Vertebrae were collected from 15 male (66±15 yrs) and 25 female (54±16 yrs) cadavers. Three dimensional finite element models were constructed using microcomputed tomography images of cylindrical specimens. Linear finite element models were used to estimate apparent modulus and stress in the cylinders during uniaxial compression. The intra-specimen mean, standard deviation (SD) and coefficient of variation (CV) of microstructural variables were calculated.

Mixed model statistical analysis of the results demonstrated that increases in the intra-specimen variability of the microstructure contribute to increases in the variability of trabecular stresses and decreases in bone stiffness. These effects were independent from the contribution from intra-specimen average of the microstructure. Further, the effects of microstructural variability on bone stiffness and stress variability were not accounted for by connectivity and anisotropy. Microstructural variability properties (SD, CV) generally increased with age, were greater in females than in males and in T12 than in L1. Significant interactions were found between age, gender, vertebra and race. These interactions suggest that microstructural variability properties varied with age differently between genders, races and vertebral levels.

Engineering theories predict that the intra-sample variability of microstructure should have an effect on the mechanical properties of a cellular material like cancellous bone [2, 23, 45, 50]. Several previous studies did consider the intra-sample variability of cancellous microstructure and its effect on bone stiffness. However, each had features which limited their contributions to understanding. Some of these studies were limited to theoretical analyses using generic or limited 2D bone geometries for mechanical analysis [46, 55]. Some considered anatomic sites that are far apart from each other or from the sites of clinical interest [1, 6]. In the latter case, small samples were obtained from whole bones, and the properties were assumed to be homogeneous within each bone sample. Studies that considered the intra-sample variability of cancellous microstructure in vertebral bone at a finer scale than the whole bone were generally of pilot nature [20, 27, 30, 61] and used very few samples. Thus the association of intra-sample variability of microstructure with donor age, gender, anatomic site and bone mechanical properties in vertebral bone remains largely unknown.

Trabecular stress distribution parameters (trabecular shear stress per apparent uniaxial stress and coefficient of variation of trabecular shear stress) as estimated from large scale finite element (FE) analyses have been associated with age [59], bone strength [14] and with the amount of in vivo microdamage [56] in human vertebral cancellous bone. Similarly, measures of microstructural variability have been associated with structural mechanical properties of whole vertebral bodies [29, 47, 60]. Clinical data also indicate that measures of microstructural variability are associated with fracture risk in spine [31], hip [15] and the wrist [34] whether measured at, or remote from, the site of interest. The variability of stresses would be expected to be associated with variability of the microstructure for bone loaded predominantly in uniaxial compression. The relationship between stress distributions and the average properties of cancellous microstructure has been examined for vertebral bone [59] but not extended to the distribution properties of the microstructure.

Details of specimen preparation, μCT scanning, reconstruction, linear FE models and calculation of apparent modulus (E_FEM) and stress distribution properties were previously reported [59]. Two main trabecular stress distribution parameters, namely, coefficient of variation of trabecular von Mises stress distributions (VMCV) and average trabecular shear variation stress per apparent uniaxial stress (VMExp/σ_app) were considered. The apparent modulus and stress distribution parameters used in the current study were the same as those in our previous study. Degree of anisotropy (DA) and connectivity density (-#Euler/Vol) were also calculated in previous work [59].

Trabecular microstructural parameters (BV/TV, Tb.Th, Tb.N and Tb.Sp) were calculated for each slice of the micro-CT image (~200 slices/specimen perpendicular to the supero-inferior direction; each 50μm thick) using 2D stereologic methods [17]. The intra-specimen mean (Av), standard deviation (SD) and coefficient of variation (CV) of each microstructural variable were calculated for each specimen. Multiple regression was used to assess the relationships between mechanical (E_FEM, VMCV and VMExp/σ_app) and microstructure parameters. Specifically, multiple regression models containing both the average and standard deviation of a microstructural parameter were used to examine the effect of the SD of a parameter in presence of its mean. Nonnormality in parameters and nonlinearity in relationships between some of the parameters were expected based on previous work [58, 59], therefore, multiple regressions were re-performed on Box-Cox-transformed variables [5]. The transformation was of the form X(^λ)=(x^λ−1)/λγ^λ−1 (λ≠0) or X(^λ)=γ ln(x) (λ=0), where γ is the geometric mean of the untransformed variable x. An optimal value of the transform parameter (λ) was determined for each variable so as to minimize sum of square of errors around the mean. All transformations are such that the transformed parameter increases with increasing untransformed parameter.

