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

Prediction of condylar movement envelope surface based on facial morphology

“…In recent years, mathematical expressions have been increasingly used in medical research [ 10 , [38] , [47] , [48] , [49] , [50] , [51] , [52] , [53] ]. Shang et al established the functional models for cleft palate patients [ 47 ], while Wellens applied these functions to analyze mandibular arch forms in mixed dentition patients with crowding [ 49 ].…”

“…Therefore, it is difficult to mathematically express the geometric morphology of envelope surfaces. In a study of mandibular movements, Shu et al used different functions to analyze condylar trajectories [ 10 ], but the study used point landmarks instead of the 3D condyle and could not complete a single function to express the condylar trajectory. We simplified the 3D envelope surface into a sagittal section curve based on the morphology.…”

“…Although TMJ movement cannot be observed directly, advancements in acquisition equipment and computers have allowed accurate, quantitative measurement of mandibular movements [ [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] ]. Several mathematical models and functional expressions have been established for the movement trajectory [ 10 , 11 ], establishing the future role of artificial intelligence in the medical field. Previous studies of the mandibular condylar process have investigated the range using condylar landmarks, but differences in landmark selection prevent the comparison of these results [ 12 , 13 ].…”

Evaluation of the effect of unilateral mastication on the morphology of temporomandibular joint from the perspective of dynamic joint space

“…Forty‐eight volunteers with normal occlusion and without TMD symptoms were included in our study (27 men and 21 women, 20.8 ± 2.5 years). All the subjects were recruited according to the following criteria 37 : (1) no history of TMJ trauma or pain, TMJ luxation, orthodontic treatment, previous cervical or oral surgery; (2) class I molar and canine relationships; (3) absence of TMD signs and symptoms; (4) positive overjet and overbite (range, 2–4 mm); (5) maximum mouth opening of at least 35 mm; (6) maximum of 2 mm of incisor crowding; (7) normal discal position relative to the condyle in closed and open‐mouth images on the follow‐up MRI examination; (8) no signs of the TMJ osteoarthritis on follow‐up computed tomography (CT) examination. A dentist assisted in recruiting and examining the subjects.…”

“…A motion capture system (NDI Polaris Vega ST, Northern Digital Inc., Waterloo, Ontario, Canada) was used to collect data with the sampling frequency of 20 Hz (Figure 1D), which was sufficient for capturing mandibular movement. [37][38][39] The volumetric accuracy of the motion capturing system was 0.12 mm RMS (Root Mean Square). The subjects wore two instruments on the head and the mandibular teeth, respectively (Figure 1D).…”