Clinical implications of a mathematical-geometrical model to predict changes in the anterior arch dimension

Anterior arch length (AL) and the alterations in its dimension following incisor movements were shown to be predictable for an individual patient using a mathematical-geometrical model based on a third-degree parabola. Although the model has been validated previously, it is hard to apply in daily orthodontic routine. Thus, the aim of this study was to modify the model using different approaches to allow its establishment in daily routine.

This retrospective study was based on a study collective, which was described previously and consisted of 50 randomly chosen dental casts and lateral cephalograms taken before (T0) and after (T1) orthodontic treatment with fixed appliances. A JAVA computer program (Oracle, Austin, TX, USA) was developed to predict AL changes following therapeutic changes of arch width, depth or incisor inclination/position, taking the type of tooth movement into account. Performing exemplary AL calculations with the computer program, general rules and nomograms were set up, followed by multiple linear regression analyses to establish easy-to-use regression equations.

The JAVA computer program is available for download. Sagittal changes showed more effect on AL than transverse modifications. Protruding incisors increased AL, but also reduced overbite. The extent of alteration in AL depended on the initial depth, width, incisor inclination, tooth movement type and distance between the incisal edge and the centre of rotation.

The computer program precisely predicts individual changes in AL but is time-consuming. The presented regression equations and nomograms, considering metric variables, are easier to apply clinically and the differences compared to the AL calculated by the computer program are negligible.