title: Glenoid diameter is an inaccurate method for percent glenoid bone loss quantification: analysis and techniques for improved accuracy.
abstract: OBJECTIVE
  To compare diameter-based glenoid bone loss quantification with a true geometric calculation for the area of a circular segment.
  
  
  METHODS
  By use of Maxima 12.01.0 mathematics modeling software (Macysma, Boston, MA), the diameter-based glenoid bone loss equation (% Bone loss = [Defect width (w)/Inferior glenoid circle diameter (D)] × 100%) was compared with a true geometric calculation for the area of a circular segment of the glenoid (Wolfram Research, Champaign, IL) rearranged in terms of w and D: Percent bone loss = (100/2π) (2 × arccos [1 - 2 (w/D)] - sin {2 × arccos [1 - 2 (w/D)]}). Percent error was calculated by taking the difference between the diameter equation and the true geometric calculation at varying true glenoid defect widths (w) (0% to 50% of diameter).
  
  
  RESULTS
  The commonly used diameter equation overestimated true glenoid bone loss at all values of w except at 0% and 50% of the diameter. The mean overestimation error was 3.9% ± 1.9% (range, 0.0% to 5.8%), with the maximum error occurring when w was 20% of the diameter: At this value, w/D × 100% (diameter equation) predicts 20% bone loss when true bone loss is actually 14.2%.
  
  
  CONCLUSIONS
  Diameter-based glenoid bone loss quantification overestimates true glenoid bone loss, with the maximum error occurring when theorized bone loss is 20%. To address situations for which a diameter-based bone loss quantification method must be performed or to improve the accuracy of surface-area calculations in previous diameter-based bone loss estimations, a corrective factor can be applied. Clinicians quantifying glenoid loss to make treatment decisions should be aware of the measurement methods used in the biomechanical studies on which they are basing their surgical decisions.
  
  
  CONCLUSIONS
  Diameter-based glenoid bone loss quantification overestimates true glenoid bone loss, with the maximum error occurring when theorized bone loss is 20%, a commonly used threshold for bone grafting.
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.
authors.forename: Sanjeev
authors.initials: S
authors.lastname: Bhatia
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.
authors.forename: Anil
authors.initials: A
authors.lastname: Saigal
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.. Electronic address: rmfrank3@gmail.com.
authors.forename: Rachel M
authors.initials: RM
authors.lastname: Frank
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.
authors.forename: Bernard R
authors.initials: BR
authors.lastname: Bach
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.
authors.forename: Brian J
authors.initials: BJ
authors.lastname: Cole
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.
authors.forename: Anthony A
authors.initials: AA
authors.lastname: Romeo
authors.affiliation: Department of Orthopaedic Surgery, Rush University Medical Center, Chicago, Illinois, U.S.A.
authors.forename: Nikhil N
authors.initials: NN
authors.lastname: Verma
mesh_terms: D001862:Bone Resorption / Q000000981:diagnostic imaging / Q000473:pathology*; D061165:Glenoid Cavity / Q000000981:diagnostic imaging / Q000473:pathology*; D006801:Humans; D007593:Joint Instability / Q000000981:diagnostic imaging / Q000473:pathology / Q000601:surgery; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods; D012540:Scapula / Q000601:surgery; D012785:Shoulder Joint / Q000000981:diagnostic imaging / Q000473:pathology / Q000601:surgery; D014057:Tomography, X-Ray Computed / Q000379:methods