Three-dimensional zone of centers of resistance in maxillary central incisors and first molars: Couple-based finite element determination.

INTRODUCTION

This study develops a finite element analysis method to define the 3-dimensional (3D) zone of center of resistance (ZCR) position for maxillary central incisors and first molars and validates its applicability under different alveolar bone levels.

METHODS

Cone-beam computed tomography scans from 40 patients were grouped: group 1 (maxillary central incisors, no bone loss), group 2 (maxillary central incisors, bone loss), group 3 (maxillary first molars, no bone loss), and group 4 (maxillary first molars, bone loss). The 3D models of teeth, a simulated 0.2-mm-thick PDL, and alveolar bone were reconstructed using Mimics software (Materialise, Leuven, Belgium) and imported into ANSYS Workbench (ANSYS Inc, Canonsburg, Pa) to calculate the tooth axis of rotation (resistance axis). A 5-step method defined the ZCR: (1) set the crown center as origin, (2) apply pure 3 N·mm couples at the crown center along the x-, y-, and z-axes, (3) find the resistance axes using displacement data, (4) use an algorithm to find best point filtering (1%-3%) where axes meet; fit a sphere to these points to get the ZCR center and radius, and (5) verify the accuracy by measuring rotation angles after applying forces at the center of the ZCR, and the 1 and 2 times radius in the 3 directions.

RESULTS

Optimal filtering percentages averaged 2.23% (group 1), 2.10% (group 2), 1.33% (group 3), and 1.63% (group 4). Alveolar resorption reduced the ZCR height. The central incisors decreased from 59.17% (standard deviation [SD]: 1.01) to 45.19% (SD: 1.61), whereas first molars decreased from 53.76% (SD: 3.03) to 46.76% (SD: 2.02) of root length. The ZCR radius decreased with alveolar bone loss-central incisors (from 0.55 to 0.49 mm) and first molars (from 0.58 to 0.48 mm). Forces applied at the center of the ZCR minimized rotation angles (x/y-axis: 0.12°; z-axis: 0.09°). Rotation increased significantly when forces were applied beyond the sphere, reaching 1.92° at twice the radius.

CONCLUSIONS

The finite element analysis method accurately and efficiently defined the 3D ZCR position and extent in central incisors and first molars. Alveolar bone loss induced apical displacement and a reduction in the ZCR extent.