Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone

AbstractMechanical properties of cortical human bone have been investigated for more than over three decades. The objectives of the present study were 1) to investigate the influence of multiscale structural characteristics of the bone tissue on its mechanical behavior and 2) to perform a micro-macro numerical modelling based on the experimental data. It should be noted that variations of the osteon lamellae elastic properties are higher (40%) at the microstructural level than those found at the macroscopic level (about 15%) for measurements performed in the same anatomical direction. Physico-chemical analyses found that organic components were found to be higher for femurs exhibiting lower mechanical properties. There is a consistency between changes observed at the different levels. These results contribute to a basic understanding of the multiscale mechanical behavior of human cortical bone.

Download Full-text

Elastic Anisotropy of Human Cortical Bone Secondary Osteons Measured by Nanoindentation

Journal of Biomechanical Engineering ◽

10.1115/1.3005162 ◽

2008 ◽

Vol 131 (2) ◽

Cited By ~ 47

Author(s):

Giampaolo Franzoso ◽

Philippe K. Zysset

Keyword(s):

Cortical Bone ◽

Elastic Properties ◽

Elastic Constants ◽

Elastic Anisotropy ◽

Elastic Model ◽

Indentation Modulus ◽

Lamellar Bone ◽

Macroscopic Level ◽

Human Cortical Bone ◽

Secondary Osteons

The identification of anisotropic elastic properties of lamellar bone based on nanoindentation data is an open problem. Therefore, the purpose of this study was to develop a method to estimate the orthotropic elastic constants of human cortical bone secondary osteons using nanoindentation in two orthogonal directions. Since the indentation modulus depends on all elastic constants and, for anisotropic materials, also on the indentation direction, a theoretical model quantifying the indentation modulus from the stiffness tensor of a given material was implemented numerically (Swadener and Pharr, 2001, “Indentation of Elastically Anisotropic Half-Spaces by Cones and Parabolae of Revolution,” Philos. Mag. A, 81(2), pp. 447–466). Nanoindentation was performed on 22 osteons of the distal femoral shaft: A new holding system was designed in order to indent the same osteon in two orthogonal directions. To interpret the experimental results and identify orthotropic elastic constants, an inverse procedure was developed by using a fabric-based elastic model for lamellar bone. The experimental indentation moduli were found to vary with the indentation direction and showed a marked anisotropy. The estimated elastic constants showed different degrees of anisotropy among secondary osteons of the same bone and these degrees of anisotropy were also found to be different than the one of cortical bone at the macroscopic level. Using the log-Euclidean norm, the relative distance between the compliance tensors of the estimated mean osteon and of cortical bone at the macroscopic level was 9.69%: Secondary osteons appeared stiffer in their axial and circumferential material directions, and with a greater bulk modulus than cortical bone, which is attributed to the absence of vascular porosity in osteonal properties. The proposed method is suitable for identification of elastic constants from nanoindentation experiments and could be adapted to other (bio)materials, for which it is possible to describe elastic properties using a fabric-based model.

Download Full-text

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

Journal of Biomechanical Engineering ◽

10.1115/1.4030407 ◽

2015 ◽

Vol 137 (8) ◽

Cited By ~ 3

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.

Download Full-text

Multi-Scale Modeling of Human Cortical Bone: Aging and Failure Studies

MRS Proceedings ◽

10.1557/proc-975-0975-dd02-06 ◽

2006 ◽

Vol 975 ◽

Cited By ~ 4

Author(s):

Elisa Budyn ◽

Thierry Hoc

Keyword(s):

