scholarly journals Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Ginu U. Unnikrishnan ◽  
John A. Gallagher ◽  
Amira I. Hussein ◽  
Glenn D. Barest ◽  
Elise F. Morgan
Keyword(s):  
Trabecular Bone ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Transverse Isotropy ◽  
Bone Adaptation ◽  
Bone Architecture ◽  
Fabric Tensor ◽  
Elastic Symmetry ◽  
Vertebral Trabecular Bone ◽  
Principal Axes

Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (μFE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age = 81.17 ± 7.7 yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin's fabric-based constitutive model (Cowin, 1985, “The Relationship Between the Elasticity Tensor and the Fabric Tensor,” Mech. Mater., 4(2), pp. 137–147.) and the orientation of the principal axes of the fabric tensor, respectively. Deviations from orthotropy were quantified by the “orthotropic error” (van Rietbergen et al., 1996, “Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture,” J. Biomech., 29(12), pp. 1653–1657), and deviations from transverse isotropy were determined by statistical comparison of the secondary and tertiary elastic moduli. The orthotropic error was greater than 50% for nearly half of the cubes, and the secondary and tertiary moduli differed from one another (p < 0.0001). Both the orthotropic error and the difference between secondary and tertiary moduli decreased with increasing bone volume fraction (BV/TV; p ≤ 0.007). Considering only the cubes with an orthotropic error less than 50%, only moderate correlations were observed between the fabric-based and the μFE-computed elastic moduli (R2 ≥ 0.337; p < 0.0001). These results indicate that when using a criterion of 5 mm for a representative volume element (RVE), transverse isotropy or orthotropy cannot be assumed for elderly human vertebral trabecular bone. Particularly at low values of BV/TV, this criterion does not ensure applicability of theories of continuous media. In light of the very sparse and inhomogeneous microstructure found in the specimens analyzed in this study, further work is needed to establish guidelines for selecting a RVE within the aged vertebral centrum.

Impact of Thresholding Techniques on Micro-CT Image Based Computational Models of Trabecular Bone

2000 ◽  
Author(s):  
Mark J. Eichler ◽  
Chi Hyun Kim ◽  
Ralph Müller ◽  
X. Edward Guo
Keyword(s):  
Mechanical Properties ◽  
Trabecular Bone ◽  
Computational Models ◽  
Volume Fraction ◽  
Bone Fractures ◽  
Bone Adaptation ◽  
Bone Architecture ◽  
Micro Ct ◽  
Bone Volume Fraction ◽  
Age Related

Abstract Age-related bone fractures are mostly influenced by trabecular bone sites. Trabecular bone constantly adapts its bone volume fraction (BV/TV) and orientation, and thus its mechanical properties, to mechanical usage. Therefore, understanding the trabecular bone adaptation process and its consequences will contribute to the better understanding of the etiology of age-related fractures. Micro-computed tomography (micro-CT) is a relatively new method to quantify the complex three-dimensional (3D) trabecular bone architecture [1,2]. Finite element computational studies can be performed on these 3D microstructural images by converting each image voxel into an element [3,4,5]. Image thresholding techniques to segment bone voxels from bone marrow voxels have a major impact on the results of these models. However, the influence of different types of thresholding techniques on the mechanical properties of bone has not been examined carefully.

Architectural changes of trabecular bone caused by the remodeling process

2005 ◽  
Vol 874 ◽  
Author(s):  
Richard Weinkamer ◽  
Markus A. Hartmann ◽  
Yves Brechet ◽  
Peter Fratzl
Keyword(s):  
Trabecular Bone ◽  
Feedback Loop ◽  
Mechanical Response ◽  
Volume Fraction ◽  
Bone Volume ◽  
Bone Architecture ◽  
Mechanical Problem ◽  
Bone Volume Fraction ◽  
Obvious Effect ◽  
Trabecular Bone Architecture

AbstractUsing a stochastic lattice model we have studied the architectural changes of trabecular bone occurring while the structure is remodeled. Our model considers the mechanical feedback loop, which control the remodeling process. A fast algorithm was employed to solve approximately the mechanical problem. A general feature of the model is that a networklike structure emerges, which further coarsens while the bone volume fraction remains unchanged. Decreasing the mechanical response of the system by either lowering the external load or the internal mechano-sensitivity leads not only to a reduction of the bone volume fraction, but results in topological changes of the trabecular bone architecture, where the loss of horizontal trabeculae is the most obvious effect.

Mapping Quantitative Trait Loci for Vertebral Trabecular Bone Volume Fraction and Microarchitecture in Mice

2003 ◽  
Vol 19 (4) ◽  
pp. 587-599 ◽  
Author(s):  
Mary L Bouxsein ◽  
Toru Uchiyama ◽  
Clifford J Rosen ◽  
Kathryn L Shultz ◽  
Leah R Donahue ◽  
...  
Keyword(s):  
Quantitative Trait Loci ◽  
Trabecular Bone ◽  
Quantitative Trait ◽  
Volume Fraction ◽  
Bone Volume ◽  
Trabecular Bone Volume ◽  
Bone Volume Fraction ◽  
Vertebral Trabecular Bone ◽  
Trait Loci

The Role of Fabric in the Large Strain Compressive Behavior of Human Trabecular Bone

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Mathieu Charlebois ◽  
Michael Pretterklieber ◽  
Philippe K. Zysset
Keyword(s):  
Mechanical Properties ◽  
Trabecular Bone ◽  
Volume Fraction ◽  
Large Strain ◽  
Dissipated Energy ◽  
Fabric Tensor ◽  
Compressive Behavior ◽  
Human Trabecular Bone ◽  
Minimum Stress

