title: Optimizing finite element predictions of local subchondral bone structural stiffness using neural network-derived density-modulus relationships for proximal tibial subchondral cortical and trabecular bone.
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. However, it is unclear what density-modulus equation(s) should be applied with subchondral cortical and subchondral trabecular bone when constructing finite element models of the tibia. Using a novel approach applying neural networks, optimization, and back-calculation against in situ experimental testing results, the objective of this study was to identify subchondral-specific equations that optimized finite element predictions of local structural stiffness at the proximal tibial subchondral surface.
  
  
  METHODS
  Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using multiple density-modulus equations (93 total variations) then mapped to corresponding finite element models. For each variation, root mean squared error was calculated between finite element prediction and in situ measured stiffness at 47 indentation sites. Resulting errors were used to train an artificial neural network, which provided an unlimited number of model variations, with corresponding error, for predicting stiffness at the subchondral bone surface. Nelder-Mead optimization was used to identify optimum density-modulus equations for predicting stiffness.
  
  
  RESULTS
  Finite element modeling predicted 81% of experimental stiffness variance (with 10.5% error) using optimized equations for subchondral cortical and trabecular bone differentiated with a 0.5g/cm3density.
  
  
  CONCLUSIONS
  In comparison with published density-modulus relationships, optimized equations offered improved predictions of local subchondral structural stiffness. Further research is needed with anisotropy inclusion, a smaller voxel size and de-blurring algorithms to improve predictions.
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: Institute for Lightweight Design and Structural Biomechanics, Vienna University of Technology, Vienna, Austria.
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, University of British Columbia, Centre for Hip Health and Mobility, Vancouver, Canada.
authors.forename: Bassam A
authors.initials: BA
authors.lastname: Masri
authors.affiliation: Department of Orthopaedics, University of British Columbia, Centre for Hip Health and Mobility, Vancouver, 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; D000071556:Cancellous Bone / Q000502:physiology*; D000071538:Cortical Bone / Q000502:physiology*; D055119:Elastic Modulus; D005260:Female; D020342:Finite Element Analysis; D006801:Humans; D008297:Male; D008875:Middle Aged; D016571:Neural Networks, Computer; D020370:Osteoarthritis, Knee / Q000000981:diagnostic imaging / Q000473:pathology / Q000503:physiopathology; D013977:Tibia / Q000502:physiology*; D014057:Tomography, X-Ray Computed
keywords: Density-modulus relationships for bone; Finite element modeling; Neural network; Proximal tibia; Subchondral bone