On the effective anisotropic elastic properties of porous hydroxyapatite, porous collagen, and cortical bone: A homogenization scheme with percolation threshold concept

2018 ◽  
Vol 24 (4) ◽  
pp. 1091-1102 ◽  
Author(s):  
Mai-Ba Vu ◽  
Tuan Nguyen-Sy
Keyword(s):  
Percolation Threshold ◽  
Cortical Bone ◽  
Elastic Properties ◽  
Organic Content ◽  
Homogenization Theory ◽  
High Porosity ◽  
Porous Hydroxyapatite ◽  
Threshold Concept ◽  
Homogenization Scheme ◽  
Anisotropic Elastic

The objective of this study is to model the effective anisotropic elastic properties of porous hydroxyapatite, wet collagen, and cortical bone by an advanced homogenization scheme with a percolation threshold concept. The theoretical basis of the anisotropic homogenization theory is first presented. A homogenization scheme with a percolation threshold concept is then introduced and validated against experimental data for porous hydroxyapatite as well as bone after decollagenization. It is also validated on a porous collagen that is a result of the demineralization of bone. Even though aligned collagen fibers are considered, similar values of the elastic stiffnesses [Formula: see text] and [Formula: see text] were found for demineralized bone due to its very high porosity. Finally the proposed method is used to model cortical bone as a mixture of hydroxyapatite mineral and soft organic content that is in turn a mixture of collagen fiber and pores filled by water. Good agreement between modeled and measured data is observed. The model presented herein is simpler than existing multi-scale homogenization schemes in the literature, but its results fit very well with the experimented trends.

Specimen Specific Multiscale Model for the Anisotropic Elastic Properties of Human Cortical Bone Tissue

2007 ◽  
Author(s):  
Justin M. Deuerling ◽  
Weimin Yue ◽  
Alejandro A. Espinoza ◽  
Ryan K. Roeder
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Structural Information ◽  
Transversely Isotropic ◽  
Longitudinal Axis ◽  
Orientation Distribution ◽  
Tissue Properties ◽  
Apatite Crystals ◽  
Micromechanical Models ◽  
Anisotropic Elastic

The elastic constants of cortical bone are orthotropic or transversely isotropic depending on the anatomic origin of the tissue. Micromechanical models have been developed to predict anisotropic elastic properties from structural information. Many have utilized microstructural features such as osteons, cement lines and Haversian canals to model the tissue properties [1]. Others have utilized nanoscale features to model the mineralized collagen fibril [2]. Quantitative texture analysis using x-ray diffraction techniques has shown that elongated apatite crystals exhibit a preferred orientation in the longitudinal axis of the bone [3]. The orientation distribution of apatite crystals provides fundamental information influencing the anisotropy of the extracellular matrix (ECM) but has not been utilized in existing micromechanical models.

Elastic Properties of Human Osteon and Osteonal Lamella Computed by a Bidirectional Micromechanical Model and Validated by Nanoindentation

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Radim Korsa ◽  
Jaroslav Lukes ◽  
Josef Sepitka ◽  
Tomas Mares
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Micromechanical Model ◽  
Degenerative Diseases ◽  
Coordinate Systems ◽  
Inverse Homogenization ◽  
Curvilinear Coordinate ◽  
Anisotropic Elastic ◽  
Good Agreement

Knowledge of the anisotropic elastic properties of osteon and osteonal lamellae provides a better understanding of various pathophysiological conditions, such as aging, osteoporosis, osteoarthritis, and other degenerative diseases. For this reason, it is important to investigate and understand the elasticity of cortical bone. We created a bidirectional micromechanical model based on inverse homogenization for predicting the elastic properties of osteon and osteonal lamellae of cortical bone. The shape, the dimensions, and the curvature of osteon and osteonal lamellae are described by appropriately chosen curvilinear coordinate systems, so that the model operates close to the real morphology of these bone components. The model was used to calculate nine orthotropic elastic constants of osteonal lamellae. The input values have the elastic properties of a single osteon. We also expressed the dependence of the elastic properties of the lamellae on the angle of orientation. To validate the model, we performed nanoindentation tests on several osteonal lamellae. We compared the experimental results with the calculated results, and there was good agreement between them. The inverted model was used to calculate the elastic properties of a single osteon, where the input values are the elastic constants of osteonal lamellae. These calculations reveal that the model can be used in both directions of homogenization, i.e., direct homogenization and also inverse homogenization. The model described here can provide either the unknown elastic properties of a single lamella from the known elastic properties at the level of a single osteon, or the unknown elastic properties of a single osteon from the known elastic properties at the level of a single lamella.

scholarly journals Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly

2019 ◽  
Vol 90 ◽  
pp. 254-266 ◽  
Author(s):  
Xiran Cai ◽  
Hélène Follet ◽  
Laura Peralta ◽  
Marc Gardegaront ◽  
Delphine Farlay ◽  
...  
Keyword(s):  
Cortical Bone ◽  
Elastic Properties ◽  
Anisotropic Elastic

scholarly journals Prediction of anisotropic elastic properties of snow from its microstructure

2016 ◽  
Vol 125 ◽  
pp. 85-100 ◽  
Author(s):  
Praveen K. Srivastava ◽  
Chaman Chandel ◽  
Puneet Mahajan ◽  
Pankaj Pankaj
Keyword(s):  
Elastic Properties ◽  
Anisotropic Elastic

Tuning the interfacial thermal conductance via the anisotropic elastic properties of graphite

Carbon ◽  
2019 ◽  
Vol 144 ◽  
pp. 109-115 ◽  
Author(s):  
Zhiyong Wei ◽  
Fan Yang ◽  
Kedong Bi ◽  
Juekuan Yang ◽  
Yunfei Chen
Keyword(s):  
Elastic Properties ◽  
Thermal Conductance ◽  
Interfacial Thermal Conductance ◽  
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).

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