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北京大学学报（医学版） ›› 2026, Vol. 58 ›› Issue (1): 115-125. doi: 10.19723/j.issn.1671-167X.2026.01.015

• 论著 • 上一篇    下一篇

基于下颌运动轨迹的𬌗架关键参数计算方法

单珅瑶1,2, 杨咏涛2, 李文博2, 温奥楠1, 高梓翔1, 商相宜2, 王勇1,2,*(), 赵一姣1,2,*()   

  1. 1. 北京大学口腔医学院·口腔医院口腔医学数字化研究中心, 国家口腔医学中心, 国家口腔疾病临床医学研究中心, 口腔生物材料和数字诊疗装备国家工程研究中心, 口腔数字医学北京市重点实验室, 国家卫生健康委员会口腔医学计算机应用工程技术研究中心, 北京 100081
    2. 北京大学医学部医学技术研究院, 北京 100191
  • 收稿日期:2025-10-11 出版日期:2026-02-18 发布日期:2025-12-10
  • 通讯作者: 王勇, 赵一姣
  • 基金资助:
    国家自然科学基金(82271039); 北京市自然科学基金(L232100); 北京市自然科学基金(L242132); 国家重点研发计划(2022YFC2405401)

Calculation method of key articulator parameters based on mandibular movement trajectory

Shenyao SHAN1,2, Yongtao YANG2, Wenbo LI2, Aonan WEN1, Zixiang GAO1, Xiangyi SHANG2, Yong WANG1,2,*(), Yijiao ZHAO1,2,*()   

  1. 1. Center for Digital Dentistry, Peking University School and Hospital of Stomatology & National Center for Stomatology & National Clinical Research Center for Oral Diseases & National Engineering Research Center of Oral Biomaterials and Digital Medical Devices & Beijing Key Laboratory of Digital Stomatology & NHC Research Center of Engineering and Technology for Computerized Dentistry, Beijing 100081, China
    2. Institute of Medical Technology, Peking University Health Science Center, Beijing 100191, China
  • Received:2025-10-11 Online:2026-02-18 Published:2025-12-10
  • Contact: Yong WANG, Yijiao ZHAO
  • Supported by:
    the National Natural Science Foundation of China(82271039); Beijing Natural Science Foundation(L232100); Beijing Natural Science Foundation(L242132); National Key Research and Development Plan of China(2022YFC2405401)

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摘要：

目的: 探索一套基于下颌运动轨迹数据计算𬌗架关键参数的数学方法, 并将该方法计算结果与现有国外下颌运动记录系统提供的参考值进行比较, 为国产化下颌运动轨迹记录系统的研发奠定相关算法基础。方法: 招募符合纳入标准的20例健康志愿者(男性7例, 女性13例), 平均年龄(31±8)岁。使用JMA Optic下颌运动记录系统采集受试者前伸及左右侧方运动数据。使用逆向工程软件建立参考平面坐标系, 完成受试者颌面部多源数据整合, 再统一坐标系。选取髁突顶点、髁突内极、髁突外极、髁突中心、经验铰链轴点及下颌切点作为下颌运动轨迹参考点, 并生成各参考点的三维运动轨迹, 进而计算前伸髁导斜度(sagittal condylar inclination, SCI)、侧方髁导斜度(transversal condylar inclination, TCI)、迅即侧移(immediate side shift, ISS)、切导斜度和尖导斜度, 以不同参考点的计算结果作为不同实验组。以JMA Optic系统提供的参考值作为对照组进行比较分析。结果: 各实验组的SCI均显著高于对照组(P < 0.001), 且存在约3.1°的系统性正偏差, 但一致性界限较窄。TCI结果因参考点而异, 仅髁突顶点组(5.7°±6.1°)显著低于对照组(9.2°±6.6°)(t=5.023, P < 0.001), 其余组与对照组间差异无统计学意义, 经验铰链轴点组与对照组间表现出最小的平均偏差与最窄的一致性界限, 该组与对照组TCI的一致性最佳。所有组别的ISS均为0.0(0.0) mm。下颌切点组的切导斜度(43.1°±8.6°)显著低于对照组(50.6°±13.7°)(t=3.749, P=0.001), 且一致性欠佳, 而下颌切点组的尖导斜度与对照组间差异无统计学意义(t=-1.873, P=0.069), 且一致性尚可。结论: 提出了一套基于下颌运动轨迹数据计算𬌗架关键参数的数学方法, 其计算路径明确、可追溯。本方法与JMA Optic系统算法在计算TCI、ISS、尖导斜度上一致性尚可, 而在计算SCI和切导斜度上一致性欠佳, 参考点的选择对参数计算结果具有直接影响。该数学方法为实现精准化、个性化的𬌗架参数设置提供了可靠的理论基础。

