Abstract
Abstract
Background
Mesialization of a mandibular second molar into a first molar extraction site is among the least predictable movements in clear aligner therapy, because force delivered at crown level generates a moment about the centre of resistance. Auxiliary lever arms and elastics move the force vector apically, but the combined influence of lever arm angulation and elastic type has not been quantified.
Methods
Ten three-dimensional finite element models of a mandible with a missing first molar were built from cone-beam computed tomography data. Each included a 0.5 mm aligner, an attachment, a miniscrew and, where applicable, a button or a lever arm angulated 0°, 30° mesially or 30° distally to the molar long axis, with intramaxillary or Class II intermaxillary elastics. A single 0.25 mm activation with 1.5 N was simulated. Displacement of four cusp tips and two root apices was recorded along three axes, and for each axis the net displacement (translation) and the crown–root difference (rotation) were calculated separately. Von Mises stresses in the periodontal ligament were recorded.
Results
Mesial tipping predominated, being greatest with a buccal button and Class II elastics (ΔX − 0.158 µm) and smallest with a lever arm angulated 30° distally plus an intramaxillary elastic (ΔX − 0.002 µm). Net mesial translation was greatest in the two configurations that produced mesial root tipping (− 0.039 and − 0.042 µm). Vertical direction depended solely on elastic type: every Class II configuration extruded the molar and every intramaxillary configuration intruded it. The vertical crown–root difference correlated inversely with the transverse one (r = − 0.98) but only weakly with the sagittal one (r = − 0.18), indicating that it reflects transverse rather than vertical rotation. Peak von Mises stress correlated only moderately with total displacement (ρ = 0.65).
Conclusions
Elastic type appears to govern the vertical direction of molar movement, whereas the angulation of the lever arm governs the magnitude and direction of tipping. A lever arm angulated 30° distally combined with an intramaxillary elastic gave the lowest tipping, the lowest total displacement and the lowest periodontal ligament stress, and is considered the most balanced of the configurations examined.