Dependence of Yield Strain on Anatomic Site for Human Trabecular Bone

1999 ◽  
Author(s):  
Elise F. Morgan ◽  
Yves P. Arramon ◽  
David L. Kopperdahl ◽  
Tony M. Keaveny

Abstract The yield strain behavior of trabecular bone has gained increased importance as evidence accumulates that remodeling and failure criteria can be expressed as a function of strain alone (Turner et al., 1997; Silva et al., 1998). These findings rely on the results of previous studies in which yield strains were found to be isotropic and generally independent of volume fraction (Turner, 1989; Kopperdahl and Keaveny, 1998; Chang et al., 1999), although relatively little work has been done to substantiate these results for human trabecular bone. Thorough consideration of the dependence of yield strain on volume fraction should include analyses of trabecular bone from different anatomic sites since site-dependent differences in trabecular architecture have been well-correlated with mechanical properties (Goulet et al., 1994). However, differences in testing protocols and in definitions of modulus and yield point (Linde, 1994) have led to discrepancies in reported yield strain values in the literature (Kopperdahl and Keaveny, 1998). This prevents inter-study comparisons of the yield strain behavior of human trabecular bone across different anatomic sites, and yet characterizing this behavior is a fundamental step both. In the validation of uniform strain adaptation models and in the development of failure criteria.

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Arnav Sanyal ◽  
Tony M. Keaveny

The biaxial failure behavior of the human trabecular bone, which has potential relevance both for fall and gait loading conditions, is not well understood, particularly for low-density bone, which can display considerable mechanical anisotropy. Addressing this issue, we investigated the biaxial normal strength behavior and the underlying failure mechanisms for human trabecular bone displaying a wide range of bone volume fraction (0.06–0.34) and elastic anisotropy. Micro-computed tomography (CT)-based nonlinear finite element analysis was used to simulate biaxial failure in 15 specimens (5 mm cubes), spanning the complete biaxial normal stress failure space in the axial-transverse plane. The specimens, treated as approximately transversely isotropic, were loaded in the principal material orientation. We found that the biaxial stress yield surface was well characterized by the superposition of two ellipses—one each for yield failure in the longitudinal and transverse loading directions—and the size, shape, and orientation of which depended on bone volume fraction and elastic anisotropy. However, when normalized by the uniaxial tensile and compressive strengths in the longitudinal and transverse directions, all of which depended on bone volume fraction, microarchitecture, and mechanical anisotropy, the resulting normalized biaxial strength behavior was well described by a single pair of (longitudinal and transverse) ellipses, with little interspecimen variation. Taken together, these results indicate that the role of bone volume fraction, microarchitecture, and mechanical anisotropy is mostly accounted for in determining the uniaxial strength behavior and the effect of these parameters on the axial-transverse biaxial normal strength behavior per se is minor.


PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e5156 ◽  
Author(s):  
Leoni Georgiou ◽  
Tracy L. Kivell ◽  
Dieter H. Pahr ◽  
Matthew M. Skinner

BackgroundIn addition to external bone shape and cortical bone thickness and distribution, the distribution and orientation of internal trabecular bone across individuals and species has yielded important functional information on how bone adapts in response to load. In particular, trabecular bone analysis has played a key role in studies of human and nonhuman primate locomotion and has shown that species with different locomotor repertoires display distinct trabecular architecture in various regions of the skeleton. In this study, we analyse trabecular structure throughout the distal femur of extant hominoids and test for differences due to locomotor loading regime.MethodsMicro-computed tomography scans ofHomo sapiens(n= 11),Pan troglodytes(n= 18),Gorilla gorilla(n= 14) andPongosp. (n= 7) were used to investigate trabecular structure throughout the distal epiphysis of the femur. We predicted that bone volume fraction (BV/TV) in the medial and lateral condyles inHomowould be distally concentrated and more anisotropic due to a habitual extended knee posture at the point of peak ground reaction force during bipedal locomotion, whereas great apes would show more posteriorly concentrated BV/TV and greater isotropy due to a flexed knee posture and more variable hindlimb use during locomotion.ResultsResults indicate some significant differences between taxa, with the most prominent being higher BV/TV in the posterosuperior region of the condyles inPanand higher BV/TV and anisotropy in the posteroinferior region inHomo. Furthermore, trabecular number, spacing and thickness differ significantly, mainly separatingGorillafrom the other apes.DiscussionThe trabecular architecture of the distal femur holds a functional signal linked to habitual behaviour; however, there was more similarity across taxa and greater intraspecific variability than expected. Specifically, there was a large degree of overlap in trabecular structure across the sample, andHomowas not as distinct as predicted. Nonetheless, this study offers a comparative sample of trabecular structure in the hominoid distal femur and can contribute to future studies of locomotion in extinct taxa.


Bone ◽  
2006 ◽  
Vol 39 (6) ◽  
pp. 1218-1225 ◽  
Author(s):  
Grant Bevill ◽  
Senthil K. Eswaran ◽  
Atul Gupta ◽  
Panayiotis Papadopoulos ◽  
Tony M. Keaveny

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Arnav Sanyal ◽  
Joanna Scheffelin ◽  
Tony M. Keaveny

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (μCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5 mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36), mechanical anisotropy (range of E3/E1 = 3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension, compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space. The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal boxlike shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized-strain space combined with a piecewise linear yield criterion in two planes for normal-shear loading (mean error ± SD: 4.6 ± 0.8% for the finite element data versus the criterion). This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture.


2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Mathieu Charlebois ◽  
Michael Pretterklieber ◽  
Philippe K. Zysset

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.


Author(s):  
Xiaowei S. Liu ◽  
X. Henry Zhang ◽  
Paul Sajda ◽  
Punam K. Saha ◽  
Felix W. Wehrli ◽  
...  

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.


1998 ◽  
Vol 31 (7) ◽  
pp. 601-608 ◽  
Author(s):  
David L Kopperdahl ◽  
Tony M Keaveny

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