关键词: 下颌运动轨迹, ??架参数, 前伸髁导斜度, 侧方髁导斜度, 切导斜度

Abstract:

Objective: 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. Methods: 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. Results: 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. Conclusion: 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.

Key words: Mandibular movement trajectory, Articulator parameters, Sagittal condylar inclination, Transversal condylar inclination, Incisal guidance inclination

中图分类号: 

  • R783.3

图1

标准上颌叉三维模型"

图2

颌面部三维多源数据整合流程"

图3

参考平面坐标系建立及参考点选取"

图4

基于参考点的下颌运动轨迹"

图5

基于参考点轨迹计算𬌗架关键参数"

表1

各实验组及对照组SCI、TCI、ISS左右侧比较"

Group n SCI/(°)，${\bar x}$±s TCI/(°)，${\bar x}$±s ISS/mm, M (IQR)
Left Right t P Left Right t P Left Right Z P
EG_condylar apex 20 39.7±7.3 40.0±8.5 -0.270 0.790 6.6±5.1 4.8±7.1 1.129 0.273 0.0(0.0) 0.0(0.0) 0.000 >0.999
EG_medial condylar pole 20 39.8±7.1 39.9±8.0 -0.191 0.851 9.0±5.6 6.6±7.5 1.453 0.162 0.0(0.0) 0.0(0.0) 0.000 >0.999
EG_lateral condylar pole 20 40.0±7.2 40.3±8.4 -0.214 0.833 11.0±5.3 9.1±5.8 1.374 0.185 0.0(0.0) 0.0(0.0) 0.000 >0.999
EG_condylar center 20 39.9±7.1 40.1±8.2 -0.240 0.813 10.7±5.5 8.6±6.5 1.367 0.188 0.0(0.0) 0.0(0.0) 0.000 >0.999
EG_empirical hinge axis point 20 39.9±7.4 40.5±8.9 -0.346 0.733 10.2±5.6 8.9±6.3 1.068 0.299 0.0(0.0) 0.0(0.0) 0.000 >0.999
CG 20 37.3±8.6 36.5±9.1 0.639 0.531 9.8±6.5 8.6±6.8 1.019 0.321 0.0(0.0) 0.0(0.0) -0.272 0.785

表2

实验组_下颌切点及对照组尖导斜度左右侧比较"

Group n Canine guidance inclination/(°)，${\bar x}$±s
Left Right t P
EG_mandibular incisor point 20 33.9±9.3 32.7±6.5 0.900 0.379
CG 20 29.7±11.5 32.8±8.7 -1.611 0.124

表3

各实验组与对照组SCI、TCI、ISS成对比较"

Group SCI/(°)，${\bar x}$±s t P TCI/(°)，${\bar x}$±s t P ISS/mm, M (IQR) Z P
EG_condylar apex 39.8±7.8 -4.635 < 0.001 5.7±6.1 5.023 < 0.001 0.0(0.0) -1.633 0.102
EG_medial condylar pole 39.8±7.5 -4.586 < 0.001 7.8±6.7 1.971 0.056 0.0(0.0) -1.633 0.102
EG_lateral condylar pole 40.1±7.7 -5.206 < 0.001 10.1±5.6 -1.213 0.233 0.0(0.0) -1.633 0.102
EG_condylar center 40.0±7.6 -4.963 < 0.001 9.7±6.0 -0.655 0.517 0.0(0.0) -1.633 0.102
EG_empirical hinge axis point 40.2±8.1 -5.318 < 0.001 9.5±5.9 -0.539 0.593 0.0(0.0) -1.633 0.102
CG 36.9±8.8 9.2±6.6 0.0(0.0)

图6

各实验组与对照组𬌗架关键参数一致性的Bland-Altman图"

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ISSN 1671-167X
CN 11-4691/R
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