The 3-dimensional zone of the center of resistance of the mandibular posterior teeth segment

Introduction: We sought the 3-dimensional (3D) zone of the center of resistance (ZCR) of mandibular posterior teeth groups (group 1: first molar; group 2: both molars; group 3: both molars and second premolar; group 4: both molars and both premolars) with the use of 3D finite element analysis. Methods: 3D finite element models comprised the mandibular posterior teeth, periodontal ligament, and alveolar bone. In the symmetric bilateral model, a 100-g midline force was applied on a median sagittal plane at 0.1-mm intervals to determine the anteroposterior and vertical positions of the ZCR (where the applied force induced translation). The most reliable buccolingual position of the ZCR was then determined in the unilateral model. The combination of the anteroposterior, vertical, and buccolingual positions was defined as the ZCR. Results: The ZCRs of groups 1-4 were, respectively, 0.48, 0.46, 0.50, and 0.53 of the mandibular first molar root length from the alveolar crest level and located slightly distobuccally at anteroposterior ratios of 2:3.0, 2:2.3, 2:2.4, and 2:2.5 to each sectional arch length and at buccolingual ratios of 2:1.5, 2:1.1, 2:1.6, and 2:2.4 to the first molar's buccolingual width. Conclusions: The ZCR can be a useful reference for 3D movement planning of mandibular posterior teeth or segments.