Effective modulus of the human intervertebral disc and its effect on vertebral bone stress.

The mechanism of vertebral wedge fractures remains unclear and may relate to typical variations in the mechanical behavior of the intervertebral disc. To gain insight, we tested 16 individual whole discs (between levels T8 and L5) from nine cadavers (mean±SD: 66±16 years), loaded in compression at different rates (0.05-20.0% strain/s), to measure a homogenized "effective" linear elastic modulus of the entire disc. The measured effective modulus, and average disc height, were then input and varied parametrically in micro-CT-based finite element models (60-µm element size, up to 80 million elements each) of six T9 human vertebrae that were virtually loaded to 3° of moderate forward-flexion via a homogenized disc. Across all specimens and loading rates, the measured effective modulus of the disc ranged from 5.8 to 42.7MPa and was significantly higher for higher rates of loading (p<0.002); average disc height ranged from 2.9 to 9.3mm. The parametric finite element analysis indicated that, as disc modulus increased and disc height decreased across these ranges, the vertebral bone stresses increased but their spatial distribution was largely unchanged: most of the highest stresses occurred in the central trabecular bone and endplates, and not anteriorly. Taken together with the literature, our findings suggest that the effective modulus of the human intervertebral disc should rarely exceed 100MPa and that typical variations in disc effective modulus (and less so, height) minimally influence the spatial distribution but can appreciably influence the magnitude of stress within the vertebral body.

Vertebral fragility and structural redundancy.

The mechanisms of age-related vertebral fragility remain unclear, but may be related to the degree of "structural redundancy" of the vertebra; ie, its ability to safely redistribute stress internally after local trabecular failure from an isolated mechanical overload. To better understand this issue, we performed biomechanical testing and nonlinear micro-CT-based finite element analysis on 12 elderly human thoracic ninth vertebral bodies (age 76.9 ± 10.8 years). After experimentally overloading the vertebrae to measure strength, we used nonlinear finite element analysis to estimate the amount of failed tissue and understand the failure mechanisms. We found that the amount of failed tissue per unit bone mass decreased with decreasing bone volume fraction (r(2) = 0.66, p < 0.01). Thus, for the weak vertebrae with low bone volume fraction, overall failure of the vertebra occurred after failure of just a tiny proportion of the bone tissue (<5%). This small proportion of failed tissue had two sources: the existence of fewer vertically oriented load paths to which load could be redistributed from failed trabeculae; and the vulnerability of the trabeculae in these few load paths to undergo bending-type failure mechanisms, which further weaken the bone. Taken together, these characteristics suggest that diminished structural redundancy may be an important aspect of age-related vertebral fragility: vertebrae with low bone volume fraction are highly susceptible to collapse because so few trabeculae are available for load redistribution if the external loads cause any trabeculae to fail.

Influence of vertical trabeculae on the compressive strength of the human vertebra.

Vertebral strength, a key etiologic factor of osteoporotic fracture, may be affected by the relative amount of vertically oriented trabeculae. To better understand this issue, we performed experimental compression testing, high-resolution micro-computed tomography (µCT), and micro-finite-element analysis on 16 elderly human thoracic ninth (T(9)) whole vertebral bodies (ages 77.5 ± 10.1 years). Individual trabeculae segmentation of the µCT images was used to classify the trabeculae by their orientation. We found that the bone volume fraction (BV/TV) of just the vertical trabeculae accounted for substantially more of the observed variation in measured vertebral strength than did the bone volume fraction of all trabeculae (r(2) = 0.83 versus 0.59, p < .005). The bone volume fraction of the oblique or horizontal trabeculae was not associated with vertebral strength. Finite-element analysis indicated that removal of the cortical shell did not appreciably alter these trends; it also revealed that the major load paths occur through parallel columns of vertically oriented bone. Taken together, these findings suggest that variation in vertebral strength across individuals is due primarily to variations in the bone volume fraction of vertical trabeculae. The vertical tissue fraction, a new bone quality parameter that we introduced to reflect these findings, was both a significant predictor of vertebral strength alone (r(2) = 0.81) and after accounting for variations in total bone volume fraction in multiple regression (total R(2) = 0.93). We conclude that the vertical tissue fraction is a potentially powerful microarchitectural determinant of vertebral strength.

Contribution of the intra-specimen variations in tissue mineralization to PTH- and raloxifene-induced changes in stiffness of rat vertebrae.

