The biomechanical role of the vertebral cortical shell remains poorly understood. Using high-resolution finite element modeling of a cohort of elderly vertebrae, we found that the biomechanical role of the shell can be substantial and that the load sharing between the cortical and trabecular bone is complex. As a result, a more integrative measure of the trabecular and cortical bone should improve noninvasive assessment of fracture risk and treatments.
Introduction: A fundamental but poorly understood issue in the assessment of both osteoporotic vertebral fracture risk and effects of treatment is the role of the trabecular bone and cortical shell in the load-carrying capacity of the vertebral body.
Materials and Methods: High-resolution μCT-based finite element models were developed for 13 elderly human vertebrae (age range: 54–87 years; 74.6 ± 9.4 years), and parameter studies—with and without endplates—were performed to determine the role of the shell versus trabecular bone and the effect of model assumptions.
Results: Across vertebrae, whereas the average thickness of the cortical shell was only 0.38 ± 0.06 mm, the shell mass fraction (shell mass/total bone mass)—not including the endplates—ranged from 0.21 to 0.39. The maximum load fraction taken by the shell varied from 0.38 to 0.54 across vertebrae and occurred at the narrowest section. The maximum load fraction taken by the trabecular bone varied from 0.76 to 0.89 across vertebrae and occurred near the endplates. Neither the maximum shell load fraction nor the maximum trabecular load fraction depended on any of the densitometric or morphologic properties of the vertebra, indicating the complex nature of the load sharing mechanism. The variation of the shell load-carrying capacity across vertebrae was significantly altered by the removal of endplates, although these models captured the overall trend within a vertebra.
Conclusions: The biomechanical role of the thin cortical shell in the vertebral body can be substantial, being about 45% at the midtransverse section but as low as 15% close to the endplates. As a result of the complexity of load sharing, sampling of only midsection trabecular bone as a strength surrogate misses important biomechanical information. A more integrative approach that combines the structural role of both cortical and trabecular bone should improve noninvasive assessment of vertebral bone strength in vivo.
THE NEED FOR improved diagnosis and treatment of osteoporosis is magnified by the inadequacy of the current clinical standard, DXA—which is 2-D in nature—to accurately predict osteoporotic fractures(1) or explain the fracture risk reduction caused by treatment effects. (2) One limitation with DXA is that it cannot distinguish between trabecular and cortical compartments. QCT, which is 3-D, can isolate the trabecular compartment, allowing the potential of providing separate assays of trabecular versus cortical compartments. For the spine, the central trabecular bone is most commonly sampled clinically. (3) However, results from cadaver studies suggest that including BMD measurements from the cortical shell might improve fracture risk prediction. (4) Moreover, the clinical performance of therapeutic treatments might depend on the relative effects on the trabecular bone versus cortical shell. (5, 6) Thus, understanding the load sharing between the cortical shell and the trabecular bone, both within individual vertebrae (spatially) and across multiple vertebrae, may ultimately lead to improved noninvasive assessment of fracture risk and drug treatment efficacy.
Despite much research on the topic, the load sharing between the cortical shell and trabecular bone in the human vertebra remains unclear. Cadaver studies have reported that the shell accounts for anywhere from 10–75% of the vertebral strength. (7–9) However, because of the technical difficulty of precisely removing the thin shell (0.25-0.4 mm thick(10–13)), researchers have more recently turned to finite element modeling. (14–21) Such studies have consistently shown that the amount of load taken by the shell compared with the trabecular bone depends on the axial distance from the endplate and reaches a maximum at the midtransverse plane. (16–18, 21) Whereas two studies using QCT-based clinical-resolution scans have shown that the contribution of the shell to vertebral strength was higher in lower density bone, (14, 20) one study reported no correlation of the shell load-carrying capacity with trabecular BMD. (16) These finite element studies used either a generic model of the shell(17, 21)—which is limited by the assumptions regarding the morphology and mechanical properties of the shell— or imaged the shell using clinical-resolution QCT scans, (14, 16, 20) which overestimates the shell thickness. (10) Thus, those models possess limited fidelity in terms of how the shell is modeled. Addressing the need for higher-resolution analyses to better elucidate mechanisms, truly mechanistic finite element models of the whole vertebral body have recently been developed from μCT scans at spatial resolutions on the order of 40–60 μm. (15, 18, 19) However, because these studies have thus far analyzed either only one(19) or two(18) human vertebrae, and involve model assumptions such as removal of the endplates, (15, 19) their results are difficult to generalize. Even so, these analyses suggest that the cortical shell, despite its thin nature, may account for on the order of 50% of the load-carrying capacity of the vertebra.
