Shear stress distributions in porous cross sections of longitudinally twisted bone

Y. C. Pao, E. L. Ritman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Controlled torsion of bone specimens (usually a rodent) is used to pin-point where the maximum shear stresses occur in the bone and to provide an index of bone strength. A method has been developed which (1) makes direct application of the binary representation of the computed tomography images of porous cross sections of the long bone twisted about its long axis to carry out the automatic, finite-element partitioning, (2) identifies the different boundary conditions for the warping analysis of any selected cross section, and (3) subsequently computes and plots the spatial distribution of computed shear stress. The governing stiffness-matrix equation for the warping function is formulated with a mixed finite-element and finite-difference approach and it is solved with a resumable, interactive process based on the pointer-matrix, Gauss-Seidel method. The developed computational algorithms have been thoroughly tested with the classical cases of non-circular (square and thin-walled tubes) cross sections. The computed warping and shear stress distributions are found to be in agreement with these textbook examples. The developed method can be applied for mapping the shear stress distribution in any transverse cross section of a longitudinally twisted bone. As illustrative examples, the warping and shear stress distributions in two transverse cross sections of a longitudinally twisted mouse femur are presented in the form of color contour maps.

Original languageEnglish (US)
Pages (from-to)185-192
Number of pages8
JournalBiomedical Engineering - Applications, Basis and Communications
Issue number4
StatePublished - Aug 25 2000


  • Gauss-Seidel iteration with pointer-matrix
  • Micro-CT binary data
  • Mixed finite-element and finite-difference derivation
  • Porous cross sections
  • Torsional warping and shear stresses

ASJC Scopus subject areas

  • Biophysics
  • Bioengineering
  • Biomedical Engineering


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