Stepwise regression models with DA, -#Euler/Vol, BV/TV.Av, BV/TV.SD, Tb.N.Av, Tb.N.SD as predictors were considered to examine whether an SD parameter can contribute further to the prediction of a mechanical parameter in presence of a set of conventional average properties. In these models, BV/TV.Av was introduced first and forced to remain in the model. The inclusion of Tb.N.Av in the predictor set caused substantial multicollinearity as indicated by a variance inflation factor (VIF) of 27.7 and 40.0 for the untransformed and transformed set of predictors, respectively. Subsequently, we removed Tb.N.Av from the predictor set which resulted in a maximum VIF of 2.25 and 2.82 for untransformed and transformed set of predictors, respectively.

Mixed model procedures were used to examine the effect of vertebra type, gender and age on the microstructure distribution properties. Because we had a mixed group of black and white donors, race was also included in the models (as identified in the medical record). Analysis started with examination of interactions between effects. The analysis proceeded in a backward stepwise fashion where nonsignificant terms were removed starting with higher order interactions followed by lower order interactions and main effects. When a significant interaction was present, the sample was separated according to the interacting terms and the sub-groups were analyzed separately. Final models were constructed by removing the nonsignificant effects and interactions from the initial model.

In multiple regression models that included both the average and standard deviation of microstructural parameters, E_FEM increased with increasing BV/TV.Av, Tb.Th.Av and Tb.N.Av, and decreased with increasing Tb.Sp.Av (Table 1; Figure 1). Conversely, both VMCV and VMExp/σ_app decreased with increasing BV/TV.Av, Tb.Th.Av and Tb.N.Av, and increased with increasing Tb.Sp.Av (p<0.0001 for all) (Table 1; Figure 2).

E_FEM decreased with increasing BV/TV.SD and Tb.Th.SD independent of the effect of their mean values (Table 1; Figure 1). Conversely, both VMCV and VMExp/σ_app increased with increasing BV/TV.SD and Tb.Th.SD independent of the effect of their mean values (p<0.01 for all) (Table 1; Figure 2). Additionally, VMCV increased with increasing Tb.N.SD and Tb.Th.SD independent of the effect of their mean values (p<0.02).

Stepwise regression models selected at least one standard deviation parameter as a significant predictor in addition to the mean of that parameter for E_FEM and VMCV but not for VMExp/σ_app (Table 2).

Average BV/TV and Tb.N decreased while Tb.Sp.Av increased with age (p<0.0001 for all) with no other significant effect in the model. Significant interaction of age and gender was found for Tb.Th.Av (p<0.009). Further analysis after separating the data between males and females indicated that Tb.Th.Av was smaller in T12 than in L1 (p<0.03) and decreased with age (p<0.002) in females (Table 3, Figure 3).

Microstructural variability properties (SD, CV) generally increased with age, were greater in females than in males and in T12 than in L1 (Tables 3–4). A number of significant interactions found between age, gender, vertebra and race suggesting that microstructural variability properties varied with age differently between genders, races and vertebral levels.

Absolute variability of microstructural properties (SD) generally increased with age, were greater in females than in males and in T12 than in L1: BV/TV.SD (p<0.009) and Tb.Th.SD (p<0.01) were greater in females than in males with no other significant effect in the models. A significant main effect of vertebral level was found (p<0.02) for the Tb.N.SD model indicating greater Tb.N.SD in T12 than in L1. A four-way interaction was noted for Tb.N.SD (p<0.05) warranting separate analysis of subgroups (Table 3). Tb.N.SD decreased with age in the T12 vertebrae of white females and black males (p<0.03) while it increased with age in L1 vertebrae of black females (p<0.05). Tb.Sp.SD was greater in T12 than in L1 (p<0.04) and increased with age (p<0.0003) (Table 3).

