IADR Abstract Archives
Simultaneous Estimation of Orthodontic Force Using Mass-Tensor Method
Objectives: The acquisition of orthodontic forces would provide real-time assistance for precise orthodontic procedures. However, direct measurement of orthodontic forces is currently unfeasible without interrupting the dentist's workflow, thus necessitating an engineering estimation approach. This study aims to develop and validate a mass-tensor method for real-time calculation of orthodontic forces in response to crown displacement, aiming to enhance the precision and efficiency of orthodontic treatment planning.
Methods: Biomechanical models of teeth, periodontal ligament (PDL), and bone complex (TPBC) were reconstructed from segmented CBCT images. The models were then discretized into tetrahedron elements, and the mass of each vertex was calculated using a mass-lumping technique. Accordingly, the mass-tensor method was established by formulating a dynamic system using Newton's law, which expressed the association between the deformation of PDL and its strain energy and elastic force. The PDL deformation at each time step was calculated using an implicit time integration scheme, and an optimization problem was solved using a descent method to obtain the elastic force in each vertex. The estimated orthodontic force under crown displacement was therefore calculated through the elastic forces PDL exerted on the tooth. The method's accuracy and efficiency were assessed through simulations on three tooth types (central incisor, lateral incisor, canine) and experiments on a phantom model using orthodontic force tester (OFT).
Results: The method demonstrated high accuracy with a difference of 8.9% compared to experimental results. Average computation times for the three tooth types were 23.73 ms, respectively, confirming real-time performance. The orthodontic forces calculated using the mass-tensor method were consistent with those obtained from the phantom model experiments.
Conclusions: The mass-tensor model provides a promising approach for real-time estimation of orthodontic forces. It offers an accurate and efficient alternative to traditional methods, potentially improving the precision and efficiency of orthodontic treatments by enabling real-time force assessment and adjustment.
Methods: Biomechanical models of teeth, periodontal ligament (PDL), and bone complex (TPBC) were reconstructed from segmented CBCT images. The models were then discretized into tetrahedron elements, and the mass of each vertex was calculated using a mass-lumping technique. Accordingly, the mass-tensor method was established by formulating a dynamic system using Newton's law, which expressed the association between the deformation of PDL and its strain energy and elastic force. The PDL deformation at each time step was calculated using an implicit time integration scheme, and an optimization problem was solved using a descent method to obtain the elastic force in each vertex. The estimated orthodontic force under crown displacement was therefore calculated through the elastic forces PDL exerted on the tooth. The method's accuracy and efficiency were assessed through simulations on three tooth types (central incisor, lateral incisor, canine) and experiments on a phantom model using orthodontic force tester (OFT).
Results: The method demonstrated high accuracy with a difference of 8.9% compared to experimental results. Average computation times for the three tooth types were 23.73 ms, respectively, confirming real-time performance. The orthodontic forces calculated using the mass-tensor method were consistent with those obtained from the phantom model experiments.
Conclusions: The mass-tensor model provides a promising approach for real-time estimation of orthodontic forces. It offers an accurate and efficient alternative to traditional methods, potentially improving the precision and efficiency of orthodontic treatments by enabling real-time force assessment and adjustment.
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