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A mathematical model was developed to compare quantitatively the effects of various types of orthodontic expansion on mandibular arch perimeter. Mandibular arch form was modeled with spline interpolation to fit a smooth curve between assigned molar, canine, and incisor positions. Starting with average arch dimensions, intermolar width, intercanine width, and midline arch length were increased individually and in combination in millimeter increments up to 5 mm, and the consequent changes in arch perimeter were measured. Increasing midline arch length by incisor advancement was nearly four times as effective in increasing arch perimeter as was molar expansion; canine expansion had an intermediate effect. Arch perimeter increments increased slightly with successive amounts of expansion for the molar, canine, and incisor. Combinations of molar-canine and canine-incisor expansion yielded results comparable to the total effects achieved by expansion of those teeth individually. Combined molar-canine expansion created increases in arch perimeter that were only slightly less than those generated by incisor advancement alone.
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