### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 185-192 |

Number of pages | 8 |

Journal | Biomedical Engineering - Applications, Basis and Communications |

Volume | 12 |

Issue number | 4 |

State | Published - Aug 25 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- 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

### Cite this

*Biomedical Engineering - Applications, Basis and Communications*,

*12*(4), 185-192.

**Shear stress distributions in porous cross sections of longitudinally twisted bone.** / Pao, Y. C.; Ritman, E. L.

Research output: Contribution to journal › Article

*Biomedical Engineering - Applications, Basis and Communications*, vol. 12, no. 4, pp. 185-192.

}

TY - JOUR

T1 - Shear stress distributions in porous cross sections of longitudinally twisted bone

AU - Pao, Y. C.

AU - Ritman, E. L.

PY - 2000/8/25

Y1 - 2000/8/25

N2 - 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.

AB - 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.

KW - Gauss-Seidel iteration with pointer-matrix

KW - Micro-CT binary data

KW - Mixed finite-element and finite-difference derivation

KW - Porous cross sections

KW - Torsional warping and shear stresses

UR - http://www.scopus.com/inward/record.url?scp=0034714013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034714013&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034714013

VL - 12

SP - 185

EP - 192

JO - Biomedical Engineering - Applications, Basis and Communications

JF - Biomedical Engineering - Applications, Basis and Communications

SN - 1016-2372

IS - 4

ER -