Mechanical Efficacy Equivalence of W-Arch and Quad-Helix Orthodontic Arch Expansion Appliances: A Finite Element Study

The quad-helix and W-arch are commonly used appliances for expanding the dental arch in orthodontic treatment. However, differences in performance between these two expanders remain unclear, and no guidelines exist for selecting one over the other. The purpose of this study was to investigate whether there were differences in dental arch expanding ability between these appliances. Maxillary arch expansions were simulated using the finite element method. The expander was assumed to be an elastic beam, while the teeth and alveolar bone were treated as rigid bodies. The periodontal ligament (PDL) was modeled as a nonlinear elastic material. The teeth moved in the same direction as the initial movement caused by the elastic deformation of the PDL. The right and left canines, premolars, and first molars were expanded symmetrically in either parallel or fan shapes. When the wire diameter of the W-arch was set to 0.032 inches its stiffness became equivalent to that of a quad-helix with a wire diameter of 0.036 inches. Canines and premolars were expanded through tipping movements. The molars initially tipped buccally, then became upright and moved bodily. Both expanders expanded the arch in almost the same manner. There was no difference in arch expansion ability between the W-arch made of 0.032-inch wire and the quad-helix made of 0.036-inch wire. The W-arch may be preferred as the first choice due to its simpler structure compared to the quad-helix.