The overall goal of this study was to better elucidate the load sharing between the cortical shell and trabecular bone within and across vertebrae. Toward this end, high-resolution μCT-based finite element models were developed for a cohort of elderly human vertebrae, and a series of parameter studies was performed to quantify the integrative structural role of the cortical shell versus trabecular bone. Specifically, our objectives were to (1) determine the dependence of the load sharing between the shell and trabecular bone on the relative amount of shell mass, trabecular bone volume fraction, and vertebral geometry; and (2) determine the effect of removal of the endplates on these trends—thus providing insight into the influence of the disc on the overall structural role of the shell. Accurate modeling of the thin porous shell using μCT-based finite element models of a cohort of vertebrae distinguishes this study from previous ones and provides a substantial degree of closure to this important clinical issue.
MATERIALS AND METHODS
Thirteen T10 whole vertebral bodies were obtained from female human cadavers (age range: 54–87 years; 74.6 ± 9.4 years). After removal of the posterior elements and soft tissues, the vertebral bodies were vacuum wrapped in plastic and μCT scanned at 30-μm resolution (Scanco 80; Scanco Medical AG, Basserdorf, Switzerland). A specimen-specific threshold value—one per vertebra—was determined using visual inspection. The shell was defined as the outer structure in the vertebral body, recognizing that the shell is a porous structure. (10) An averaging technique was used within an image processing software (IDL; Research Systems, Boulder, CO, USA) to identify the nonuniform porous shell in all the transverse cross-sections excluding the endplates. (19) Based on the maximum and minimum thickness measurements of the cortical shell reported by Silva et al., (10) the average size of a pore in the shell was calculated as 180 μm. Any bone encountered within 180 μm of the outer structure of the shell was identified as part of the shell (Fig. 1).
To better understand load sharing and the effect of endplate removal, which has been used in previous experimental and computational studies, (19, 22) two linearly elastic finite element models—an intact vertebral body with the endplates augmented by disc material and a transected vertebral body with the endplates removed—were developed for each vertebra (Fig. 2). The disc material added to the intact vertebral body model extended to a height of 2.5 mm(23) to model one-half of the disc on the top and bottom of the vertebral body. Using a numerical convergence analysis, an isotropic finite element size of 60 μm was chosen based on a compromise between the computational savings involved (∼80%) and the resulting error (6.5% ± 3.5% for the shell load fraction—shell load/ total load) compared with 30-μm resolution. Both the shell and trabecular tissue were assigned the same hard tissue properties (elastic modulus of 18.5 GPa and Poisson's ratio of 0.3) because the cortical shell is often described as condensed trabeculae. (10, 24, 25) The disc was assumed to be degenerated because the mean age of the cadaver specimens was 75 years. Based on evidence from the literature that the degenerated nucleus pulposus loses its fluid-like behavior, (26, 27) the disc was modeled as a homogeneous material having elastic properties typical of the annulus (compressive elastic modulus of 8 MPa(28) and Poisson's ratio of 0.45(29, 30)).
Depending on the vertebra size, the resulting finite element models had up to 60 million elements and 220 million degrees of freedom and required highly specialized software and hardware for analysis. All analyses were run on an IBM Power4 supercomputer (IBM, Armonk, NY, USA) using a maximum of 440 processors in parallel and 900 GB memory, and a custom code with a parallel mesh partitioner and algebraic multigrid solver. (31) To simulate compressive loading of each vertebra, a constant apparent level compressive strain of 1% was applied to each vertebra using different displacement magnitudes based on the height of each vertebra. The top surface of each model was displaced in the superior-inferior direction using roller-type boundary conditions, whereas the bottom surface was fixed using minimal frictionless constraints to prevent rigid body motion.
