title: A novel method for the three-dimensional (3-D) analysis of orthodontic tooth movement-calculation of rotation about and translation along the finite helical axis.
abstract: The purpose of this study was to establish a novel method for evaluating orthodontic tooth movement in three-dimensional (3-D) space. The present system consisted of the following procedures at a given treatment period: (1) 3-D tooth positions were measured with a 3-D surface-scanning system using a slit laser beam; (2) the 3-D shape data were registered automatically at the maxillary first molars, and the coordinate systems were normalized; (3) the rotation matrix and translation vector were calculated from the automatic registration of the two position data for a given tooth; (4) the finite helical axes of teeth were calculated as the locus of zero rotational displacement; and (5) tooth movement was presented as rotation about and translation along the finite helical axis. To test this system, a male patient (age 22 yr 2 months) with Angle Class III malocclusion and moderate crowding of the anterior teeth, who had been treated using a standard multi-bracket appliance, was used as a model case in this study. Impressions for a dental cast model were taken at five phases; immediately before and after application of the appliance, and 10 days, 1 month and 2 months after beginning treatment. The results demonstrated that the present analytical method can more simply describe the movement of a given tooth by rotation about and translation along the finite helical axis, and provides quantitative visual 3-D information on complicated tooth movement during orthodontic treatment.
authors.affiliation: School of Dentistry, Department of Orthodontics, Health Sciences University of Hokkaido, Kanazawa 1757, Ishikari-Tobetsu, 061-0293, Hokkaido, Japan. kazu@hoku-iryo-u.ac.jp
authors.forename: Kazuo
authors.initials: K
authors.lastname: Hayashi
authors.forename: Yoshima
authors.initials: Y
authors.lastname: Araki
authors.forename: Jun
authors.initials: J
authors.lastname: Uechi
authors.forename: Hiroki
authors.initials: H
authors.lastname: Ohno
authors.forename: Itaru
authors.initials: I
authors.lastname: Mizoguchi
mesh_terms: D000328:Adult; D006801:Humans; D021621:Imaging, Three-Dimensional; D008297:Male; D008433:Mathematics; D014087:Tooth Movement Techniques / Q000706:statistics & numerical data*