A finite element analysis of the optimal bending angles in a running loop for mesial translation of a mandibular molar using indirect skeletal anchorage.

OBJECTIVES: To estimate the optimal bending angles in the running loop for mesial translation of a mandibular second molar using indirect skeletal anchorage and to clarify the mechanics of tipping and rotating the molar.

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 the force systems.

RESULTS: When using a running loop without bends, the molar tipped mesially 14.4° and lingually 0.6°, rotated counterclockwise 4.1°, and the incisors retracted 0.02 mm and intruded 0.05 mm. These angles were about the same as those estimated by the beam theory. When the amount of tip back and toe-in angles was 11.0°, mesial translation of the molar was achieved, and incisors retracted 0.10 mm and intruded 0.30 mm.

CONCLUSIONS: Mesial translation of a mandibular second molar without any significant movement of anterior teeth was achieved during protraction by controlling the tip back and toe-in angles and enhancing anterior anchorage with the combined use of a running loop and indirect skeletal anchorage.