Various explanatory variables were calculated from the transected model at 60-μm resolution to describe the densitometric and morphologic properties of the vertebra. The morphology parameters studied were the trabecular bone volume fraction, average shell thickness, shell mass fraction (shell bone mass/total bone mass), and vertebral curvature. The trabecular bone volume fraction was determined from the maximum size cuboid of trabecular bone in the vertebral body, typically 20 mm on a side (Fig. 1). The average shell thickness was calculated from the shell image data by processing one transverse cross-section at a time and averaging over all thickness measurements. (19) The vertebral curvature was defined as the average of the curvatures in the midfrontal and midsagittal vertebral sections (Fig. 3).
Several output parameters were used to characterize the load sharing between the cortical shell and trabecular bone in the region excluding the endplates. The shell load fraction (defined as the ratio of shell load to total load) was calculated for each transverse cross-section and plotted as a function of axial position. The total load was calculated as the product of the sum of axial stresses in all elements at a particular transverse cross-section and the cross-sectional area of each element. The shell load was calculated similarly by calculating the axial load taken by the cortical shell elements. From this, the maximum values of load fraction for the cortical shell and trabecular bone over any transverse section were determined for both the intact and transected models of each vertebra. The maximum trabecular load fraction equivalently represents the minimum shell load fraction (trabecular load fraction = 1 − shell load fraction). To describe the variation in the shell load fraction within a vertebral body along the inferior-superior axis, the percent variation in shell load fraction was calculated across transverse slices (Fig. 4).
To provide insight into some factors that might influence the load sharing in the vertebral body, a pairwise correlation analysis was performed between the outcome variables describing the load sharing and the explanatory variables describing the densitometric and morphologic properties of the vertebral body. Comparison of the correlation analyses with the intact and transected model highlighted the effects of endplate removal and in that way provided unique insight into the complexity of the load sharing behavior.
The maximum shell load fraction (determined using the intact models), which occurred typically at the midtransverse cross-section within each vertebral body, varied between 0.38 and 0.54 across the 13 vertebrae, whereas the maximum trabecular load fraction, which typically occurred near the endplates, varied from 0.76 to 0.89. Across vertebrae, the average value of the maximum shell load fraction was 0.45, whereas that of maximum trabecular load fraction was 0.85 (Fig. 5). Although the average ± SD shell thickness across vertebrae was only 0.38 ± 0.06 mm, the shell mass fraction (not including the endplates) ranged from 0.21 to 0.39, and tended to be greater in vertebrae having lower values of trabecular bone volume fraction (r2 = 0.30, p = 0.05).
The maximum load fraction of the shell and trabecular bone in the intact models did not depend on any of the explanatory variables (Table 1). In particular, measures of maximum load fraction were not significantly correlated with measures of mass fraction in the intact models (Fig. 6). The percent variation of the shell load fraction within a vertebra correlated only weakly with the curvature of the vertebral body (r2 = 0.40, p = 0.02).
Table Table 1.. Correlation Coefficient (r) for Pairwise Correlations Between Output Parameters and Explanatory Variables for the Intact and Transected Models
Removal of the endplate resulted in a wider range of values for the maximum load fraction taken by the shell and trabecular bone in the transected models (Fig. 5). Although the load sharing predicted by the transected model followed the general load sharing variation within each vertebral body (Fig. 7), it overpredicted the maximum shell load fraction by 21% on average. The correlation analyses from the transected model showed highly significant dependencies that were not present in the intact model (Table 1). For example, the maximum shell load fraction, which was not significantly correlated with shell mass fraction in the intact model that contained the endplate and disc, was highly correlated with shell mass fraction in the transected model (Fig. 6).