There are large differences in vertebral fracture risk between men and women. However, the exact sources of this difference are unclear. Very few studies noted gender-specific differences in vertebral cancellous bone microstructure [36]. No difference was noted between men and women in vertebral cancellous bone strength, bone volume fraction or ash density, or in their respective relationship with age [12, 35, 36, 51] when bone samples of similar size and anatomic location were examined. Differences in the anisotropy, bone loss patterns and transverse strength have been observed between male and female vertebral cancellous bone in some age groups after age-stratification. However, the microstructural changes were not consistent from age group to age group so as to explain the strength changes. For example, a greater distance between horizontal trabeculae was noted in females from above 75 years of age compared to females in the 50–75 years of age group. This difference suggests a greater susceptibility to fracture in the former, especially when loaded in the horizontal direction. However, when the samples were tested by loading horizontally, their strength was not different (0.31±0.12 MPa to 0.30±0.18 MPa) (others found similar results [36]), despite predictions to the contrary [21, 52]. Therefore, differences in uniaxial strength and average microstructure between male and female vertebral cancellous bone do not appear to explain the large differences in occurrence of vertebral fractures between them. The current results show that women have significantly greater cancellous bone variability than men in the anterior portion of T12 and L1 vertebrae. This previously unobserved difference in bone quality between males and females may be important in explaining the higher propensity of female vertebrae to fracture. There is some clinical evidence that the heterogeneity of cancellous bone properties can separate vertebral fracture patients from non-fracture patients [10, 31] suggesting that bone heterogeneity may be useful for predicting vertebral fracture risk.

Some of the differences in fracture risk between men and women may be attributable to the larger crossectional area of male vertebrae and their greater ability to expand with age than female vertebrae [4, 11, 37]. It was predicted that female vertebrae will lose strength at a higher rate than male vertebrae with age, primarily due to a greater loss of BMD in females than in males rather than due to crossectional area changes [4]. On the other hand, experimentally measured vertebral strength appears to decrease at a similar rate with age in men and women [37]. Nonetheless, a greater loss of whole vertebral bone mass with age in females than in males, together with identical rate of age-related bone mass loss in the central anterior region in Mosekilde studies, suggests that the loss of bone mass in women is more regional than in men. Such a bone loss pattern would result in an increased heterogeneity of bone mass in women compared to men. Together, these results suggest that the differences in microstructural heterogeneity observed between men and women in the current study might exist at the whole bone level as well.

There are differences in vertebral fracture risk between black and white races as well; blacks have a lower incidence of fractures (eg. [49]). Blacks are generally reported to have higher bone mass than whites, which is generally attributed to different rates of bone mass accumulation during growth [16]. However, the differences in vertebral cancellous bone architecture between blacks and whites are less well understood. BV/TV, trabecular thickness and turnover rates were generally evaluated from iliac crest bone and the differences between blacks and whites are largely dependent upon gender and geographic origin. Higher Tb.Th has been reported for African blacks than for whites in the iliac crest bone [44]. BV/TV has also been reported to be higher in African blacks than in whites but for men only [44]. While turnover rate has been reported to be higher in African blacks than in whites [43], it has been reported to be lower in American blacks than in whites [18, 53]. The relationship of microstructural parameters with age was also both gender- and race-dependent for African blacks: Trabecular thickness decreased in all groups except black males, trabecular number decreased in all groups except black females and, analogously with changes in trabecular number, trabecular separation increased in all groups except black females [44]. It is difficult to know to what extent the previous findings from iliac crest can be extrapolated to vertebra due to substantial differences between iliac crest and vertebral cancellous bone properties within an individual [38, 48]. Nevertheless, given these previous results, it is not surprising that we have found high order interactions of race with age and gender for our parameters. To our knowledge, age-related changes in cancellous bone heterogeneity, moreover, differences by race and gender have not been documented previously. Further understanding of these differences may provide insight into the role of genetic and environmental factors in regulation of bone microstructure.

The significant differences observed in the variability of cancellous microstructure between T12 and L1 were less than 10% but were greater than were observed for the average microstructure (Table 4) [59]. The variability parameters were also less well-correlated between the T12 and L1 of the same individual than were the average parameters (Table 4) [59]. These results suggest that while variations in average bone microstructure can be explained by factors common to the T12-L1 segment of the spine, the organization of this microstructure as measured by the variability of trabecular morphology is more dependent on local factors. The differences in microstructural variability between vertebrae that are far apart is expected to be greater than between the T12 and L1 [58]. As such, variability of trabecular microstructure within a vertebra may be a sufficiently sensitive parameter to detect small differences between vertebrae that are similar in their average microstructure.

