A simple mathematical study of anterior dental relations: Part I.

A mathematical study of the anterior dental relations could provide a rationale for the work of Neff and Bolton. Bolton used normal occlusions of permanent teeth to obtain his range of comparisons of tooth width ratios; a model that needs no normals is described in this study. Use of this model and its development could support or disprove further hypotheses regarding anterior occlusion. Manipulation of the model could allow a means of estimating the influence of several dental measurement variables on the relation between upper and lower dental arches. The formulae allow changes in the form and size of one or both arches individually and a comparison of an upper arch to different upper arches and a lower arch to different lower arches; and further, they allow these combinations of upper and lower arches to relate to each other. A reference plane between the arches is established to relate opposing arches to each other. The model is developed using the archform and angular measures of Bonwill and the mesiodistal widths of Bolton. Scope is provided in the model to allow for alteration of antero-posterior relations, spacing and crowding. Values for different amounts of overjet of incisors and maxillary canine tip could be generated by altering the figures to those of other authors' hypotheticals or by the use of individual patient data.