Damage in trabecular bone at small strains.

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 theoretical analysis of long-term bisphosphonate effects on trabecular bone volume and microdamage.

Bisphosphonates increase bone mass and reduce fracture risk, but their anti-resorptive action may lead to increases in fatigue microdamage. To investigate how bisphosphonate effects influence changes in bone volume and microdamage in the long term, a strain-adaptive model of bone remodeling and microdamage balance was developed for a continuum-level volume of postmenopausal trabecular bone by invoking Frost's mechanostat hypothesis. Both disuse and fatigue microdamage were assumed to stimulate the activation frequency of basic multicellular units (BMUs) such that bone remodeling served to remove excess bone mass and microdamage. Bisphosphonate effects were simulated as follows: low, intermediate, high, or complete suppression of BMU activation frequency either without a change in resorption by the BMU or with an independent decrease in resorption while the bone formation process was unaffected (i.e., formation initially exceeded resorption). Of the bisphosphonate effects, a reduction in resorption relative to formation dictated the long-term gain in bone volume while the potency of activation frequency suppression controlled the rate of gain. A plateau in the bone mass gain that typically occurs in clinical studies of bisphosphonate treatment was predicted by the model because the resultant reduction in strain forced bone formation by the BMU to decrease over time until it matched the reduction in BMU resorption. A greater suppression of activation frequency proportionally increased microdamage, but the accumulation was limited over the long term as long as remodeling was incompletely suppressed. The results of the model suggest creating bisphosphonates that provide minimal suppression of remodeling and a large decrease in BMU resorption because this would minimize damage accumulation and increase bone mass, respectively.

Long stemmed total knee arthroplasty with interlocking screws: a computational bone adaptation study.

The ability of an interlocking screw fixation technique to minimize bone loss related to stress shielding in the tibia was investigated and compared to the abilities of cement and press-fit fixation. Full bony ingrowth has been associated with greater stress shielding than partial ingrowth; therefore, the effect of intimate bonding of the stem to bone on subsequent bone loss was also studied. A damage- and disuse-based remodeling theory was coupled with a two-dimensional finite element model of the tibia to predict changes in bone remodeling following long stemmed total knee arthroplasty (TKA) for four different fixation techniques (cement, press-fit, interlock with bony ingrowth, and interlock without bony ingrowth). Remodeling changes commenced with the model state variables--bone area fraction, mechanical stimulus, damage, and remodeling activity--at steady-state values predicted by the intact tibia simulation. After TKA and irrespective of fixation technique, the model predicted elevated remodeling due to disuse, in which more bone was removed than replenished. In regions below the tibial tray and along the cortices, the interlocking stem with full bony ingrowth and the cemented stem caused the least amount of bone loss. An interlocking stem with a smooth, matted finish did not reduce the bone loss associated with interlocking fixation.

Similarity in the fatigue behavior of trabecular bone across site and species.

Within the context of improving knowledge of the structure-function relations for trabecular bone for cyclic loading, we hypothesized that the S-N curve for cyclic compressive loading of trabecular bone, after accounting for differences in monotonic strength behavior, does not depend on either site or species. Thirty-five cores of fresh-frozen elderly human vertebral trabecular bone, harvested from nine donors (mean+/-S.D., age=74+/-17 years), were biomechanically tested in compression at sigma/E(0) values (ratio of applied stress to pre-fatigue elastic modulus) ranging from 0.0026 to 0.0070, and compared against literature data (J. Biomech. Eng. 120 (1998) 647-654) for young bovine tibial trabecular bone (n=37). As reported for the bovine bone, the number of cycles to failure for the human vertebral bone was related to sigma/E(0) by a power-law relation (r(2)=0.54, n=35). Quantitative comparison of these data against those reported for the bovine bone supported our hypothesis. Namely, when the differences in mean monotonic yield strain between the two types of bone were accounted for, a single S-N curve worked well for the pooled data (r(2)=0.75, n=72). Since elderly human vertebral and young bovine tibial trabecular bone represent two very different types of trabecular bone in terms of volume fraction and architecture, these findings suggest that the dominant failure mechanisms in trabecular bone for cyclic loading occur at the ultrastructural level.

Contribution of inter-site variations in architecture to trabecular bone apparent yield strains.

Apparent yield strains for trabecular bone are uniform within an anatomic site but can vary across site. The overall goal of this study was to characterize the contribution of inter-site differences in trabecular architecture to corresponding variations in apparent yield strains. High-resolution, small deformation finite element analyses were used to compute apparent compressive and tensile yield strains in four sites (n = 7 specimens per site): human proximal tibia, greater trochanter, femoral neck, and bovine proximal tibia. These sites display differences in compressive, but not tensile, apparent yield strains. Inter-site differences in architecture were captured implicitly in the model geometries, and these differences were isolated as the sole source of variability across sites by using identical tissue properties in all models. Thus, the effects inter-site variations in architecture on yield strain could be assessed by comparing computed yield strains across site. No inter-site differences in computed yield strains were found for either loading mode (p > 0.19), indicating that, within the context of small deformations, inter-site variations in architecture do not affect apparent yield strains. However, results of ancillary analyses designed to test the validity of the small deformation assumption strongly suggested that the propensity to undergo large deformations constitutes an important contribution of architecture to inter-site variations in apparent compressive yield strains. Large deformations substantially reduced apparent compressive, but not tensile, yield strains. These findings indicate the importance of incorporating large deformation capabilities in computational analyses of trabecular bone. This may be critical when investigating the biomechanical consequences of trabecular thinning and loss.

Predictions on preserving bone mass in knee arthroplasty with bisphosphonates.

Using a computational model of bone adaptation, we investigated the long-term ability of bisphosphonates to minimize proximal bone loss that is associated with stress shielding in the tibia after long-stemmed total knee arthroplasty (TKA). When invoking bisphosphonate effects, the remodeling activity was suppressed, and the resorption size was reduced. Compared with the untreated simulation, bisphosphonate slowed the rate of bone loss after TKA (42% reduction in bone loss at 1 year). Activating the drug 3 months before the surgery reversed bone loss associated with the reduction in such activities as walking, but it did not provide any substantial benefit in the long-term. Late bisphosphonate treatment did not reverse the bone loss that occurred 3.5 years after TKA, although it preserved 3% of bone normally lost without treatment.