Three-dimensional nonlinear prediction of tooth movement from the force system and root morphology

Abstract

Objectives To determine the different impact of moment-to-force ratio (M:F) variation for each tooth and spatial plane and to develop a mathematical model to predict the orthodontic movement for every tooth. Materials and Methods Two full sets of teeth were obtained combining cone-beam computed tomography (CBCT) and optical scans for two patients. Subsequently, a finite element analysis was performed for 510 different force systems for each tooth to evaluate the centers of rotation. Results The center of CROT locations were analyzed, showing that the M:F effect was related to the spatial plane on which the moment was applied, to the force direction, and to the tooth morphology. The tooth dimensions on each plane were mathematically used to derive their influence on the tooth movement. Conclusion This study established the basis for an orthodontist to determine how the teeth move and their axes of resistance, depending on their morphology alone. The movement is controlled by a parameter (k), which depends on tooth dimensions and force system features. The k for a tooth can be calculated using a CBCT and a specific set of covariates.

A multi-patient analysis of the center of rotation trajectories using finite element models of the human mandible

“…It can also be seen that linear increments in the magnitude of the couples nonlinearly increases the distance between the neighboring CRots of each tooth. The same behavior was reported by Savignano et al [ 20 , 23 ]. Moreover, the CRot trajectories begin from the CRes of the tooth, and by increasing the M : F , the trajectories move towards the crowns of the teeth, and then, they change their directions to the back of the teeth.…”

“…The investigation of the effects of the direction of the loading conditions on the CRot trajectories in Fig 5 reveals that although rotating the couples about each axis results in similar CRot trajectories for different rotation angles, equally rotating the direction of the couple about the three principal axes results in different patterns for the CRot positions, especially in labiolingual direction. Besides, by increasing the magnitude of the couples in a specific direction, the distances between two neighboring CRots changes nonlinearly which is in line with the results of the state-of-the-art [ 20 , 23 ], indicating that changing the M : F nonlinearly affects the position of the CRots.…”

“…As our third scenario, we investigate the influence of the force’s direction on tooth movement and the position of the CRot, and compare our results with those obtained by Savignano et al [ 20 , 23 ]. More specifically, the effect of the force direction is investigated at the CRes of the left premolar of Patient 1 , while the load direction changes in one of the three principal planes of the tooth, and a perpendicular moment is applied to the studied plane.…”

“…Due to the importance of the PDL tissue in transferring loads from the tooth to the alveolar bone [ 39 , 43 ], a Mooney-Rivlin Hyperelastic (MRH) material model is used to simulate its nonlinear behavior [ 42 , 44 ]. Furthermore, for the simplicity of the model and following the literature [ 14 , 20 , 23 , 39 ], the gingival tissue is discarded from our computational model due to its extremely low elasticity modulus compared to that of the other tissues, i.e., PDL, bone, and tooth.…”

“…However, the mentioned study is limited to a single tooth analysis with a limited load magnitude range applied to the CRes due to using a linear elastic material model for the PDL layer. Although two patients are considered in a recent work [ 23 ], an inter-patient analysis is missing in general.…”