Application of a Fourier series to analysis of the relationship between mandibular form and facial morphology.

The shape of the mandible is used by orthodontists as an aid to orthodontic treatment planning, with different shapes displaying different growth characteristics and being associated with different functional patterns. However, the quantification of shape using conventional linear and angular variables does not always include details of some of the more subtle aspects of form. Fourier analysis enables accurate representation, with few coefficients, of a mandibular outer line from articulare to infradentale. The aim of this study was to investigate, using a cluster analysis, the relationship between variation in mandibular form and overall facial morphology. A cluster analysis of the Fourier amplitudes classified mandibular forms into one of seven groups for both males and females. The cluster analysis showed that the gonial angle and the inclination of lower incisor were associated with facial type according to the mandibular variables. Furthermore, the Fourier descriptions of mandibular form could be related to the observed variation in facial form, each of the clusters based on mandibular form being associated with demonstrable differences in dentofacial morphology.