Applications of an anisotropic parameter to cortical bone

Sean Kohles

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

An equational description of the extent of the anisotropy in cortical bone is presented from both the perspective of plane stress (two-dimensional stress state) and plane strain (three-dimensional stress state). The orthotropic elastic properties that are incorporated in these states are used to provide a more thorough and refined description of planar and volumetric anisotropy in comparison to the commonly used ratio of elastic moduli. The resulting anistropic parametric equations (η(σ) and η(ε)) are applied to the elastic material properties measured from cortical bone within rats, dogs, cows and humans as reported in 12 previous studies. The resulting calculated parameters reduce the typically nine independent properties down to three parameters which in turn represent the degree of anisotropy within the three orthogonal planes of symmetry as are common in cortical bone. It was found that no statistical difference existed between the plane stress versus plane strain parameter in all but two studies (p > 0.10). Planar and volumetric anisotropies were compared to the isotropic condition (η(σ) = η(ε) = 1.0) for all of the included studies. All of the studies reported cortical bone properties that were volumetrically anisotropic (p <0.05), however, a common plane of isotropy was noted in the radial-circumferential (1-2) plane (p > 0.05). Future use of these parametric equations will allow further illucidation of the issue of mesomechanical and micromechanial levels of anisotropy within other tissues and materials of interest. (C) 2000 Kluwer Academic Publishers.

Original languageEnglish (US)
Pages (from-to)261-265
Number of pages5
JournalJournal of Materials Science: Materials in Medicine
Volume11
Issue number4
DOIs
StatePublished - 2000
Externally publishedYes

Fingerprint

Anisotropy
Bone
Elastic Modulus
Rats
Materials properties
Elastic moduli
Cortical Bone
Dogs
Tissue

ASJC Scopus subject areas

  • Biophysics
  • Chemical Engineering(all)
  • Bioengineering

Cite this

Applications of an anisotropic parameter to cortical bone. / Kohles, Sean.

In: Journal of Materials Science: Materials in Medicine, Vol. 11, No. 4, 2000, p. 261-265.

Research output: Contribution to journalArticle

@article{95be396e18c4449995d6c3306173200b,
title = "Applications of an anisotropic parameter to cortical bone",
abstract = "An equational description of the extent of the anisotropy in cortical bone is presented from both the perspective of plane stress (two-dimensional stress state) and plane strain (three-dimensional stress state). The orthotropic elastic properties that are incorporated in these states are used to provide a more thorough and refined description of planar and volumetric anisotropy in comparison to the commonly used ratio of elastic moduli. The resulting anistropic parametric equations (η(σ) and η(ε)) are applied to the elastic material properties measured from cortical bone within rats, dogs, cows and humans as reported in 12 previous studies. The resulting calculated parameters reduce the typically nine independent properties down to three parameters which in turn represent the degree of anisotropy within the three orthogonal planes of symmetry as are common in cortical bone. It was found that no statistical difference existed between the plane stress versus plane strain parameter in all but two studies (p > 0.10). Planar and volumetric anisotropies were compared to the isotropic condition (η(σ) = η(ε) = 1.0) for all of the included studies. All of the studies reported cortical bone properties that were volumetrically anisotropic (p <0.05), however, a common plane of isotropy was noted in the radial-circumferential (1-2) plane (p > 0.05). Future use of these parametric equations will allow further illucidation of the issue of mesomechanical and micromechanial levels of anisotropy within other tissues and materials of interest. (C) 2000 Kluwer Academic Publishers.",
author = "Sean Kohles",
year = "2000",
doi = "10.1023/A:1008940914693",
language = "English (US)",
volume = "11",
pages = "261--265",
journal = "Journal of Materials Science: Materials in Medicine",
issn = "0957-4530",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - Applications of an anisotropic parameter to cortical bone

AU - Kohles, Sean

PY - 2000

Y1 - 2000

N2 - An equational description of the extent of the anisotropy in cortical bone is presented from both the perspective of plane stress (two-dimensional stress state) and plane strain (three-dimensional stress state). The orthotropic elastic properties that are incorporated in these states are used to provide a more thorough and refined description of planar and volumetric anisotropy in comparison to the commonly used ratio of elastic moduli. The resulting anistropic parametric equations (η(σ) and η(ε)) are applied to the elastic material properties measured from cortical bone within rats, dogs, cows and humans as reported in 12 previous studies. The resulting calculated parameters reduce the typically nine independent properties down to three parameters which in turn represent the degree of anisotropy within the three orthogonal planes of symmetry as are common in cortical bone. It was found that no statistical difference existed between the plane stress versus plane strain parameter in all but two studies (p > 0.10). Planar and volumetric anisotropies were compared to the isotropic condition (η(σ) = η(ε) = 1.0) for all of the included studies. All of the studies reported cortical bone properties that were volumetrically anisotropic (p <0.05), however, a common plane of isotropy was noted in the radial-circumferential (1-2) plane (p > 0.05). Future use of these parametric equations will allow further illucidation of the issue of mesomechanical and micromechanial levels of anisotropy within other tissues and materials of interest. (C) 2000 Kluwer Academic Publishers.

AB - An equational description of the extent of the anisotropy in cortical bone is presented from both the perspective of plane stress (two-dimensional stress state) and plane strain (three-dimensional stress state). The orthotropic elastic properties that are incorporated in these states are used to provide a more thorough and refined description of planar and volumetric anisotropy in comparison to the commonly used ratio of elastic moduli. The resulting anistropic parametric equations (η(σ) and η(ε)) are applied to the elastic material properties measured from cortical bone within rats, dogs, cows and humans as reported in 12 previous studies. The resulting calculated parameters reduce the typically nine independent properties down to three parameters which in turn represent the degree of anisotropy within the three orthogonal planes of symmetry as are common in cortical bone. It was found that no statistical difference existed between the plane stress versus plane strain parameter in all but two studies (p > 0.10). Planar and volumetric anisotropies were compared to the isotropic condition (η(σ) = η(ε) = 1.0) for all of the included studies. All of the studies reported cortical bone properties that were volumetrically anisotropic (p <0.05), however, a common plane of isotropy was noted in the radial-circumferential (1-2) plane (p > 0.05). Future use of these parametric equations will allow further illucidation of the issue of mesomechanical and micromechanial levels of anisotropy within other tissues and materials of interest. (C) 2000 Kluwer Academic Publishers.

UR - http://www.scopus.com/inward/record.url?scp=0034080933&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034080933&partnerID=8YFLogxK

U2 - 10.1023/A:1008940914693

DO - 10.1023/A:1008940914693

M3 - Article

VL - 11

SP - 261

EP - 265

JO - Journal of Materials Science: Materials in Medicine

JF - Journal of Materials Science: Materials in Medicine

SN - 0957-4530

IS - 4

ER -