[Calculation method of key articulator parameters based on mandibular movement trajectory]

To explore a mathematical method for calculating key articulator parameters based on mandibular movement trajectory data, and to compare the results of this method with reference values provided by existing foreign mandibular movement recording system, thereby establishing an algorithmic basis for developing a domestic mandibular movement recording system.

Twenty healthy volunteers (7 males, 13 females) meeting inclusion criteria were recruited, with a mean age of (31±8) years. Mandibular movement data during protrusive and left/right lateral movements were recorded using the JMA Optic foreign mandibular movement recording system. A reference plane coordinate system was established using reverse engineering software, the multi-source maxillofacial data were integrated, and the coordinate systems were then unified. The condylar apex, medial condylar pole, lateral condylar pole, condylar center, empirical hinge axis point, and mandibular incisor point were selected as reference points for mandibular movement trajectories. Three-dimensional movement trajectories were generated for each reference point to calculate the sagittal condylar inclination (SCI), transverse condylar inclination (TCI), immediate side shift (ISS), incisal guidance inclination and canine guidance inclination. The calculation results from different reference points served as distinct experimental groups. Reference values provided by the JMA Optic system were used as the control group for comparative analysis.

The SCI values of all the experimental groups were significantly higher than that of the control group (P < 0.001), with a systematic positive bias of approximately 3.1°, though the limits of agreement were relatively narrow. The TCI results varied depending on the reference point: Only the condylar apex group (5.7°±6.1°) was significantly lower than the control group (9.2°±6.6°) (t=5.023, P < 0.001). Differences between the remaining groups and the control group were not statistically significant. The empirical hinge axis point group showed the smallest mean bias and the narrowest limits of agreement, indicating optimal consistency with the control group's TCI. The ISS values were 0.0 (0.0) mm in all the groups. The incisal guidance inclination of the mandibular incisor point group (43.1°±8.6°) was significantly lower than that of the control group (50.6°±13.7°) (t=3.749, P=0.001) with poor consistency. However, the canine guidance inclination of the mandibular incisor point group showed no statistically significant difference compared with the control group (t=-1.873, P=0.069), with acceptable consistency.

This study proposed a mathematical method for calculating key articulator parameters based on mandibular movement trajectory data, with a clear and traceable computational pathway. The proposed method showed acceptable consistency with the JMA Optic system algorithm in calculating TCI, ISS, and canine guidance inclination, but poor consistency in calculating SCI and incisal guidance inclination. The selection of reference points directly influenced the results of parameter calculation. This mathematical method provided a reliable theoretical foundation for achieving precise, personalized articulator parameter settings.