Quantification of function regulator therapy using elliptical Fourier functions.

The application of various functional appliances to correct antero-posterior skeletal discrepancies in the treatment of Class III malocclusion has received increased attention. In this context, elliptical Fourier functions (EFF) are particularly useful for eliciting boundary-outline information. This longitudinal study was undertaken to visually and numerically describe the shape alterations arising as a response to treatment with the FR-3 appliance of Fränkel. The subjects chosen were Caucasians (n = 14) from the Glasgow Dental Hospital and School who presented with Class III incisor relationships. Lateral cephalometric head-films were available prior to the initiation of treatment, at the end of active treatment, and at least one year out of retention. Maxillary and mandibular boundary outlines were carefully traced. A set of points, 42 on the maxilla, and 78 on the mandible, were precisely located. These points were then digitized and used to compute EFF's with 20 harmonics. These equations were then standardized for size. Subsequently, 102 maxillary and 150 mandibular closely spaced points on the outline were calculated from the EFF's. After superimposition on the centroid, expected vectors were then computed to these points from the centroid. Statistically significant dento-alveolar shape changes could be discerned with treatment. These involved a localized anterior repositioning of the maxillary incisal aspect with a concomitant posterior displacement of the mandibular incisal aspect. There was no evidence of shape changes in the basal areas of either the maxilla or mandible. This method of fitting Fourier descriptors, specifically EFF's, provides a precise numerical and visual description of the changes arising from functional regulator therapy.