The Effect of Intra-Vertebral Heterogeneity in Microstructure on Vertebral Strength and Failure Patterns

Abstract

Purpose

The overall goal of this study was to determine the influence of intra-vertebral heterogeneity in microstructure on vertebral failure.

Methods

Trabecular density and microarchitecture were quantified for 32 thoracic vertebrae using micro-computed tomography (μCT)-based analyses of 4.81mm, contiguous cubes throughout the centrum. Intra-vertebral heterogeneity in density was defined as the inter-quartile range and quartile coefficient of variation of the cube densities. The vertebrae were compressed to failure to measure stiffness, strength, and toughness. Pre- and post-compression μCT images were analyzed using digital volume correlation to quantify failure patterns in the vertebrae, as defined by the distributions of residual strain.

Results

Failure patterns consisted of large deformations in the mid-transverse plane with concomitant endplate biconcavity and were linked to the intra-vertebral distribution of bone tissue. Low values of connectivity density and trabecular number, and high values of trabecular separation, were associated with high strains. However, local microstructural properties were not the sole determinants of failure. For instance, the mid-transverse plane experienced the highest strain (p<0.008) yet had the highest density, lowest structure model index, and lowest anisotropy (p<0.013). Accounting for the intra-vertebral heterogeneity in density improved predictions of strength and stiffness as compared to predictions based only on mean density (strength: R² = 0.75 vs. 0.61, p<0.001; stiffness: R² = 0.44 vs. 0.26, p=0.001).

Conclusions

Local variations in microstructure are associated with failure patterns in the vertebra. Non-invasive assessments of the intra-vertebral heterogeneity in density—which are feasible in clinical settings—can improve predictions of vertebral strength and stiffness.

Introduction

Vertebral fractures afflict approximately 12–20% of men and women over the age of 50 years [1]. These fractures are associated with increased morbidity, mortality, and risk of future fractures in the spine as well as in other anatomic sites [2,3]. Tools that enable accurate identification of individuals at high risk for vertebral fracture stand to reduce substantially the burden of osteoporotic fractures. Current methods of estimating fracture risk in the spine are based on average measures of bone mineral density (BMD) in the centrum, yet these measures explain only ~60% of the variance in vertebral strength [4] and do not discriminate well between fracture and non-fracture cohorts [5,6]. These limitations of average-BMD measurements are likely due to contributions of other factors, such as cortical thickness and curvature [4,7], and the heterogeneous distribution of bone tissue throughout the centrum [8–11]. With existing imaging modalities such as computed tomography (CT), spatial variations in density and microarchitecture throughout the vertebra can be assessed non-invasively. The challenge remains to determine how to use information on intra-vertebral heterogeneity to improve failure predictions.

Prior research has established that substantial regional variations in density and microarchitecture exist throughout the vertebra and has also suggested several biomechanical consequences of these variations. The posterior regions of the centrum tend to have higher density [12,13], volume fraction, and trabecular number, and lower structure model index (SMI) and trabecular separation [14], than the anterior regions. Bone density is also lower in the superior than inferior regions [12,14]. These regional variations may arise in part from changes in load transfer that occur with disc degeneration and sclerosis of the posterior elements [15]. Notably, an area of very low density, the superior-anterior region, is highly deformed in most wedge-shaped fractures [16,17], which are one of the most common types of age-related vertebral fractures. That fracture patterns may be linked to regional variations in trabecular structure is supported by studies of trabecular bone. For example, specimens of vertebral trabecular bone loaded in compression and torsion collapse initially in regions of low volume fraction [18,19], and larger intra-specimen variations in trabecular thickness and tissue modulus are associated with lower apparent moduli [20,21].

Accounting for intra-vertebral heterogeneity in density has been shown to improve failure predictions for vertebrae tested ex vivo. An early study found that using density measurements from multiple regions of the vertebral body, as well as the variances in density within the individual regions, resulted in better predictions of vertebral strength as compared to using the average density in the centrum [8]. More recently, the intra-vertebral heterogeneity in density, as defined by the coefficient of variation in density measurements in six regions of the centrum [22,10], or by the ratio of density in the anterior vs. posterior regions [11], was found to correlate inversely with vertebral strength [10,11,22] stiffness [10,22], and toughness [11]. However, thus far, intra-vertebral heterogeneity in density has been evaluated based only on a subset of regions within the centrum. Moreover, these prior studies have focused on vertebral strength rather than also considering mechanisms of failure. Study of how failure patterns in the vertebra relate to the distribution of bone tissue might provide key insight into these mechanisms, thus identifying new approaches for non-invasive estimation of bone strength and fracture risk. Specifically, these relationships may elucidate how certain regional variations in trabecular structure can predispose the vertebra to fracture and how a given drug therapy might reduce such predisposition.

