Kim Sung-Goo, Kim Dae-Seung, Choi Soon-Chul, Lee Sam-Sun, Heo Min-Suk, Huh Kyung-Hoe, Hwang Soon-Jung, Yi Won-Jin
Department of Oral and Maxillofacial Radiology, School of Dentistry, Seoul National University, Seoul, Korea.
Oral Surg Oral Med Oral Pathol Oral Radiol Endod. 2010 Nov;110(5):e52-60. doi: 10.1016/j.tripleo.2010.07.006.
To investigate the rotational variations of three-dimensional (3D) trajectories at anatomic landmarks by different mandibular kinematics, we applied principal axes of inertia to the 3D trajectories. The principal rotations were determined directly from the anatomy-based trajectories produced by a patient-specific temporomandibular joint simulation. As a preliminary study, the principal rotations for a pilot group of patients with mandibular deviation were correlated with the deviation.
Three-dimensional mandibular movements from the patients with mandibular deviation were tracked based on a patient-specific splint and an optical tracking system. The dental occlusion recorded on the splint provided synchronization for initial movement in the tracking and the simulation phases. The translation and rotation recorded during tracking were applied sequentially to the mandibular model in relation to a fixed maxilla model. The sequential positions of the points of interest based on the reference coordinate system could also be simulated and traced by the same method. The landmarks selected for analysis were the points of the bilateral condyles and of the mandibular incisor. The moment of inertia tensor was calculated with respect to the 3D trajectory points. Using the unit vectors along the principal axes derived from the tensor matrix, α, β, and γ rotations (horizontal, sagittal, and frontal planes) around the z-, y-, and x-axes, respectively, were determined to represent the principal directions as principal rotations.
The measured rotations were correlated with the deviation in 3 orthogonal planes. Under the influence of the mandibular asymmetry, the orientations of the principal axis at the condyles increase counterclockwise in the horizontal plane and clockwise in the frontal plane. At the incisor point, the horizontal and frontal angles increase counterclockwise, but the sagittal angles increase clockwise. The interrelations between different rotations and between landmarks, defined as a correlation coefficient between principal rotations, decrease as the deviation increases.
Three-dimensional trajectories at selected landmarks based on the reference coordinate system were evaluated using principal axes of inertia to investigate the functional characteristics of the mandible with a deviation. The movement asymmetry between the condyles increases as the deviation increases in all directions. The principal rotations at the condyles can be explained by those at the incisor with varying degrees despite the deviation.
为了通过不同的下颌运动学研究解剖标志点处三维（3D）轨迹的旋转变化，我们将惯性主轴应用于3D轨迹。主旋转是直接从患者特异性颞下颌关节模拟产生的基于解剖结构的轨迹中确定的。作为一项初步研究，一组下颌偏斜患者的主旋转与偏斜情况相关。
基于患者特异性夹板和光学跟踪系统，对下颌偏斜患者的三维下颌运动进行跟踪。夹板上记录的牙合关系为跟踪和模拟阶段的初始运动提供了同步。跟踪过程中记录的平移和旋转依次应用于相对于固定上颌模型的下颌模型。基于参考坐标系的感兴趣点的连续位置也可以通过相同方法进行模拟和追踪。选择用于分析的标志点是双侧髁突点和下颌切牙点。相对于3D轨迹点计算惯性张量。使用沿张量矩阵导出的主轴的单位向量，分别确定围绕z轴、y轴和x轴的α、β和γ旋转（水平面、矢状面和额面），以表示作为主旋转的主方向。
测量的旋转与三个正交平面中的偏斜相关。在下颌不对称的影响下，髁突处主轴的方向在水平面逆时针增加，在额面顺时针增加。在切牙点，水平角和额面角逆时针增加，但矢状角顺时针增加。不同旋转之间以及标志点之间（定义为主旋转之间的相关系数）的相互关系随着偏斜增加而减小。
使用惯性主轴评估基于参考坐标系的选定标志点处的三维轨迹，以研究偏斜下颌骨的功能特征。随着偏斜在各个方向上增加，髁突之间的运动不对称性增加。尽管存在偏斜，但髁突处的主旋转在不同程度上可以由切牙处的主旋转来解释。
