Modified Centroid of Root Projection Method for Determining the Center of Resistance of a Tooth

Center of resistance (CR) has been widely accepted in dentistry as a reference point for controlling tooth moment, which depends on the direction of loading and the morphology of the periodontal ligament (PDL). In clinical practice, dentists estimate the location of CR based on the morphology of the root of teeth, which may lead to a misestimation of orthodontic treatment. A quick method was proposed to efficiently determine the CR by identifying the centroid of the root projection (CRP), according to the orthodontic force. However, the original CRP method was limited to single-rooted teeth, and it did not provide a strategy for handling the overlapping roots projection of multirooted teeth. To address this issue, we expanded the CRP method to accommodate multirooted teeth by calculating a weighted average of each root’s projection. We further validated the modified CRP method using finite element analysis (FEA) simulation for both single-rooted and multirooted teeth considering mesial–distal and buccal–lingual force directions. The evaluation of displacement distribution along the projection direction allowed us to assess translation and rotation movements, which confirmed that the centroid of root projection can accurately serve as the CR for the multirooted teeth. Additionally, we observed heterogeneous stress distributions in the multirooted teeth. Considering the well-acknowledged bone remodeling effect in response to local stress states, this indicated that comprehensive indexes beyond the CR are desired for evaluating or controlling tooth movement.