Prediction of optimal bending angles of a running loop to achieve bodily protraction of a molar using the finite element method
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Objective: The purpose of this study was to predict the optimal bending angles of a running loop for bodily protraction of the mandibular first molars and to clarify the mechanics of molar tipping and rotation. Methods: A three-dimensional finite element model was developed for predicting tooth movement, and a mechanical model based on the beam theory was constructed for clarifying force systems. Results: When a running loop without bends was used, the molar tipped mesially by 9.6o and rotated counterclockwise by 5.4o. These angles were almost similar to those predicted by the beam theory. When the amount of tip-back and toe-in angles were 11.5o and 9.9o, respectively, bodily movement of the molar was achieved. When the bend angles were increased to 14.2o and 18.7o, the molar tipped distally by 4.9o and rotated clockwise by 1.5o. Conclusions: Bodily movement of a mandibular first molar was achieved during protraction by controlling the tip-back and toe-in angles with the use of a running loop. The beam theory was effective for understanding the mechanics of molar tipping and rotation, as well as for predicting the optimal bending angles.[Korean J Orthod 2018;48(1):3-10]
Abstract
Objective: The purpose of this study was to predict the optimal bending angles of a running loop for bodily protraction of the mandibular first molars and to clarify the mechanics of molar tipping and rotation. Methods: A three-dimensional finite element model was developed for predicting tooth movement, and a mechanical model based on the beam theory was constructed for clarifying force systems. Results: When a running loop without bends was used, the molar tipped mesially by 9.6o and rotated counterclockwise by 5.4o. These angles were almost similar to those predicted by the beam theory. When the amount of tip-back and toe-in angles were 11.5o and 9.9o, respectively, bodily movement of the molar was achieved. When the bend angles were increased to 14.2o and 18.7o, the molar tipped distally by 4.9o and rotated clockwise by 1.5o. Conclusions: Bodily movement of a mandibular first molar was achieved during protraction by controlling the tip-back and toe-in angles with the use of a running loop. The beam theory was effective for understanding the mechanics of molar tipping and rotation, as well as for predicting the optimal bending angles.[Korean J Orthod 2018;48(1):3-10]
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