Given the potential clinical importance of the cortical shell with respect to both fracture risk and drug treatment assessments, the goal of this study was to elucidate the load sharing between the cortical shell and trabecular bone within and across vertebrae. The percent bone mass attributable to the cortical shell—not including the endplates—was surprisingly large, ranging from 21% to 39% across vertebrae, even though the average shell thickness was only on the order of 0.38 mm. The maximum fraction of load taken by this thin shell at midsection was substantial and varied between 0.38 and 0.54. In contrast, the maximum load fraction in the trabecular bone ranged from 0.76 to 0.89 across vertebrae and typically occurred near the endplates. Perhaps most importantly, neither the maximum shell load fraction nor the maximum trabecular load fraction depended on any of densitometric or morphologic properties of the vertebra, indicating that no single factor (among those studied) can determine the complex load sharing mechanism between the cortical shell and the trabecular bone. Removal of the endplates and disc reduced this inherent complexity of the vertebral body structure, and although these models were able to capture the overall trend of the load sharing within a vertebra (Fig. 7), the variation of the shell load-carrying capacity across vertebrae was appreciably altered (Fig. 6). Taken together, these quantitative results elucidate the relative biomechanical roles of the cortical shell and trabecular bone in the human thoracic vertebra, results that have broad clinical significance. In particular, they emphasize the need for a more biomechanically integrative approach in assessing vertebral strength.
A major strength of this study was that we applied the relatively new and highly insightful μCT-based finite element modeling technique to analyze multiple whole vertebrae, thereby providing external validity and the ability to determine those factors that influenced the relative load sharing between the shell and trabecular bone. Assuming a constant hard tissue density of 2 g/cm3 and a linear relation between QCT BMD and apparent density, (32) our cohort of elderly vertebrae spanned a range of QCT BMD values for the trabecular bone both above (n = 6) and below (n = 7) a reported clinical fracture threshold of 110 mg/cm3. (3) From a more technical perspective, the thin, porous shell was characterized in detail using the μCT scans, and our average thickness of 0.38 mm agreed well with direct measurements reported elsewhere. (10–13) Combining analyses of the intact models—which describe the load sharing in a more physiological manner—and the transected models—which have been previously used in experimental(22) and computational(19) studies—provided a better understanding of the complex nature of the load sharing and showed the simplification introduced through the removal of the disc and endplates. From a computational perspective, our study used the state-of-the-art in large scale supercomputer methods, (31) including a numerical convergence study to justify our discretization strategy.
Despite these strengths, there were some limitations. First, although the disc is viscoelastic in nature, it was modeled as a homogeneous elastic material. This is justified because we are focusing on the stress distributions in the bone and not the disc itself. Based on existing literature that the degenerated nucleus pulposus has a solid-like behavior, (26, 27) the entire disc material was assigned the properties of the annulus, representative of a state of degeneration more typical of the aged vertebrae used in this study and having more direct clinical relevance to osteoporosis. Moreover, the compressive modulus of the annulus was determined from the axial tests on bone-annulus-bone specimens at the physiologic loading rates. (28) The effect of varying the elastic modulus and the Poisson's ratio of the disc on the load sharing was tested for one specimen (Appendix). Results suggested that our estimate of the maximum shell load fraction should be accurate within an error bound on the order of 8%. Second, the same homogeneous material properties were assumed for both cortical and trabecular tissue, which is well justified by the existing literature on this issue. (10, 24, 25) Moreover, previous studies(33–35) have reported high correlations between experimental and model-predicted apparent level properties using models with homogeneous material properties. Third, linear elastic analyses were performed on all models, and thus overall strength of the vertebra was not obtained. Because measures of stiffness determined from finite element models are highly correlated with experimentally measured strength, (36–38) the trends reported here should mirror those for strength behavior, although we did not address strength explicitly. Fourth, the loading mode used in all the analyses was uniform compression. Because most osteoporotic vertebral fractures are wedge fractures, (39) the response to combined compression and anterior-posterior bending is of clinical interest. Although the role of the shell under such loading conditions is unclear at this juncture, it is well possible that the shell may play a more important role under such loading conditions because peripheral bone has a greater structural role in bending behavior for the vertebra. (40)
Accurate modeling of the whole vertebral body with realistic boundary conditions has helped us resolve the conflicting literature on the structural role of the cortical shell. The range of maximum load fraction taken by the shell reported here (0.38-0.54) is consistent with the limited data available from a previous high-resolution finite element analyses. (18) In that study, two vertebrae representing extreme T score values had reported maximum shell load fractions of 40% (normal vertebra) and 55% (osteoporotic vertebra). Because removal of the shell results in the unloading of the peripheral trabeculae because they no longer are connected to any bone material, (19) the role of the shell reported by the experimental studies that removed the shell(7–9) is expected to be higher than the range observed here. Moreover, any possible damage to the peripheral trabecular bone during shell removal would not result in appreciable reductions in strength beyond that caused by loss of the shell. This reasoning is consistent with the 45–75% reduction in vertebral strength observed by Rockoff et al. (7) and a 40% mean strength reduction reported by Yoganandan et al. (9) We suggest that the low average value of strength reduction (10%) reported by McBroom et al. (8) is possibly a result of their concern not to damage the underlying trabecular bone—that in fact they did not remove all the shell by their careful manual sanding process. Using QCT-based finite element models at 1-mm resolution, Homminga et al. (16) reported similar values to that reported here for the maximum shell load fraction (30-65%) and found that load sharing in situ at the midsection was not correlated with trabecular BMD, again consistent with this more detailed study. Taken together, the bulk of the available evidence indicates that the role of the shell at the midsection is substantial, sustaining about 45% of the total compressive load on average.
