title: Do alterations in vertebral and disc dimensions affect an elliptical model of thoracic kyphosis?
abstract: METHODS
  Mathematical modeling, using least squares method, of thoracic kyphosis was constructed as digitized points from radiographs of 50 healthy patients.
  
  
  OBJECTIVE
  To determine a simple geometric model of the thoracic kyphosis.
  
  
  BACKGROUND
  Thoracic kyphosis is an important parameter of health, but geometric models of kyphosis are rare. Few papers report vertebral body and disc height data.
  
  
  METHODS
  Thoracic vertebral bodies were digitized on lateral radiographs of 50 healthy patients. The average path of the posterior vertebral body corners of T1 through T12 was modeled, in the least squares sense, with a portion of an ellipse. The best-fit ellipse was sectioned with different model partitions using four sets of vertebral body heights and disc heights. Segmental and global angles derived from these four models were compared with reported values in the literature.
  
  
  RESULTS
  A 72 degrees portion of an ellipse, with a minor-to-major axis ratio of 0.69, can closely approximate the path of the posterior body corners from the inferior of T1 to the superior of T12. The posterior vertebral body heights and disc heights have an average ratio of approximately 5:1. Segmental angles from T3-T4 through T11-T12 for all four models are close to other reported values. The thoracic spine has a height-to-length ratio of approximately 0.96.
  
  
  CONCLUSIONS
  Thoracic kyphosis from inferior-posterior T1 to superior-posterior T12 can be closely modeled (least squares error per point < 1 mm) with a 72 degrees piece of an ellipse with a minor-to-major axis ratio of 0.69. The major axis is parallel to the posterior body margin of T12, whereas the minor axis passes through the superior endplate of T12. Segmental angles derived from this elliptical modeling are in the range of values from healthy patients.
authors.affiliation: Biomechanics Laboratory, University of Quebec at Three Rivers, Quebec, Canada. cbpdcs@idealspine.com
authors.forename: Donald D
authors.initials: DD
authors.lastname: Harrison
authors.forename: Deed E
authors.initials: DE
authors.lastname: Harrison
authors.forename: Tadeusz J
authors.initials: TJ
authors.lastname: Janik
authors.forename: Rene
authors.initials: R
authors.lastname: Cailliet
authors.forename: Jason
authors.initials: J
authors.lastname: Haas
mesh_terms: D006801:Humans; D007403:Intervertebral Disc / Q000000981:diagnostic imaging / Q000473:pathology*; D007738:Kyphosis / Q000473:pathology*; D008159:Lumbar Vertebrae / Q000000981:diagnostic imaging / Q000473:pathology*; D008962:Models, Theoretical; D011859:Radiography; D013904:Thoracic Vertebrae / Q000473:pathology*