Correlation of anisotropic elastic and transport properties of cancellous bone

2002 ◽  
Author(s):  
J.B. Roberts ◽  
S.S. Kohles
Keyword(s):  
Transport Properties ◽  
Cancellous Bone ◽  
Anisotropic Elastic

scholarly journals Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

2021 ◽  
Author(s):  
Christoph Oefner ◽  
Elena Riemer ◽  
Kerstin Funke ◽  
Michael Werner ◽  
Christoph-Eckhard Heyde ◽  
...  
Keyword(s):  
Finite Element ◽  
Lumbar Spine ◽  
Cancellous Bone ◽  
Elastic Constants ◽  
Bone Volume ◽  
Human Bone ◽  
Homogenization Theory ◽  
Elastic Parameters ◽  
Anisotropic Elastic

AbstractIn biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R2 ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).

Anisotropic elastic properties of cancellous bone from a human edentulous mandible

2000 ◽  
Vol 11 (5) ◽  
pp. 415-421 ◽  
Author(s):  
Aisling M. O'Mahony ◽  
John L. Williams ◽  
Jerald O. Katz ◽  
Paulette Spencer
Keyword(s):  
Elastic Properties ◽  
Cancellous Bone ◽  
Edentulous Mandible ◽  
Anisotropic Elastic

The Dependence of the Elastic Constants of Cancellous Bone Upon Volume Fraction

1999 ◽  
Author(s):  
Guoyu Yang ◽  
Stephen C. Cowin ◽  
Jesper Kabel ◽  
Anders Odgaard ◽  
Bert van Rietbergen ◽  
...  
Keyword(s):  
Cancellous Bone ◽  
Elastic Constants ◽  
Volume Fraction ◽  
Explicit Representation ◽  
Clinical Test ◽  
In Vivo Evaluation ◽  
Elastic Symmetry ◽  
Human Cancellous Bone ◽  
Anisotropic Elastic

Abstract A simple and explicit representation for the anisotropic elastic constants of human cancellous bone was determined using a new method of analysis on a data base consisting of 141 human cancellous bone specimens. The method of analysis shows that human cancellous bone has orthotropic elastic symmetry at the 95% confidence level and it also provides expressions for all the orthotropic elastic constants as functions of the volume fraction of solid only; no stereological measures of trabecular architecture are involved. This result should be employed to improve the in vivo evaluation of cancellous bone stiffness and strength from a standard clinical test.

An Evolutionary Wolff’s Law for Trabecular Architecture

1992 ◽  
Vol 114 (1) ◽  
pp. 129-136 ◽  
Author(s):  
S. C. Cowin ◽  
A. M. Sadegh ◽  
G. M. Luo
Keyword(s):  
Cancellous Bone ◽  
Continuum Model ◽  
Temporal Evolution ◽  
Feedback Mechanism ◽  
Bone Architecture ◽  
Rate Coefficients ◽  
Stress And Strain ◽  
Trabecular Architecture ◽  
Wolff’S Law ◽  
Anisotropic Elastic

A continuum model is proposed to describe the temporal evolution of both the density changes and the reorientation of the trabecular architecture given the applied stress state in the bone and certain material parameters of the bone. The data upon which the proposed model is to be based consist of experimentally determined remodeling rate coefficients and quantitative stereological and anisotropic elastic constant measurements of cancellous bone. The model shows that the system of differential equations governing the temporal changes in architecture is necessarily nonlinear. This nonlinearity is fundamental in that it stems from the fact that, during remodeling, the relationship between stress and strain is changing as the stress and strain variables themselves are changing. In order to preserve the remodeling property of the model, terms that are of the order strain times the changes in density and/or microstructural properties must be retained. If these terms were dropped, there would be no feedback mechanism for architectural adaptation and no adaptation of the trabecular architecture. There is, therefore, no linearized version of this model of the temporal evolution of trabecular architecture. An application of the model is illustrated by an example problem in which the temporal evolution of homogeneous trabecular architecture is predicted. A limitation of the proposed continuum model is the length scale below which it cannot be applied. The model cannot be applied in regions of cancellous bone where the trabecular bone architecture is relatively inhomogeneous or at a bone-implant interface.

scholarly journals The Anisotropic Elastic Constants of Cancellous Bone

2000 ◽  
Author(s):  
Stephen C. Cowin
Keyword(s):  
Data Analysis ◽  
Elastic Constant ◽  
Data Base ◽  
Cancellous Bone ◽  
Elastic Constants ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Variable Composition ◽  
Elastic Symmetry ◽  
Anisotropic Elastic

Abstract A method of data analysis for a set of elastic constant measurements is applied to an excellent data base for cancellous bone. For these materials the identification of the type of elastic symmetry is complicated by the variable composition of the material. The data analysis method permits the identification of the type of elastic symmetry to be accomplished independent of the examination of the variable composition. This method of analysis may be applied to any set of elastic constant measurements, but is illustrated here by application to an extraordinary data base of cancellous bone elastic constants. The solid volume fraction or bulk density is the compositional variable for the elastic constants of these natural materials. The final results are the solid volume fraction dependent orthotropic Hooke’s law for cancellous bone.

Spectroscopic Diagnostics of Tokamaks

1988 ◽  
Vol 102 ◽  
pp. 165-174
Author(s):  
C. de Michelis
Keyword(s):  
Transport Properties ◽  
Power Losses ◽  
Spectroscopic Diagnostics ◽  
Important Concern

AbstractImpurities being an important concern in tokamaks, spectroscopy plays a key role in their understanding. Techniques for the evaluation of concentrations, power losses and transport properties are surveyed, and a few developments are outlined.

Structure and Orientation of As Precipitates in LT-MBE Grown GaAs

1991 ◽  
Vol 49 ◽  
pp. 900-901 ◽  
Author(s):  
Alain Claverie ◽  
Zuzanna Liliental-Weber
Keyword(s):  
Transport Properties ◽  
Layer Thickness ◽  
Growth Temperature ◽  
Low Temperatures ◽  
Lattice Parameter ◽  
Crystalline Quality ◽  
Insulating Properties ◽  
Lt Gaas

GaAs layers grown by MBE at low temperatures (in the 200°C range, LT-GaAs) have been reported to have very interesting electronic and transport properties. Previous studies have shown that, before annealing, the crystalline quality of the layers is related to the growth temperature. Lowering the temperature or increasing the layer thickness generally results in some columnar polycrystalline growth. For the best “temperature-thickness” combinations, the layers may be very As rich (up to 1.25%) resulting in an up to 0.15% increase of the lattice parameter, consistent with the excess As. Only after annealing are the technologically important semi-insulating properties of these layers observed. When annealed in As atmosphere at about 600°C a decrease of the lattice parameter to the substrate value is observed. TEM studies show formation of precipitates which are supposed to be As related since the average As concentration remains almost unchanged upon annealing.

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