Errors Induced by Off-Axis Measurement of the Elastic Properties of Bone

1988 ◽  
Vol 110 (3) ◽  
pp. 213-215 ◽  
Author(s):  
C. H. Turner ◽  
S. C. Cowin
Keyword(s):  
Cortical Bone ◽  
Bone Tissue ◽  
Cancellous Bone ◽  
Elastic Constants ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Misalignment Angle ◽  
Elastic Symmetry ◽  
Shear Moduli ◽  
Young’S Moduli

Misalignment between the axes of measurement and the material symmetry axes of bone causes error in anisotropic elastic property measurements. Measurements of Poisson’s ratio were strongly affected by misalignment errors. The mean errors in the measured Young’s moduli were 9.5 and 1.3 percent for cancellous and cortical bone, respectively, at a misalignment angle of 10 degrees. Mean errors of 1.1 and 5.0 percent in the measured shear moduli for cancellous and cortical bone, respectively, were found at a misalignment angle of 10 degrees. Although, cancellous bone tissue was assumed to have orthotropic elastic symmetry, the possibility of the greater symmetry of transverse isotropy was investigated. When the nine orthotropic elastic constants were forced to approximate the five transverse isotropic elastic constants, errors of over 60 percent were introduced. Therefore, it was concluded that cancellous bone is truly orthotropic and not transversely isotropic. A similar but less strong result for cortical bone tissue was obtained.

Effect of Cortical and Cancellous Bone Anisotropy on Peri-Implant Stresses and Strains in the Posterior Mandible

2000 ◽  
Author(s):  
Aisling M. O’Mahony ◽  
John L. Williams
Keyword(s):  
Cortical Bone ◽  
Dental Implant ◽  
Cancellous Bone ◽  
Elastic Constants ◽  
Transverse Isotropy ◽  
The Other ◽  
Bone Implant ◽  
Horizontal Loading ◽  
Principal Strains

Abstract We computed the bone-implant interface stresses for a bullet-shaped dental implant in the human mandible under combined vertical and horizontal loading. We also calculated the principal strains in the bone surrounding the implant. Two cases were compared: One in which the bone was considered to have isotropic elastic constants and the other in which transverse isotropy was assumed. Anisotropy increased the peak stresses and strains around both the implant-cancellous and implant-cortical bone interfaces.

First-Principle Investigation of Structural, Elastic, Electronic and Thermal Properties of Dysprosium Hafnate Oxides

2018 ◽  
Author(s):  
Hui Niu
Keyword(s):  
Thermal Properties ◽  
Elastic Constants ◽  
Density Functional ◽  
Functional Theory ◽  
Shear Moduli ◽  
Charge Densities ◽  
Young’S Moduli ◽  
Densities Of States ◽  
Complete Set ◽  
The Mean

Systematic first-principles calculations based on density functional theory were performed on Dy2HfxO3+2x (x = 0, 1, and 2) compositions. A complete set of elastic parameters including elastic constants, Hill’s bulk moduli, Young’s moduli, shear moduli and Poisson’s ratio were calculated. Analyses of densities of states and charge densities and electron localization functions suggest that the oxide bonds are highly ionic with some degree of covalency in the Hf-O bonds. Thermal properties including the mean sound velocity, Debye temperature, and minimum thermal conductivity were obtained from the elastic constants.

CALCULATED STRUCTURAL AND ELASTIC PROPERTIES OF M2InC(M=Sc, Ti, V, Zr, Nb, Hf, Ta)

2008 ◽  
Vol 22 (22) ◽  
pp. 2063-2076 ◽  
Author(s):  
A. BOUHEMADOU
Keyword(s):  
Experimental Data ◽  
Theoretical Prediction ◽  
Ab Initio Calculations ◽  
Sound Velocity ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Finite Strain ◽  
Applied Pressure ◽  
Shear Moduli ◽  
Young’S Moduli

Using ab initio calculations, we have studied the structural and elastic properties of M 2 InC , with M = Sc , Ti , V , Zr , Nb , Hf and Ta . Geometrical optimization of the unit cell is in agreement with the available experimental data. We have observed a quadratic dependence of the lattice parameters versus the applied pressure. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M 2 InC aggregates. We estimated the Debye temperature of M 2 InC from the average sound velocity. This is the first quantitative theoretical prediction of the elastic properties of Sc 2 InC , Ti 2 InC , V 2 InC , Zr 2 InC , Nb 2 InC , Hf 2 InC and Ta 2 InC compounds, and it still awaits experimental confirmation.

scholarly journals Mineralized bone loss at different sites in dialysis patients: implications for prevention.

1998 ◽  
Vol 9 (7) ◽  
pp. 1225-1233
Author(s):  
H C Schober ◽  
Z H Han ◽  
A J Foldes ◽  
M S Shih ◽  
D S Rao ◽  
...  
Keyword(s):  
Bone Loss ◽  
Cortical Bone ◽  
Bone Tissue ◽  
Cancellous Bone ◽  
Bone Volume ◽  
Ethnic Composition ◽  
Maintenance Hemodialysis ◽  
Appendicular Skeleton ◽  
Structural Abnormality ◽  
Patient Groups

To characterize the magnitude and location of mineralized bone loss, 40 patients (20 men, 20 women, 29 white, 11 black) with clinically significant renal osteodystrophy who could be unambiguously classified based on histologic criteria as having osteitis fibrosa (OF; 20 cases) or osteomalacia (OM; 20 cases) were studied; they had been on maintenance hemodialysis for 4.6 +/- 3.0 yr. One hundred forty-two healthy women of similar age and ethnic composition served as control subjects. In all subjects, the proportions of mineralized bone, osteoid, and porosity (nonbone soft tissue) were measured separately in cortical and cancellous bone tissue, from intact full-thickness biopsies of the ilium, representative of the axial skeleton. The results were related to the volumes of cortical and cancellous bone tissue separately and to the volume of the entire biopsy core. Approximately three-quarters of the patients had measurements in the appendicular skeleton by single photon absorptiometry of the radius and morphometry of the metacarpal. Disease effects did not differ significantly between ethnic groups. Mineralized cortical bone volume (per unit of core volume) was reduced by approximately 45% in both patient groups. Mineralized cancellous bone volume was significantly increased by 36% in the patients with OF and nonsignificantly reduced by 9% in the patients with OM; however, the reduction in the latter patients was significant in relation to tissue volume. The combined total deficit for both types of iliac bone was approximately 20% in the patients with OF and approximately 40% in the patients with OM. Significant reductions in appendicular cortical bone were demonstrated in both patient groups at both measurement sites. Regardless of the current histologic classification, the major structural abnormality in the skeleton is generalized thinning of cortical bone due to increased net endocortical resorption, the most characteristic effect on bone of hyperparathyroidism. Protection of the skeleton from the adverse consequences of renal failure will require therapeutic intervention in patients with no symptoms of either renal or bone disease.

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.

Prediction of Cortical Bone Elastic Constants by a Two-Level Micromechanical Model Using a Generalized Self-Consistent Method

2005 ◽  
Vol 128 (3) ◽  
pp. 309-316 ◽  
Author(s):  
X. Neil Dong ◽  
X. Edward Guo
Keyword(s):  
Experimental Data ◽  
Cortical Bone ◽  
Elastic Constants ◽  
Micromechanical Model ◽  
Transversely Isotropic ◽  
Two Phase ◽  
Self Consistent ◽  
Isotropic Elasticity ◽  
Consistent Method ◽  
Haversian Canals

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.

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.

Sign in / Sign up

Export Citation Format

Share Document