Studying the effect of endplate removal provided unique appreciation of the complex nature of the in situ load sharing between the shell and trabecular bone. Consistent with a generic model(21) in which the shell and trabecular bone shared load as springs in parallel, the results from the transected models showed that the shell load fraction depended on the average shell thickness (Table 1). However, inclusion of the endplates with disc introduced an additional complexity, the effect of which was strongly specimen-specific (Fig. 7) and not easily explained by a parallel-spring analogy. Because of the disc and its relation to the endplate, as well as the highly variable curvature of the shell and endplate, the load transfer from endplate to cortical shell is complex and not obviously dependent on mass fraction ratios. As a result, a more biomechanically integrative approach, in which the structural contributions of the cortical shell, trabecular bone, endplate, and overall vertebral geometry are accounted for, may be required to properly assess vertebral strength.
Finally, our results have practical implications for in vivo noninvasive assessment of vertebral strength. The biomechanical role of the thin cortical shell is maximum at the midsection, whereas the role of trabecular bone is greatest near the endplates. As a result, when sampling trabecular bone as a surrogate for vertebral strength, the midsection is the least appropriate region of interest because the role of the trabecular bone is least there. This would explain why that approach has not been highly successful at predicting biomechanically measured vertebral strength in the cadaver laboratory. (36) We conclude therefore that improvements in the assessment of both osteoporosis fracture risk and treatment effects should be achievable by better describing the integrative structural behavior of the entire vertebra rather than focusing on just the trabecular bone, particularly at midsection. If precision issues can be addressed, improvements in the current clinical standard for diagnosing osteoporosis may be possible by adopting a lateral DXA(41, 42) rather than anterior-posterior DXA, because this would provide a more integral measure of cortical and trabecular bone and eliminate the confounding posterior elements. Other approaches such as clinical-resolution QCT-based integral measures of BMD(6, 43) and/or QCT-based finite element models(14, 16, 36) may also provide improvements in clinical fracture risk prediction, although clinical studies are required to show this.
Funding was provided by National Institute of Health Grant AR49828. Computational resources were available through Grants UCB-254 and UCB-266 from the National Partnership for Computational Infrastructure. All the finite element analyses were performed on an IBM Power4 supercomputer (Datastar, San Diego Supercomputer Center). Human tissue was obtained from National Disease Research Interchange and the University of California at San Francisco. μCT scanning was performed at Exponent Inc., Philadelphia, PA, USA. We thank Dr Dan Mazzucco and Jennifer Vondran for imaging the specimens and Eric Wong for assistance with specimen preparation.
The authors have no conflict of interest.
We performed a sensitivity study to account for the uncertainty associated with the assumed disc material properties. One specimen was analyzed, in which the elastic modulus and Poisson's ratio of the disc were varied over what we considered to be possible physiological values. (28, 30) With the Poisson's ratio fixed, changes in elastic modulus from 8 to 11 MPa had a negligible effect (<1%) on the maximum shell load fraction. With the elastic modulus of the disc held fixed, variation in the Poisson's ratio from 0.30 to 0.49 resulted in values of the maximum shell load fraction ranging from 0.53 to 0.46. Thus, the percent error of our estimate of the maximum shell load fraction (0.49) should be on the order of 8%.