title: Quantification of three-dimensional vertebral rotations in scoliosis: what are the true values?
abstract: METHODS
  The aim of this study is to quantify differences between three-dimensional rotations in space and their calculated values, either on two-dimensional projections (radiographs or computed tomographic scans) or three-dimensional calculations using various mathematical procedures.
  
  
  OBJECTIVE
  To use a vertebral model to quantify differences between three-dimensional rotations and their calculated values, using two-dimensional projections or various three-dimensional mathematical procedures.
  
  
  METHODS
  A specific program allowed us to move a geometric vertebral model in space using given values and sequences of lateral, sagittal, and axial rotations. Differences in positions due to different sequences were visualized and quantified. Differences due to rotation around global or vertebral axes were considered.
  
  
  RESULTS
  For rotations of about 10 degrees, differences are about 2 degrees between three-dimensional and projected angles. Differences increase when combined rotations are large, as generally occurs in a scoliotic spine. They reach 16 degrees for lateral and sagittal rotations of 30 degrees.
  
  
  CONCLUSIONS
  Axial rotation measured on transverse projection is misleading for vertebrae rotated in space. Moreover, dealing with large three-dimensional rotations is meaningful only if the used mathematical convention is given.
authors.affiliation: Laboratoire de Biomécanique, Ecole Nationale Supérieure d'Arts et Métiers (ENSAM), Paris, France.
authors.forename: W
authors.initials: W
authors.lastname: Skalli
authors.forename: F
authors.initials: F
authors.lastname: Lavaste
authors.forename: J L
authors.initials: JL
authors.lastname: Descrimes
mesh_terms: D003198:Computer Simulation; D006801:Humans; D008433:Mathematics; D012600:Scoliosis / Q000000981:diagnostic imaging / Q000473:pathology*; D013131:Spine / Q000000981:diagnostic imaging / Q000473:pathology*; D014057:Tomography, X-Ray Computed