Internal strain gradients quantified in bone under load using high-energy X-ray scattering

S. R. Stock*, Fang Yuan, L. C. Brinson, J. D. Almer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


High-energy synchrotron X-ray scattering (>60. keV) allows noninvasive quantification of internal strains within bone. In this proof-of-principle study, wide angle X-ray scattering maps internal strain vs position in cortical bone (murine tibia, bovine femur) under compression, specifically using the response of the mineral phase of carbonated hydroxyapatite. The technique relies on the response of the carbonated hydroxyapatite unit cells and their Debye cones (from nanocrystals correctly oriented for diffraction) to applied stress. Unstressed, the Debye cones produce circular rings on the two-dimensional X-ray detector while applied stress deforms the rings to ellipses centered on the transmitted beam. Ring ellipticity is then converted to strain via standard methods. Strain is measured repeatedly, at each specimen location for each applied stress. Experimental strains from wide angle X-ray scattering and an attached strain gage show bending of the rat tibia and agree qualitatively with results of a simplified finite element model. At their greatest, the apatite-derived strains approach 2500 με on one side of the tibia and are near zero on the other. Strains maps around a hole in the femoral bone block demonstrate the effect of the stress concentrator as loading increased and agree qualitatively with the finite element model. Experimentally, residual strains of approximately 2000 μ ε are present initially, and strain rises to approximately 4500 μ ε at 95. MPa applied stress (about 1000 μ ε above the strain in the surrounding material). The experimental data suggest uneven loading which is reproduced qualitatively with finite element modeling.

Original languageEnglish (US)
Pages (from-to)291-296
Number of pages6
JournalJournal of Biomechanics
Issue number2
StatePublished - Jan 11 2011


  • Bone
  • Finite element analysis
  • Internal stress measurement
  • Wide angle X-ray scattering (WAXS)
  • X-ray diffraction

ASJC Scopus subject areas

  • Biophysics
  • Orthopedics and Sports Medicine
  • Biomedical Engineering
  • Rehabilitation

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