A morphological study of the relationship between arch dimensions and craniofacial structures in adolescents with Class II Division 1 malocclusions and various facial types

Introduction: The objective of this study was to evaluate dental arch forms associated with various facial types in adolescents with Class II Division 1 malocclusions by using mathematical functions to describe the arch form at clinical bracket points. Methods: Pretreatment lateral cephalograms and dental study casts of 73 white Brazilians were divided into 3 groups according to facial type: 17 brachyfacial, 24 mesofacial, and 32 dolichofacial. Fifteen landmarks on each dental cast were digitized. Computer-generated mathematical arch forms (fourth-degree polynomial equation and beta function) were used to evaluate arch form differences by superimposition. Results: The constant term related to dental arch depth of the brachyfacial subjects was significantly greater than that of the mesofacial subjects in the maxillary arch (P = .004). Superimposition of maxillary arch analysis showed that the posterior segment width of the mathematically computed arch form tended to increase from dolichofacial type to brachyfacial type. The arch forms drawn by the 2 equations coincided at the incisal and molar regions. Conclusions: The beta function is appropriate for predicting the finishing arch form, and the polynomial equation is appropriate for the analysis (diagnosis) of various Class II malocclusions, including ovoid, tapered, and square arch forms and dental arch asymmetry.