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Chin J Dent Res. 2014;17(1):37-42.

Three-dimensional analysis using finite element method of anterior teeth inclination and center of resistance location.



To locate the centre of resistance of consolidated units of four and six anterior teeth during retraction.


Twelve three-dimensional (3D) models were designed in SolidWorks of the anterior segment with four and six teeth and their supporting structure. A proper force system was applied in each model to retract the teeth bodily. The exact location of the centre of resistances (CRes) was determined. It was found that the path of CRes change in four-tooth and six-tooth units according to the anterior teeth torque.


A posterior shift of the CRes by increasing the inclination of teeth was shown. However, vertical position has a fluctuant behaviour. First it moves apically, then it moves incisally. Furthermore, results suggest that in en masse retraction, translation can be achieved with a smaller amount of moment-to-force ratio than in four-incisor retraction. In other words, for bodily retraction of anterior incisor segments, we should apply force in a more apical position.


Different anterior torques between 7 and 35 degrees, cannot affect the CRes position dramatically. The area of CRes shifting is 0.92 mm (anterioposteriorly) x 0.74 mm (superior-inferiorly) in the six-tooth unit in the teeth model and 0.85 mm (anterioposteriorly) x 0.82 mm (superior-inferiorly) in the teeth and bone model. In the four-tooth model, the area of CRes shifting is 0.97 mm (anterioposteriorly) x 0.93 mm (superior-inferiorly) in tooth model and 0.77 mm (anterioposteriorly) x 0.87 mm (superior-inferiorly) in the teeth and bone model.

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