A novel measurement method for the morphology of the mandibular ramus using homologous modelling

Objectives: It is important to assess the mandibular morphology when orthognathic surgery, especially mandibular ramus osteotomy, is performed. Several studies on three-dimensional (3D) facial asymmetry have reported differences in linear and angle measurements between the deviated and contralateral sides in asymmetric mandibles. However, methods used in these studies cannot analyse the 3D morphology of the ramus. In this study, we aimed to evaluate the differences in mandibular ramus between the deviated and contralateral sides in asymmetric mandibles using traditional measurements as well as 3D shape analysis. Methods: 15 Japanese females with jaw deformities treated by orthodontic surgery were enrolled. 3D CT images were reconstructed, and 14 landmarks were identified on the model surface. Ten linear and four angle measurements were calculated using these landmarks. Homologous ramus models were constructed for each sample, and after converting all homologous models to the right side, 30 homologous models of the ramus were analysed using principal component analysis. Results: Firstly, eight principal components explained >80% of the total variance. Differences between the deviated and contralateral sides in measurements and scores of the eight principal components were tested. Significant difference at the 5% level between the deviated and contralateral sides was observed in five linear measurements, three angle measurements and the third principal component. The variance of the deviated side was significantly larger in the diameter between the mandibular notch and coronoid process, horizontal dilated angle of the mandibular ramus and vertical dilated angle of the mandibular ramus. The variance of the contralateral side was significantly larger in the height of mandibular ramus, height of posterior of mandibular ramus, condylar width, height of condylar head and mandibular angle. The squared multiple correlation coefficient adjusted for the degrees of freedom was 0.815. The third principal component showed the difference between the deviated and contralateral sides. Shape variation represented by the third principal component visually indicated that the contralateral side was larger and had inwardly directed coronoid process and the deviated side had a mandibular angle that was turned inwards to a greater extent. Conclusions: In conclusion, we successfully created a homologous model of the mandibular ramus and demonstrated the effectiveness of this model in the 3D comparison of the ramus morphology between the contralateral and deviated sides in asymmetric mandibles.