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

Publication ,  Journal Article
Stock, SR; Yuan, F; Brinson, LC; Almer, JD
Published in: Journal of biomechanics
January 2011

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 με are present initially, and strain rises to approximately 4500 με at 95 MPa applied stress (about 1000 με above the strain in the surrounding material). The experimental data suggest uneven loading which is reproduced qualitatively with finite element modeling.

Duke Scholars

Published In

Journal of biomechanics

DOI

EISSN

1873-2380

ISSN

0021-9290

Publication Date

January 2011

Volume

44

Issue

2

Start / End Page

291 / 296

Related Subject Headings

  • X-Rays
  • X-Ray Microtomography
  • Tibia
  • Synchrotrons
  • Stress, Mechanical
  • Scattering, Radiation
  • Rats, Sprague-Dawley
  • Rats
  • Pressure
  • Finite Element Analysis
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Stock, S. R., Yuan, F., Brinson, L. C., & Almer, J. D. (2011). Internal strain gradients quantified in bone under load using high-energy X-ray scattering. Journal of Biomechanics, 44(2), 291–296. https://doi.org/10.1016/j.jbiomech.2010.10.015
Stock, S. R., Fang Yuan, L. C. Brinson, and J. D. Almer. “Internal strain gradients quantified in bone under load using high-energy X-ray scattering.Journal of Biomechanics 44, no. 2 (January 2011): 291–96. https://doi.org/10.1016/j.jbiomech.2010.10.015.
Stock SR, Yuan F, Brinson LC, Almer JD. Internal strain gradients quantified in bone under load using high-energy X-ray scattering. Journal of biomechanics. 2011 Jan;44(2):291–6.
Stock, S. R., et al. “Internal strain gradients quantified in bone under load using high-energy X-ray scattering.Journal of Biomechanics, vol. 44, no. 2, Jan. 2011, pp. 291–96. Epmc, doi:10.1016/j.jbiomech.2010.10.015.
Stock SR, Yuan F, Brinson LC, Almer JD. Internal strain gradients quantified in bone under load using high-energy X-ray scattering. Journal of biomechanics. 2011 Jan;44(2):291–296.
Journal cover image

Published In

Journal of biomechanics

DOI

EISSN

1873-2380

ISSN

0021-9290

Publication Date

January 2011

Volume

44

Issue

2

Start / End Page

291 / 296

Related Subject Headings

  • X-Rays
  • X-Ray Microtomography
  • Tibia
  • Synchrotrons
  • Stress, Mechanical
  • Scattering, Radiation
  • Rats, Sprague-Dawley
  • Rats
  • Pressure
  • Finite Element Analysis