Three-dimensional effects in retraction appliance design.

The clinical importance of the three-dimensional effects of the force systems supplied by appliance designs used for retraction has long been appreciated. However, quantification of these force systems is not as well known. In this work, a numerical method is used to provide quantitative insight into three-dimensional effects for typical appliance designs. One problem that occurs clinically is the axial rotation of a single rooted tooth as a result of the forces being applied by the retraction device on the tooth's buccal surface. An out-of-plane preactivated bend can be used to counteract this rotation. The proposed numerical method can accurately determine the force systems resulting from this out-of-plane preactivation as well as the in-plane force systems. It is shown that the out-of-plane effects are independent of the in-plane behaviour so that the usual forces and moment to force ratios are maintained.