Spatial relationships between bone formation and mechanical stress within cancellous bone.

Bone adapts to mechanical stimuli. While in vivo mechanical loading has been shown to increase the density of cancellous bone, theory suggests that the relationship between tissue stress/strain and subsequent bone formation occurs at the scale of individual trabeculae. Here we examine bone formation one week following mechanical stimulus. Three bouts of cyclic loading (300 cycles/day on 3 consecutive days) were applied to caudal vertebrae of female rats (n=7). Bone formation was determined using three-dimensional images of fluorescent markers of bone formation (0.7×0.7×5.0µm(3)) and local tissue stress/strain was determined using high-resolution finite element models. Three days of mechanical stimuli resulted in an increase in mineralizing surface (loaded: 17.68±2.17%; control: 9.05±3.20%; mean±SD) and an increase in the volume of bone formed (loaded: 7.09±1.97%; control: 1.44±0.50%). The number of bone formation sites was greater in loaded animals (650.71±118.54) than pinned not loaded controls (310.71±91.55), a difference that was explained by the number of formation sites at regions with large local tissue strain energy density (SED). In addition, the probability of observing bone formation was greater at locations of the microstructure experiencing greater SED, but did not exceed 32%, consistent with prior work. Our findings demonstrate that bone formation in the week following a short term mechanical stimulus occurs near regions of bone tissue experiencing high tissue SED, although the ability of finite element models to predict the locations of bone formation remains modest and further improvements may require accounting for additional factors such as osteocyte distribution or fluid flow.

Finite element models predict the location of microdamage in cancellous bone following uniaxial loading.

High-resolution finite element models derived from micro-computed tomography images are often used to study the effects of trabecular microarchitecture and loading mode on tissue stress, but the degree to which existing finite element methods correctly predict the location of tissue failure is not well characterized. In the current study, we determined the relationship between the location of highly strained tissue, as determined from high-resolution finite element models, and the location of tissue microdamage, as determined from three-dimensional fluoroscopy imaging, which was performed after the microdamage was generated in-vitro by mechanical testing. Fourteen specimens of human vertebral cancellous bone were assessed (8 male donors, 2 female donors, 47-78 years of age). Regions of stained microdamage, were 50-75% more likely to form in highly strained tissue (principal strains exceeding 0.4%) than elsewhere, and generally the locations of the regions of microdamage were significantly correlated (p<0.05) with the locations of highly strained tissue. This spatial correlation was stronger for the largest regions of microdamage (≥1,000,000µm(3) in volume); 87% of large regions of microdamage were located near highly strained tissue. Together, these findings demonstrate that there is a strong correlation between regions of microdamage and regions of high strain in human cancellous bone, particularly for the biomechanically more important large instances of microdamage.

Fatigue-induced microdamage in cancellous bone occurs distant from resorption cavities and trabecular surfaces.

Impaired bone toughness is increasingly recognized as a contributor to fragility fractures. At the tissue level, toughness is related to the ability of bone tissue to resist the development of microscopic cracks or other tissue damage. While most of our understanding of microdamage is derived from studies of cortical bone, the majority of fragility fractures occur in regions of the skeleton dominated by cancellous bone. The development of tissue microdamage in cancellous bone may differ from that in cortical bone due to differences in microstructure and tissue ultrastructure. To gain insight into how microdamage accumulates in cancellous bone we determined the changes in number, size and location of microdamage sites following different amounts of cyclic compressive loading. Human vertebral cancellous bone specimens (n=32, 10 male donors, 6 female donors, age 76 ± 8.8, mean ± SD) were subjected to sub-failure cyclic compressive loading and microdamage was evaluated in three-dimensions. Only a few large microdamage sites (the largest 10%) accounted for 70% of all microdamage caused by cyclic loading. The number of large microdamage sites was a better predictor of reductions in Young's modulus caused by cyclic loading than overall damage volume fraction (DV/BV). The majority of microdamage volume (69.12 ± 7.04%) was located more than 30 µm (the average erosion depth) from trabecular surfaces, suggesting that microdamage occurs primarily within interstitial regions of cancellous bone. Additionally, microdamage was less likely to be near resorption cavities than other bone surfaces (p<0.05), challenging the idea that stress risers caused by resorption cavities influence fatigue failure of cancellous bone. Together, these findings suggest that reductions in apparent level mechanical performance during fatigue loading are the result of only a few large microdamage sites and that microdamage accumulation in fatigue is likely dominated by heterogeneity in tissue material properties rather than stress concentrations caused by micro-scale geometry.

The effects of misalignment during in vivo loading of bone: techniques to detect the proximity of objects in three-dimensional models.

Theories of mechanical adaptation of bone suggest that mechanical loading causes bone formation at discrete locations within bone microstructure experiencing the greatest mechanical stress/strain. Experimental testing of such theories requires in vivo loading experiments and high-resolution finite element models to determine the distribution of mechanical stresses. Finite element models of in vivo loading experiments typically assume idealized boundary conditions with applied load perfectly oriented on the bone, however small misalignments in load orientation during an in vivo experiment are unavoidable, and potentially confound the ability of finite element models to predict locations of bone formation at the scale of micrometers. Here we demonstrate two different three-dimensional spatial correlation methods to determine the effects of misalignment in load orientation on the locations of high mechanical stress/strain in the rodent tail loading model. We find that, in cancellous bone, the locations of tissue with high stress are maintained under reasonable misalignments in load orientation (p<0.01). In cortical bone, however, angular misalignments in the dorsal direction can alter the locations of high mechanical stress, but the locations of tissue with high stress are maintained under other misalignments (p<0.01). We conclude that, when using finite element models of the rodent tail loading model, small misalignments in loading orientation do not affect the predicted locations of high mechanical stress within cancellous bone.

Three-dimensional characterization of resorption cavity size and location in human vertebral trabecular bone.

The number and size of resorption cavities in cancellous bone are believed to influence rates of bone loss, local tissue stress and strain and potentially whole bone strength. Traditional two-dimensional approaches to measuring resorption cavities in cancellous bone report the percent of the bone surface covered by cavities or osteoclasts, but cannot measure cavity number or size. Here we use three-dimensional imaging (voxel size 0.7×0.7×5.0 µm) to characterize resorption cavity location, number and size in human vertebral cancellous bone from nine elderly donors (7 male, 2 female, ages 47-80 years). Cavities were 30.10 ± 8.56 µm in maximum depth, 80.60 ± 22.23∗10(3) µm(2) in surface area and 614.16 ± 311.93∗10(3) µm(3) in volume (mean ± SD). The average number of cavities per unit tissue volume (N.Cv/TV) was 1.25 ± 0.77 mm(-3). The ratio of maximum cavity depth to local trabecular thickness was 30.46 ± 7.03% and maximum cavity depth was greater on thicker trabeculae (p<0.05, r(2)=0.14). Half of the resorption cavities were located entirely on nodes (the intersection of two or more trabeculae) within the trabecular structure. Cavities that were not entirely on nodes were predominately on plate-like trabeculae oriented in the cranial-caudal (longitudinal) direction. Cavities on plate-like trabeculae were larger in maximum cavity depth, cavity surface area and cavity volume than cavities on rod-like trabeculae (p<0.05). We conclude from these findings that cavity size and location are related to local trabecular microarchitecture.