An evaluation of the shape of some popular nickel titanium alloy preformed arch wires

The mathematical Beta function is shown to be an accurate planar representation of the natural human arch form defined by the spacial coordinates of the labial and buccal dental/bracket interfacing surfaces in the maxillary and mandibular arches. Graphic planar representations of the corresponding bracket base spacial coordinates of 33 popular preformed nickel titanium arch wires and bracket assemblies were superimposed on each of the relevant maxillary and mandibular natural forms, The arch forms of the preformed nickel titanium arch wires and bracket assemblies did not emulate the natural human arch form. The average mandibular natural human arch form first molar/canine width ratio is 2.38/1; the same preformed arch wire/bracket ratio is 1.87/1. These ratios for the maxillary arch are 1.92/1 and 1.54/1, respectively. The average canine width exceeded the natural canine width by 5.95 mm in the mandibular arch and 8.23 mm in the maxillary arch. The corresponding mandibular first molar and maxillary first molar widths exceeded the natural human first molar arch width by 0.84 mm and 2.68 mm, respectively. These findings have implications with respect to posttreatment stability and facial esthetics. "Round tripping" teeth resulting from subsequent change to stainless steel arch wires to restore a more natural human arch form and size may result in deleterious tissue effects.