The increase in VMCV and VMExp/σ_app with increasing variability of the microstructure is consistent with previous findings that cancellous bone strength decreases with increasing VMCV [14] and vertebral strength decreases with increasing heterogeneity of bone mass [8, 29]. Together with the observation that increased microdamage content is associated with increased VMCV and VMExp/σ_app in vertebral bone, the current results suggest that microstructural heterogeneity is a measure of stress concentration in cancellous bone. The effect of microstructural variability on VMCV seems more prominent than on VMExp/σ_app, possibly due to the fact that VMExp/σ_app is a ratio of volume averages whereas the stress variability is directly incorporated in VMCV. The results of our multiple regression analyses indicate that microstructural heterogeneity contributes to trabecular stress variability independently from the average of the same parameter and independently from a set of conventionally measured microstructural parameters. These results suggest that vertebral strength prediction would be improved when microstructural heterogeneity information is available.

Consideration must be given to qualities of bone other than uniaxial strength, however. The existing data indicate that bone heterogeneity can reflect additional aspects of vertebral failure such as structural ductility [60] and fatigue resistance [33]. Further, cellular materials with irregularly shaped and distributed cells like cancellous bone have higher creep rates than those with regular cells even if they are stiffer [2]. Similarly, analysis of the effect of random removal of struts within a foam on the creep rate indicates that removal of only a few percent of the struts can dramatically increase the creep rate by one to two orders of magnitude whereas the effect of uniform thinning is not as dramatic [23]. The differences we found in microstructural variability between genders, race and anatomic sites may manifest differences in the fatigue and/or creep behavior of bone between these populations. Nonetheless, due to the complex nature of in vivo fractures, it is important that clinical data are obtained to ultimately test the utility of bone heterogeneity in predicting fracture.

Some limitations outlined in our previous study also apply to the current study [59]. Briefly, voxel size used in the reconstruction of image volumes, homogeneous element properties used in the FE analyses, exclusion of vertebral regions other than the central anterior portion of the vertebral bodies and use of stereologic methods in calculation of microstructural parameters were identified as limitations. Slice-by-slice stereologic calculation of trabecular microstructure is subject to errors and will provide values that are different from those calculated by direct methods [9, 19]. However, dividing the sample volume in smaller regions of interest was necessary and the slice-by-slice approach provided a large number of data points from which distribution parameters could be calculated. It should be noted that BV/TV calculated from the slice-by-slice approach and that directly calculated by voxel counting had over 99% correlation (data not shown) in the current sample. This is consistent with a previous report that microstructural parameters calculated using direct methods are highly correlated to those calculated using a model-based method [9]. While microstructural heterogeneity has information content distinct from the average as well as from connectivity and anisotropy, its relationship with other microstructural properties such plate- vs rod-likeness of trabeculae remains to be elucidated. Also, consideration of the spatial distribution in addition to the statistical distribution properties of microstructure could provide further information on the nature of the heterogeneity [61]. This study was also limited to an investigation of the cancellous tissue from the anterior region. It is desirable to ultimately extend the results to the whole vertebrae. However, it is important to note that cancellous bone properties from the anterior region are strongly associated with whole vertebral strength [8, 28]. Thus, our study, while limited, is still very relevant to overall vertebral bone quality. The effect of modulus heterogeneity on finite element calculations of cancellous bone stiffness and stress distributions has been reported to be 6–20% [3, 40, 41]. However, the determination of mineralization distributions and modulus assignment based on micro-CT gray levels can be problematic due to artifacts inherent in the micro-CT scans [25] or due to lack of established relationships to accurately convert these values to modulus. Anatomic site, species and tissue processing differences could also result in a difference in the magnitude of this effect. It should also be pointed out that elastic moduli directly measured by nanoindentation had less variability than estimated by micro-CT gray levels and had little to no effect in FE calculation of apparent modulus of human vertebral bone in recent studies [7, 54]. Thus, these limitations are expected to have minor effects on our results but not affect our conclusions about cancellous tissue. In the end, the use of these conditions allows for direct comparisons between the current study and the previous ones that focused on average microstructural properties and trabecular stress variability [14, 22, 56, 57, 59].

The current study did not focus on the biological factors underlying microstructural heterogeneity, although mechanical loading might be expected to play a role. For example, it has been reported that low magnitude vibrations caused changes in the microstructure of trabecular bone which were associated with a reduced skewness of trabecular stresses and strains [24]. Previous work also suggested that status of the intervertebral disc and the end plate is associated with the regional microstructural and mechanical properties of cancellous bone [26], stress distributions within a vertebra [13, 32, 39] and the whole vertebral mechanical properties [39].