Finite Element ◽

Stress Intensity ◽

Cortical Bone ◽

Failure Mechanism ◽

Stress Intensity Factors ◽

Load Parameter ◽

Multiple Cracks ◽

Intensity Factors ◽

Multi Scale ◽

Human Cortical Bone

ABSTRACTA multi-scale analysis for unit cells of human cortical bone is presented. Two studies are conducted: the first study concerns the effect of aging over the structural and mechanical properties of human cortical bone; the second study is devoted to the failure mechanism and the development of cracks in cortical bone under various loading conditions. Experiments are conducted on human specimen of different ages in order to measure relevant geometrical and mechanical parameters and obtain microscopic data that will be injected into finite element models. First a continuum FEM model will compute macroscopic information that will be validated through comparison with the experimental measurements. For the failure mechanism study, an XFEM model will be developed in order to allow the growth of multiple cracks until complete failure of the cell. An elastic-damage criterion will be used in order to place the initial cracks in maximum strain locations. To follow the global response of the cell, the stress intensity factors are computed at each crack tip and a load parameter is adjusted so that the stress intensity factors remain at the critical value. In the case of competitive crack tips, a stability analysis is performed by computing the second derivative of the potential energy for each crack. Fatigue loading will be also investigated. The discretization utilizes the eXtended Finite Element Method and requires no remeshing as the cracks grow. The crack geometries are arbitrary with respect to the mesh, and are described by a vector level set. Special boundary conditions and the algorithm for detecting crack bridging and crack entering Haversian canals which allows the cracks to grow until maximum failure and/or percolation is presented.

Download Full-text

Inhomogeneities in anisotropic elastic constants of cortical bone

10.1109/ultsym.1989.67143 ◽

2003 ◽

Cited By ~ 6

Author(s):

A. Meunier ◽

O. Riot ◽

P. Christel ◽

J.L. Katz ◽

L. Sedel

Keyword(s):

Cortical Bone ◽

Elastic Constants ◽

Anisotropic Elastic

Download Full-text

Human cortical bone: the SiNuPrOs model. Part II – a multi-scale study of permeability

Computer Methods in Biomechanics & Biomedical Engineering ◽

10.1080/10255840903045037 ◽

2010 ◽

Vol 13 (1) ◽

pp. 81-89 ◽

Cited By ~ 9

Author(s):

M. Predoi-Racila ◽

M.C. Stroe ◽

J.M. Crolet

Keyword(s):

Cortical Bone ◽

Multi Scale ◽

Human Cortical Bone

Download Full-text

Three-dimensional Reconstruction of Microscopic Image Based on Multi-ST Algorithm

Journal of Imaging Science and Technology ◽

10.2352/j.imagingsci.technol.2020.64.2.020506 ◽

2020 ◽

Vol 64 (2) ◽

pp. 20506-1-20506-7

Author(s):

Min Zhu ◽

Rongfu Zhang ◽

Pei Ma ◽

Xuedian Zhang ◽

Qi Guo

Keyword(s):

3D Reconstruction ◽

Three Dimensional ◽

Scale Model ◽

Microscopic Image ◽

Multi Scale ◽

Gaussian Pyramid ◽

Cost Aggregation ◽

Dimensional Reconstruction ◽

Image Pairs ◽

Accurate Matching

Abstract Three-dimensional (3D) reconstruction is extensively used in microscopic applications. Reducing excessive error points and achieving accurate matching of weak texture regions have been the classical challenges for 3D microscopic vision. A Multi-ST algorithm was proposed to improve matching accuracy. The process is performed in two main stages: scaled microscopic images and regularized cost aggregation. First, microscopic image pairs with different scales were extracted according to the Gaussian pyramid criterion. Second, a novel cost aggregation approach based on the regularized multi-scale model was implemented into all scales to obtain the final cost. To evaluate the performances of the proposed Multi-ST algorithm and compare different algorithms, seven groups of images from the Middlebury dataset and four groups of experimental images obtained by a binocular microscopic system were analyzed. Disparity maps and reconstruction maps generated by the proposed approach contained more information and fewer outliers or artifacts. Furthermore, 3D reconstruction of the plug gauges using the Multi-ST algorithm showed that the error was less than 0.025 mm.

Download Full-text