title: Common 3-dimensional coordinate system for assessment of directional changes.
abstract: BACKGROUND
  The aims of this study were to evaluate how head orientation interferes with the amounts of directional change in 3-dimensional (3D) space and to propose a method to obtain a common coordinate system using 3D surface models.
  
  
  METHODS
  Three-dimensional volumetric label maps were built for pretreatment (T1) and posttreatment (T2) from cone-beam computed tomography images of 30 growing subjects. Seven landmarks were labeled in all T1 and T2 volumetric label maps. Registrations of T1 and T2 images relative to the cranial base were performed, and 3D surface models were generated. All T1 surface models were moved by orienting the Frankfort horizontal, midsagittal, and transporionic planes to match the axial, sagittal, and coronal planes, respectively, at a common coordinate system in the Slicer software (open-source, version 4.3.1; http://www.slicer.org). The matrix generated for each T1 model was applied to each corresponding registered T2 surface model, obtaining a common head orientation. The 3D differences between the T1 and registered T2 models, and the amounts of directional change in each plane of the 3D space, were quantified for before and after head orientation. Two assessments were performed: (1) at 1 time point (mandibular width and length), and (2) for longitudinal changes (maxillary and mandibular differences). The differences between measurements before and after head orientation were quantified. Statistical analysis was performed by evaluating the means and standard deviations with paired t tests (mandibular width and length) and Wilcoxon tests (longitudinal changes). For 16 subjects, 2 observers working independently performed the head orientations twice with a 1-week interval between them. Intraclass correlation coefficients and the Bland-Altman method tested intraobserver and interobserver agreements of the x, y, and z coordinates for 7 landmarks.
  
  
  RESULTS
  The 3D differences were not affected by the head orientation. The amounts of directional change in each plane of 3D space at 1 time point were strongly influenced by head orientation. The longitudinal changes in each plane of 3D space showed differences smaller than 0.5 mm. Excellent intraobserver and interobserver repeatability and reproducibility (>99%) were observed.
  
  
  CONCLUSIONS
  The amount of directional change in each plane of 3D space is strongly influenced by head orientation. The proposed method of head orientation to obtain a common 3D coordinate system is reproducible.
authors.affiliation: Associate professor, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; Brazilian National Counsel of Technological and Scientific Development (CNPq) researcher, postdoctoral fellow, School of Dentistry, University of Michigan, Ann Arbor, Mich. Electronic address: antonioruellas@yahoo.com.br.
authors.forename: Antonio Carlos de Oliveira
authors.initials: AC
authors.lastname: Ruellas
authors.affiliation: Postgraduate student, University of São Paulo, São Paulo, Brazil; visiting student, School of Dentistry, University of Michigan, Ann Arbor, Mich.
authors.forename: Cristiano
authors.initials: C
authors.lastname: Tonello
authors.affiliation: Postgraduate student, Araraquara Dental School, Paulista State University, Araraquara, São Paulo, Brazil.
authors.forename: Liliane Rosas
authors.initials: LR
authors.lastname: Gomes
authors.affiliation: Postgraduate student, Bauru Dental School, University of São Paulo, Bauru, Brazil.
authors.forename: Marilia Sayako
authors.initials: MS
authors.lastname: Yatabe
authors.affiliation: Graduate student, School of Chemistry Electronics and Telecommunications, Lyon, France; intern, School of Dentistry, University of Michigan, Ann Arbor, Mich.
authors.forename: Lucie
authors.initials: L
authors.lastname: Macron
authors.affiliation: Graduate student, School of Chemistry Electronics and Telecommunications, Lyon, France; intern, School of Dentistry, University of Michigan, Ann Arbor, Mich.
authors.forename: Julia
authors.initials: J
authors.lastname: Lopinto
authors.affiliation: Associate professor, Department of Pediatric Dentistry, Araraquara Dental School, Paulista State University, Araraquara, São Paulo, Brazil.
authors.forename: Joao Roberto
authors.initials: JR
authors.lastname: Goncalves
authors.affiliation: Associate professor, Bauru Dental School and Hospital for Rehabilitation of Craniofacial Anomalies, University of São Paulo, Bauru, Brazil.
authors.forename: Daniela Gamba
authors.initials: DG
authors.lastname: Garib Carreira
authors.affiliation: Associate professor, Department of Plastic Surgery, University of São Paulo, Brazilian National Counsel of Technological and Scientific Development (CNPq) researcher. São Paulo, Brazil.
authors.forename: Nivaldo
authors.initials: N
authors.lastname: Alonso
authors.affiliation: Associate professor, Graduate Program in Orthodontics, Pontifical Catholic University of Minas Gerais, Belo Horizonte, Brazil.
authors.forename: Bernardo Quiroga
authors.initials: BQ
authors.lastname: Souki
authors.affiliation: Assistant professor, Department of Health, Southwest Bahia State University, Jequié, Bahia, Brazil.
authors.forename: Raildo da Silva
authors.initials: Rda S
authors.lastname: Coqueiro
authors.affiliation: Assistant professor, Department of Orthodontics and Pediatric Dentistry, School of Dentistry, University of Michigan, Ann Arbor, Mich.
authors.forename: Lucia Helena Soares
authors.initials: LH
authors.lastname: Cevidanes
mesh_terms: D000293:Adolescent; D002648:Child; D003198:Computer Simulation; D006257:Head; D006801:Humans; D021621:Imaging, Three-Dimensional; D008334:Mandible / Q000033:anatomy & histology*; D008953:Models, Anatomic; D015588:Observer Variation; D000072458:Orientation, Spatial