Mechanical force system of double key loop with finite element analysis

The mechanics of double key loop (DKL) are not well defined, and this finite element study was designed to explore its force system.

A simplified 3-dimensional finite element model of single and double key loops with an archwire between the lateral incisor and second premolar was established in Ansys Workbench 17.0. Activation in Type-1 (retraction at the distal end), Type-2 (retraction at the distal key) and Type-3 (Type-2 plus ligation between keys) was simulated. The vertical force, load/deflection ratio and moment/force ratio of stainless-steel and titanium-molybdenum alloy (TMA) loops were calculated and compared.

The double key loop generated approximately 40% of the force of a single key loop. Type-2 loading of DKL showed a higher L/D ratio than Type-1 loading with a similar M/F ratio. Type-3 loading of DKL showed the highest M/F ratio with a similar L/D ratio as single key loop. The M/F ratio in Type-3 loading increased with the decreasing of retraction force. The DKL of TMA produced approximately 40% of the force and moment compared with those of SS in all loading types. When activated at equal distances below 1 mm, the M/F ratios of SS and TMA DKL with equal preactivation angles were almost the same.

The M/F ratio on anterior teeth increases with the preactivation angle and deactivation of DKL. The M/F ratio at a certain distance of activation mainly depends on the preactivation angle instead of the wire material. TMA is recommended as a substitute for SS in DKL for a lower magnitude of force.