Osteoporosis-related vertebral body fractures involve large compressive strains of trabecular bone. The small strain mechanical properties of the trabecular bone such as the elastic modulus or ultimate strength can be estimated using the volume fraction and a second order fabric tensor, but it remains unclear if similar estimations may be extended to large strain properties. Accordingly, the aim of this work is to identify the role of volume fraction and especially fabric in the large strain compressive behavior of human trabecular bone from various anatomical locations. Trabecular bone biopsies were extracted from human T12 vertebrae (n=31), distal radii (n=43), femoral head (n=44), and calcanei (n=30), scanned using microcomputed tomography to quantify bone volume fraction (BV/TV) and the fabric tensor (M), and tested either in unconfined or confined compression up to very large strains (∼70%). The mechanical parameters of the resulting stress-strain curves were analyzed using regression models to examine the respective influence of BV/TV and fabric eigenvalues. The compressive stress-strain curves demonstrated linear elasticity, yielding with hardening up to an ultimate stress, softening toward a minimum stress, and a steady rehardening followed by a rapid densification. For the pooled experiments, the average minimum stress was 1.89±1.77 MPa, while the corresponding mean strain was 7.15±1.84%. The minimum stress showed a weaker dependence with fabric as the elastic modulus or ultimate strength. For the confined experiments, the stress at a logarithmic strain of 1.2 was 8.08±7.91 MPa, and the dissipated energy density was 5.67±4.42 MPa. The latter variable was strongly related to the volume fraction (R2=0.83) but the correlation improved only marginally with the inclusion of fabric (R2=0.84). The influence of fabric on the mechanical properties of human trabecular bone decreases with increasing strain, while the role of volume fraction remains important. In particular, the ratio of the minimum versus the maximum stress, i.e., the relative amount of softening, decreases strongly with fabric, while the dissipated energy density is dominated by the volume fraction. The collected results will prove to be useful for modeling the softening and densification of the trabecular bone using the finite element method.

Contributions of Trabecular Rods of Various Orientations in Determining the Elastic Properties of Human Vertebral Trabecular Bone

2007 ◽  
Author(s):  
Xiaowei S. Liu ◽  
X. Henry Zhang ◽  
Paul Sajda ◽  
Punam K. Saha ◽  
Felix W. Wehrli ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Trabecular Bone ◽  
Elastic Properties ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Micro Computed Tomography ◽  
Bone Volume Fraction ◽  
Human Trabecular Bone ◽  
Vertebral Trabecular Bone ◽  
Age Related

Osteoporosis is an age-related disease characterized by low bone mass and architectural deterioration. Other than bone volume fraction (BV/TV), microarchitecture of trabecular bone, such as trabecular type (rods or plates), connectivity, and orientation of the trabecular network is also believed to be important in governing the mechanical properties of trabecular bone. A recent study [1] showed that the microarchitecture alone affects elastic moduli of trabecular bone and, further, that trabecular plates make a far greater contribution than rods. In human vertebral trabecular bone, the roles of transverse vs. vertical rods in conferring mechanical properties of trabecular bone have been debated [2, 3]. It has been suggested that the role of transverse trabecular rod is critical in determining elastic modulus of vertebral trabecular bone. However, without explicit classifications of trabecular type, or orientation assessment at an individual trabecula level, it is not possible yet to test this hypothesis in human trabecular bone samples despite the development of three-dimensional (3D) micro computed tomography (μCT) and μCT based finite element (FE) models of human trabecular bone. With the newly developed technique of complete volumetric decomposition and individual trabecula based orientation analyses [4], now it is possible to quantitatively examine the contributions of trabecular rods of various orientations in the elastic properties of vertebral trabecular bone.

Adaptive Bone Remodeling to Capture the Trabecular Bone Morphology of the Proximal Femur

2014 ◽  
Author(s):  
S. Mohammad Ali Banijamali ◽  
Ramin Oftadeh ◽  
Ashkan Vaziri ◽  
Hamid Nayeb-Hashemi
Keyword(s):  
Trabecular Bone ◽  
Cross Sections ◽  
Volume Fraction ◽  
Bone Structure ◽  
Local Stress ◽  
Stair Climbing ◽  
Frame Structure ◽  
Bone Architecture ◽  
Bone Morphology ◽  
Bone Volume Fraction

In this study, a model of femur which resembles bone natural structure has been developed. The model initially consists of a solid shell representing cortical bone encompassing a cubical network of interconnected rods with circular cross-sections representing trabecular bone part. A computational efficient program has been developed which iteratively changes the structure of trabecular bone by keeping the local stress in the structure within a defined stress range. The stress is controlled by either enhancing existing beam elements or removing beams from the initial trabecular frame structure. Trabecular bone structure is obtained for two load cases: walking and stair climbing. The results show that as the magnitude of the loads increase, the internal structure gets denser in critical zones. The higher density is achieved using loading associated with the stair climbing. Walking which is considered as the routine daily activity, results in the less internal density in different regions of the bone. The results show that the converged bone architecture consisting of rods and plates are consistent with the natural bone morphology of femur. Furthermore, the bone volume fraction at the critical regions of the converged structure is in a good agreement with previously measured data obtained from combinations of Dual X-ray Absorptiometry (DXA) and Computed Tomography (CT).

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