INTRODUCTION: This investigation was carried out to correlate the normal arch forms of male and female subjects derived mathematically by the beta function with commercially available preformed rectangular nickel-titanium archwires. METHODS: The mathematical beta function was used to derive planar projections of natural archforms by using the spatial coordinates of the labial bracket interfacing surfaces in the maxillary and mandibular arches of both sexes. Graphic planar representations of corresponding bracket base spatial coordinates of archforms of 30 popular rectangular nickel-titanium archwire-bracket assemblies (derived through the same mathematical function) were superimposed on relevant maxillary and mandibular arches. RESULTS: The rectangular nickel-titanium archwire-bracket assemblies exceeded the intercanine width by averages of 7.159 mm in the maxillary arches of females, 6.289 mm in the maxillary arches of males, 6.667 mm in the mandibular arches of females, and 5.337 mm in the mandibular arches of males. The average intermolar width exceeded the natural width by 2.893 mm in the maxillary arches and 1.861 mm in the mandibular arches. The average intermolar-intercanine width ratios for natural arches (2.11 for mandibular and 1.75 for maxillary) were greater than the ratios for the wire-bracket assemblies (1.78 for mandibular and 1.53 for maxillary). CONCLUSIONS: The prefomed rectangular nickel-titanium archwires might result in wider arch forms. The intercanine width difference is greater than the intermolar width. The differences were more pronounced for arches in female subjects compared with those in males. These findings influence posttreatment retention, stability, and facial esthetics. A subsequent change to stainless steel wires to restore a more natural form and size can lead to round tripping and increased treatment duration.
INTRODUCTION: This investigation was carried out to correlate the normal arch forms of male and female subjects derived mathematically by the beta function with commercially available preformed rectangular nickel-titanium archwires. METHODS: The mathematical beta function was used to derive planar projections of natural archforms by using the spatial coordinates of the labial bracket interfacing surfaces in the maxillary and mandibular arches of both sexes. Graphic planar representations of corresponding bracket base spatial coordinates of archforms of 30 popular rectangular nickel-titanium archwire-bracket assemblies (derived through the same mathematical function) were superimposed on relevant maxillary and mandibular arches. RESULTS: The rectangular nickel-titanium archwire-bracket assemblies exceeded the intercanine width by averages of 7.159 mm in the maxillary arches of females, 6.289 mm in the maxillary arches of males, 6.667 mm in the mandibular arches of females, and 5.337 mm in the mandibular arches of males. The average intermolar width exceeded the natural width by 2.893 mm in the maxillary arches and 1.861 mm in the mandibular arches. The average intermolar-intercanine width ratios for natural arches (2.11 for mandibular and 1.75 for maxillary) were greater than the ratios for the wire-bracket assemblies (1.78 for mandibular and 1.53 for maxillary). CONCLUSIONS: The prefomed rectangular nickel-titanium archwires might result in wider arch forms. The intercanine width difference is greater than the intermolar width. The differences were more pronounced for arches in female subjects compared with those in males. These findings influence posttreatment retention, stability, and facial esthetics. A subsequent change to stainless steel wires to restore a more natural form and size can lead to round tripping and increased treatment duration.