title: A method for calculating the exact angle required during pedicle subtraction osteotomy for fixed sagittal deformity: comparison with the trigonometric method.
abstract: OBJECTIVE
  Pedicle subtraction osteotomy (PSO) has emerged as a powerful procedure for correcting fixed sagittal deformity. There has only been one attempt to quantify the magnitude of correction needed to restore sagittal balance; the trigonometric method for calculating the desired PSO angle is an approximation. We propose a method for calculating the exact angle required for PSO and explore how this angle differs from that obtained via the trigonometric method in illustrative cases.
  
  
  METHODS
  We conducted a mathematical analysis of the spine with application in illustrative cases. The trigonometric method calculates the necessary angular correction at the axial level of the PSO, but along the sacral vertical line. However, the angular measurement should take place at the true axis of rotation, the apex of the PSO. Measurements were taken from full-length standing x-rays, and both methods were explored.
  
  
  RESULTS
  The trigonometric method for calculating PSO angle is an exact measurement only if the apex of the PSO site lies on the sacral vertical line. As the apex of the PSO site moves anterior to that line, the trigonometric approximation underestimates the actual angle. As the apex of the PSO moves posterior to that line, the trigonometric approximation overestimates the actual angle.
  
  
  CONCLUSIONS
  The trigonometric method for calculating the PSO angle required for surgical deformity correction is an approximation, but its validity in clinical practice was confirmed by this study. The exact angle is obtained by a method centered on the apex of the PSO site. Although the difference between these angles is small, it is an important conceptual point for spine surgeons. Measurement of the exact angle is easily performed and should replace the trigonometric method for calculating the required PSO angle when standard digital measurement tools are available.
authors.affiliation: Department of Neurological Surgery, Feinberg School of Medicine, Northwestern University, Chicago, Illinois 60611, USA. b-yang1@md.northwestern.edu
authors.forename: Benson P
authors.initials: BP
authors.lastname: Yang
authors.forename: Stephen L
authors.initials: SL
authors.lastname: Ondra
mesh_terms: D000368:Aged; D000465:Algorithms; D005260:Female; D006801:Humans; D007738:Kyphosis / Q000000981:diagnostic imaging* / Q000601:surgery*; D007796:Laminectomy / Q000379:methods*; D008875:Middle Aged; D010027:Osteotomy / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013131:Spine / Q000002:abnormalities* / Q000601:surgery*; D016896:Treatment Outcome