Mathematical analysis of the condylar trajectories in asymptomatic subjects during mandibular motions.

The understandings of motional regular and dynamic information during the mandibular motions are essential to investigate the dysfunctions of temporomandibular joints (TMJ). This study aims to develop a method to record the mandibular movements and analyze the condylar trajectory, velocity, and acceleration in asymptomatic individuals during mandibular motions. Thirteen asymptomatic subjects were strictly selected without symptoms of temporomandibular disorders (TMDs). An optical tracking system was chosen for recording mandibular motions. Curve fitting was used for fitting the trajectories of condyles, notches and lower incisor, and the articular eminence outlines. The sagittal plane (YoZ) provided a better view for condylar trajectories during mouth opening and mandibular protrusion, whereas the coronal plane (XoZ) offered a superior view during lateral protrusions. A parabola had good performance in fitting the trajectories of the condyle, incisor, and outlines with a superior goodness of fit (r2) during mouth opening and mandibular protrusion; linear functions were suitable for fitting the trajectories of the contralateral condyle during lateral protrusions. The velocity during the opening process was lower than that during the closing process, and so were the accelerations. The sagittal space between the articular eminences and condyles during mouth opening and mandibular protrusion were close, 2.8 and 2.7 mm, respectively. The sagittal space, velocity, and acceleration can provide dynamic information of TMJs. Three-dimensional motion analyses of temporomandibular joints during the mandibular motions were conducted to exact the mathematic information of temporomandibular joints. From curve fitting process, the fluctuation can be eliminated and the dynamic information can be obtained. And the parabola was better for the condylar trajectories in the sagittal plane of opening and mandibular protrusion. As to the lateral protrusions, the linear function is suitable for the condylar trajectories in coronal plane. The condylar curve of asymptomatic subjects can set as a reference to diagnose and treat for the patients with associated dysfunctions.