Evaluation of the linearity of soft- to hard-tissue movement after orthognathic surgery

Introduction: Our aim in this study was to investigate whether a linear relationship exists between soft- to hard-tissue changes for both maxillary and mandibular landmarks over a wide range of skeletal changes. Methods: The sample consisted of 30 Chinese patients with Class III malocclusion treated with bilateral sagittal split osteotomy and LeFort I advancement. Lateral cephalograms were taken within 2 months before surgery and at least 6 months after surgery. Soft- and hard-tissue changes were recorded by computer supported measurements of presurgical and postsurgical lateral cephalograms. To evaluate the linear association between soft- and hard-tissue movement, a quadratic function of hard-tissue movement adjusted for sex was initially fitted to the data. The residual plots were used to examine the appropriateness of the fitted quadratic function, and the lack of fit was examined by the F test. A linear function was fitted to the data when the quadratic term was not significant. Results: Visual inspection of the scatter plots of the 5 pairs of corresponding soft- and hard-tissue landmarks showed that relationships between the soft and hard tissues were reasonably linear for both male and female subjects, except for the Sn-ANS pair that showed a curvilinear relationship. Statistical tests confirmed that the association for the Sn-ANS pair was quadratic. Conclusions: The results of this study provide evidence of a linear relationship between soft- to hard-tissue changes for mandibular landmarks over a wide range of skeletal changes. The nonlinear response of maxillary soft tissues to underlying hard-tissue change in the Sn-ANS pair supports the use of nonlinear ratios for selected maxillary soft- to hard-tissue movements in simulation software