Influence of tooth dimension on the initial mobility based on plaster casts and X-ray images : A numerical study

The goal was to determine the influence of different geometric parameters of the tooth on the initial tooth mobility and the position of the center of resistance employing numerical models based on scaled X-ray images and plaster casts.

The dimensions of tooth 21 were measured in 21 patients, using radiographs and dental casts. Length and mesiodistal width of the tooth were obtained from the X-ray image and the orovestibular diameter from the plaster cast. Finite element models were generated. Cortical and cancellous bone and the periodontal ligament were simulated to create realistic models. Root length (11-17 mm), mesiodistal width (6-10 mm) and orovestibular thickness (7-9 mm) were varied in 1-mm steps to generate 105 models. In the simulation, each model was loaded with a force of 10 N in vestibulopalatinal direction and with a torque of 10 Nmm to determine tooth displacements and center of resistance.

Initial tooth displacement and thus mobility increased with decreasing total root surface. The shortest, slimmest and thinnest tooth showed a total deflection of 0.14 mm at the incisal edge, while the longest, widest and thickest tooth showed a total deflection of 0.10 mm. Changes in mesiodistal width had the greatest influence on initial tooth mobility and changes in orovestibular thickness the least. The teeth's center of resistance was positioned between 37 and 43% of the root length measured from the cervical margin of the alveolar bone. The center of resistance of the longest dental root investigated was located around 6% more cervically compared to the one of the shortest dental root. The influence of root width and thickness on the position of the center of resistance was significantly lower than root length.

Geometric parameters significantly impact initial tooth mobility and position of the center of resistance. Thus, tooth dimensions should be considered in orthodontic treatment planning. Dental radiographs represent a sufficient validation tool to estimate the quality of a pure dental tipping during orthodontic treatment, as the orovestibular thickness has little influence. However, for three-dimensional tooth displacements all geometric parameters should be determined accurately using plaster casts or DVT.