志点,且定义简单。