title: Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship.
abstract: BACKGROUND
  Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error.
  
  
  METHODS
  Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points).
  
  
  RESULTS
  Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%.
  
  
  CONCLUSIONS
  Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness.
authors.affiliation: Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada. Electronic address: majid.nazemi@gmail.com.
authors.forename: S Majid
authors.initials: SM
authors.lastname: Nazemi
authors.affiliation: Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada.
authors.forename: Morteza
authors.initials: M
authors.lastname: Amini
authors.affiliation: College of Kinesiology, University of Saskatchewan, Saskatoon, Canada.
authors.forename: Saija A
authors.initials: SA
authors.lastname: Kontulainen
authors.affiliation: Robarts Research Institute, Western University, London, Canada.
authors.forename: Jaques S
authors.initials: JS
authors.lastname: Milner
authors.affiliation: Robarts Research Institute, Western University, London, Canada.
authors.forename: David W
authors.initials: DW
authors.lastname: Holdsworth
authors.affiliation: Department of Orthopaedics and Centre for Hip Health and Mobility, University of British Columbia, Vancouver, BC, Canada.
authors.forename: Bassam A
authors.initials: BA
authors.lastname: Masri
authors.affiliation: Department of Orthopaedics and Centre for Hip Health and Mobility, University of British Columbia, Vancouver, BC, Canada.
authors.forename: David R
authors.initials: DR
authors.lastname: Wilson
authors.affiliation: Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada. Electronic address: jd.johnston@usask.ca.
authors.forename: James D
authors.initials: JD
authors.lastname: Johnston
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D015519:Bone Density / Q000502:physiology; D002102:Cadaver; D019245:Compressive Strength / Q000502:physiology; D055119:Elastic Modulus / Q000502:physiology*; D005260:Female; D020342:Finite Element Analysis; D006801:Humans; D008297:Male; D008875:Middle Aged; D020370:Osteoarthritis, Knee / Q000000981:diagnostic imaging / Q000503:physiopathology*; D012044:Regression Analysis; D013314:Stress, Mechanical; D013977:Tibia / Q000000981:diagnostic imaging / Q000503:physiopathology*; D014057:Tomography, X-Ray Computed / Q000379:methods; D014129:Trabecular Meshwork / Q000502:physiology
keywords: Density–modulus relationships for bone; Elastic modulus of bone; Finite element modeling; Model validation; Proximal tibia