RESUMO
PURPOSE: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: 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.
RESUMO
PURPOSE: For resolving anterior dental crowding or spacing, it is of key interest in personalised orthodontic diagnostics and treatment planning to predict the extent of space gained or lost in the anterior dental arch by changing incisor inclination or position. To facilitate the determination of anterior arch length (AL) and to predict its alterations following tooth movements, a mathematical-geometrical model, based on a third-degree parabola, was established. The aim of this study was to validate this model and assess its diagnostic precision. METHODS: This retrospective diagnostic study evaluated 50 randomly chosen dental casts taken before (T0) and after (T1) orthodontic treatment with fixed appliances. Plaster models were digitally photographed, allowing two-dimensional digital measurements of arch width, depth and length. A computer programme based on the mathematical-geometrical model to be validated was created to calculate AL for any given arch width and depth. Mean differences and correlation coefficients as well as Bland-Altman plots were used to compare the measured and the calculated (predicted) AL, evaluating the precision of the model. RESULTS: Inter- and intrarater reliability tests showed reliable measurements of arch width, depth and length. Measured and calculated (predicted) AL revealed high concordance according to concordance correlation coefficient (CCC), intraclass correlation coefficient (ICC), and Bland-Altman analyses and negligible differences between the mean values. CONCLUSIONS: The mathematical-geometrical model calculated anterior AL without significant difference to the measured AL, indicating its validity. The model can thus be used clinically for predicting alterations of AL following therapeutic changes of incisor inclination/position.