The intra-specimen spatial variation in mineralization of bone tissue can be changed by drug treatments that alter bone remodeling. However, the contribution of such changes to the overall biomechanical effect of a treatment on bone strength is not known. To provide insight into this issue, we used a rat model to determine the effects of ovariectomy, parathyroid hormone, and raloxifene (vs. sham) on the contribution of spatial variations in mineralization to treatment-induced changes in vertebral stiffness. Mineral density was measured from 6-microm voxel-sized quantitative micro-CT scans. Whole-vertebral and trabecular stiffness values were estimated using finite element analysis of these micro-CT scans, first including all intra-specimen variations in mineral density in the model and then excluding such variations by using a specimen-specific average density throughout each specimen. As expected, we found appreciable effects of treatment on overall bone stiffness, the effect being greater for the trabecular compartment (up to 52% reduction vs. sham, p<0.0001) than the whole vertebra (p=0.055). Intra-specimen mean mineralization was not changed with treatment but the intra-specimen variation in mineralization was, although the effect was small (4%). Intra-specimen spatial variations in mineralization accounted for 10-12% and 5-6% of overall stiffness of the trabecular compartment and whole vertebral body, respectively. However, after accounting for all treatment effects on bone geometry and trabecular microstructure, any treatment effects due to changes in mineralization were negligible (<2%), although statistically detectable (p<0.02). We conclude that, despite a role in the general biomechanical behavior of bone, the spatial variations in tissue mineralization, as measured by quantitative micro-CT, did not appreciably contribute to ovariectomy-, PTH-, or raloxifene-induced changes in stiffness of the whole bone or the trabecular compartment in these rat vertebrae.

Role of trabecular microarchitecture in whole-vertebral body biomechanical behavior.

The role of trabecular microarchitecture in whole-vertebral biomechanical behavior remains unclear, and its influence may be obscured by such factors as overall bone mass, bone geometry, and the presence of the cortical shell. To address this issue, 22 human T(9) vertebral bodies (11 female; 11 male; age range: 53-97 yr, 81.5 +/- 9.6 yr) were scanned with microCT and analyzed for measures of trabecular microarchitecture, BMC, cross-sectional area, and cortical thickness. Sixteen of the vertebrae were biomechanically tested to measure compressive strength. To estimate vertebral compressive stiffness with and without the cortical shell for all 22 vertebrae, two high-resolution finite element models per specimen-one intact model and one with the shell removed-were created from the microCT scans and virtually compressed. Results indicated that BMC and the structural model index (SMI) were the individual parameters most highly associated with strength (R(2) = 0.57 each). Adding microarchitecture variables to BMC in a stepwise multiple regression model improved this association (R(2) = 0.85). However, the microarchitecture variables in that regression model (degree of anisotropy, bone volume fraction) differed from those when BMC was not included in the model (SMI, mean trabecular thickness), and the association was slightly weaker for the latter (R(2) = 0.76). The finite element results indicated that the physical presence of the cortical shell did not alter the relationships between microarchitecture and vertebral stiffness. We conclude that trabecular microarchitecture is associated with whole-vertebral biomechanical behavior and that the role of microarchitecture is mediated by BMC but not by the cortical shell.

Gap junctions and osteoblast-like cell gene expression in response to fluid flow.

Bone formation occurs in vivo in response to mechanical stimuli, but the signaling pathways involved remain unclear. The ability of bone cells to communicate with each other in the presence of an applied load may influence the overall osteogenic response. The goal of this research was to determine whether inhibiting cell-to-cell gap junctional communication between bone-forming cells would affect the ensemble cell response to an applied mechanical stimulus in vitro. In this study, we investigated the effects of controlled oscillatory fluid flow (OFF) on osteoblastic cells in the presence and the absence of a gap-junction blocker. MC3T3-E1 Clone 14 cells in a monolayer were exposed to 2 h of OFF at a rate sufficient to create a shear stress of 20 dyne/cm(2) at the cell surface, and changes in steady-state mRNA levels for a number of key proteins known to be involved in osteogenesis were measured. Of the five proteins investigated, mRNA levels for osteopontin (OPN) and osteocalcin were found to be significantly increased 24 h postflow. These experiments were repeated in the presence of 18 beta-glycyrrhetinic acid (BGA), a known gap-junction blocker, to determine whether gap-junction intercellular communication is necessary for this response. We found that the increase in OPN mRNA levels is not observed in the presence of BGA, suggesting that gap junctions are involved in the signaling process. Interestingly, enzyme linked immunosorbent assay data showed that levels of secreted OPN protein increased 48 h postflow and that this increase was unaffected by the presence of intact gap junctions.