Damage in trabecular bone at small strains

Abstract

Evidence that damage decreases bone quality, increases fracture susceptibility, and serves as a remodeling stimulus motivates further study of what loading magnitudes induce damage in trabecular bone. In particular, whether damage occurs at the smaller strains characteristic of habitual, as opposed to traumatic, loading is not known. The overall goal of this study was to characterize damage accumulation in trabecular bone at small strains (0.20 - 0.45% strain). A continuum damage mechanics approach was taken whereby damage was quantified by changes in modulus and residual strain. Human vertebral specimens (n = 7) were tested in compression using a multi-cycle load - unload protocol in which the maximum applied strain for each cycle, epsilonmax, was increased incrementally from epsilonmax = 0.20% on the first loading cycle to epsilonmax = 0.45% on the last cycle. Modulus and residual strain were measured for each cycle. Both changes in modulus and residual strains commenced at small strains, beginning as early as 0.24 and 0.20% strain, respectively. Strong correlations between changes in modulus and residual strains were observed (r = 0.51 - 0.98). Fully nonlinear, high-resolution finite element analyses indicated that even at small apparent strains, tissue-level strains were sufficiently high to cause local yielding. These results demonstrate that damage in trabecular bone occurs at apparent strains less than half the apparent compressive yield strain reported previously for human vertebral trabecular bone. Further, these findings imply that, as a consequence of the highly porous trabecular structure, tissue yielding can initiate at very low apparent strains and that this local failure has detectable and negative consequences on the apparent mechanical properties of trabecular bone.

A non-invasive in vitro technique for the three-dimensional quantification of microdamage in trabecular bone

“…Consistent with previous works, this trend indicates the increasing accumulation of loading-induced microdamage with increasing strains in trabecular bone. [5,13,23]. Because cancellous bone samples were mechanically tested using artifact-free methods [19,20], measurements of modulus reduction and applied strains can be assured to be accurate.…”

“…In the context of mechanical modulus reduction, also known as damage fraction, (D=1-1-E effective /E), many definitions have been proposed for the "effective modulus" term (E effective ), including a reloading modulus [29], loading-unloading intersection modulus [3], a "perfect damage" modulus [31,32], a stress-divided-by-strain secant modulus [5], and anelastic-recovery protocol accounting for viscoelastic effects [33]. All but the secant modulus method [5] requires subsequent load cycles, which would cause additional microdamage formation.…”

“…All but the secant modulus method [5] requires subsequent load cycles, which would cause additional microdamage formation. Consequently, to preserve the initial strain-dependent microdamage formation, we selected the secant modulus method for this study.…”

Modelling of bone fracture and strength at different length scales: a review

“…Next, we will briefly outline several representative studies modelling strength, damage, fracture and softening mechanisms of a single trabecula and trabecular bone. Different approaches have been employed including elastic-plastic constitutive laws and progressive damage evolution by element deletion [187][188][189][190][191][192][193][194][195][196][197][198][199][200][201]. Due to the complex architecture of trabecular bone, many of the models used micro-computed tomography (mCT) based three-dimensional voxel FEM models, which give an accurate representation of trabecular bone geometry [192][193][194][195].…”

Bone Mass Preservation and Fracture Risk Assessment with Bisphosphonate Therapy During Spaceflight

“…Together, bone mass (quantity) and bone quality determine the ability of bone to resist fracture [50,51]. For this simulation, we examined changes in bone mass and bone quality in terms ofBMD and microdamage accumulation, respectively.…”