Continuous arch wire closing loop design, optimization, and verification. Part I

In Part I, a systematic approach to closing loop design for use in continuous arch wires is presented. The design process uses Castigliano's theorem to derive equations for moment-to-force ratio (M/F) in terms of loop geometry. The equations are used to optimize designs by optimizing M/F to produce tooth movement via translation. Further refinements are performed with finite element simulations of designs. In Part II, predicted results are verified experimentally. The result of this process is a new design, the Opus loop, which is capable of delivering a nonvarying target M/F within the range of 8.0 to 9.1 mm inherently, without adding residual moments via twist or bends (commonly gable bends) anywhere in the arch wire or loop before insertion. The resulting precise force systems delivered with nonvarying M/F can move groups of teeth more accurately to achieve predetermined anteroposterior treatment goals for esthetics and/or stability. In Part II the experimental results show that the loops must be bent accurately to achieve their design potential. The negative impact on M/F of various dimensional changes to the loop design are presented. Experimental data are presented illustrating the improved performance of the new design over standard available designs. Suggested applications of the design for varying anchorage requirements are presented, along with a case report in which rigorous protraction requirements were met.