Individualized Catenary Curves: Their Relationship to Arch Form and Perimeter

Study casts of the lower arches of 35 children in whom arch alignment was considered acceptable, were examined using a reflex microscope. Arch perimeter was calculated mathematically from a method which required measurement of the mesio-distal widths of the teeth only. This was described as the 'overlap' method. Arch perimeter was also calculated using individualized catenary curves for each subject. Two calculations were made, recording arch width either at the distal contact points of the first permanent molars or between their mesio-buccal cusps. Arch perimeter measured from the length of the catenary curves was consistently shorter than that calculated by the overlap method. The variation ranged from 0.02 to 4.58 mm. The catenary constructed using the distal molar contacts gave a better representation of the actual arch form: the mean discrepancy was 2.36 mm, compared with 2.86 mm with the second method where arch width was measured between mesio-buccal cusps. Both techniques for calculation of arch perimeter were highly reproducible. The catenary curve only approximated arch form well when the arch was relatively narrow across the inter canine region. For square arches this method was unsatisfactory. It is suggested that alternative techniques would be more reliable and the overlap method described here is considered satisfactory.