The goal of this study was to determine the influence of intra-vertebral heterogeneity in structure on vertebral mechanical properties and failure patterns, the latter as defined by the spatial distributions of deformations that remain in the vertebra after compression testing. The objectives were: 1) to quantify the distributions of trabecular microarchitecture, density, and residual deformation throughout the vertebra; 2) to identify relationships between failure patterns and spatial variations in trabecular microarchitecture and density; and 3) to determine the dependence of vertebral mechanical properties on the intra-vertebral heterogeneity in density.

Methods

Specimen Preparation

Thirty-two vertebrae (16 T10 and 16 T11) were dissected from fresh-frozen spine segments from 16 donors (age range 70–91 years; mean 80.4 ± 6.1 years; 8 male and 8 female). Tissue of the intervertebral discs was removed from both endplates with a scalpel, and the posterior elements were removed using an autopsy saw. Vertebrae were wrapped in saline-soaked gauze followed by plastic wrap and were stored in plastic bags at −20°C when not in use.

Imaging and Mechanical Testing

Vertebrae were scanned using micro-computed tomography (μCT) at a resolution of 37 μm/voxel (μCT 80, Scanco Medical, Brüttisellen, Switzerland). The voltage, current and integration time settings were 70 kVp, 114 mA and 300 ms, respectively. A Gaussian filter was used (τ =0.8, support =1, Scanco Medical). Bone was segmented using a threshold value of 15% of grayscale intensities as determined by an iterative threshold technique ([23], Scanco Medical). The vertebrae were then prepared for mechanical testing by potting the top and bottom endplates in circular plastic dishes filled with 2–4 mm of polymethyl methacrylate. Care was taken to align the superior-inferior axis of the vertebrae with the loading axis and to keep the vertebrae hydrated at all times (Figure 1A). Specimens were compressed between two steel platens to a preload of 50 N to ensure proper seating. Five preconditioning cycles between 200 and 400 N were performed at a rate of 50 N/s, and then the force was held at 300 N for 5 minutes [24] (Instron 8874, Instron, Canton, MA). Finally, the vertebrae were loaded to failure at a rate of 0.15 mm/sec [24]. The ultimate force was defined as the maximum force sustained by the vertebra (Figure 1B). Stiffness was calculated as the maximum tangent modulus over a 1%-strain window [25]. Toughness was quantified as the area under the load-displacement curve up to the ultimate point. A second μCT scan of each vertebra was performed after mechanical testing.

Fig. 1.

(A) Experimental setup for mechanical testing; (B) Representative load-displacement curve; (C) Representative, transverse μCT cross-section showing the locations of the elliptical VOI and the 4.81mm cubes; (D) Representative histograms and box-and-whisker plots showing the distribution of BV/TV values (normalized by the total number of values, to give relative frequency) for the cubes in two vertebrae, one with low QCV and IQR and another with high QCV and IQR: In each box-and-whisker plot, the left side of the box is positioned at the 25^th percentile (Q₁; the value below which 25% of the values are found), the right side is positioned at the 75^th percentile (Q₃; the value below which 75% of the values are found), and the solid and dashed lines within the box represent the median and mean of the values, respectively. The two vertebrae have very similar median and mean BV/TV values to each other, but one has a higher inter-vertebral variation in BV/TV due to the presence of a relatively larger number cubes in the right-hand tail of the distribution.

Microarchitecture and Intra-Vertebral Heterogeneity

Using the pre-test scans, volume fraction (BV/TV), trabecular separation (Tb.Sp*), trabecular number (Tb.N*), connectivity density (ConnD), degree of anisotropy (DA), structural model index (SMI; a measure of how rod-like vs. plate-like the structure is [26]) and cross-sectional area (CSA) were calculated for a volume of interest (VOI) that was defined for each vertebra as the largest elliptical cylinder that fit entirely within the centrum (Figure 1C). The apparent mineral density (ρ_app) was also computed for this VOI and was calculated as the average grayvalue of the bone and marrow space combined, converted to units of mineral density via a standard curve generated from scans of a hydroxyapatite phantom (Scanco Medical). Intra-vertebral heterogeneity in density, defined as the quartile coefficient of variation and inter-quartile range for apparent mineral density (QCV_app and IQR_app, respectively) and volume fraction (QCV_BV/TV and IQR_BV/TV, respectively), were calculated by dividing each vertebra into contiguous cubes of side length 4.81 mm (130 pixels) (Figure 1C)—a length scale at which trabecular bone can be treated as a continuum [27]. The QCV is calculated as:

$$\mathit{QCV}-\frac{Q_3-Q_1}{Q_3+Q_1}$$ (Eq. 1)

where, Q₁ and Q₃ are the first and third quartile values, respectively (Figure 1D). We note that the quantity Q₃ – Q₁ is the inter-quartile range. For non-normal distributions of data, the quartile coefficient of variation is a better measure of relative dispersion than is the coefficient of variation. ρ_app, BV/TV, Tb.Sp*, Tb.N*, ConnD, DA, and SMI were also calculated for these cubes. Trabecular thickness (Tb.Th*) and tissue mineral density (TMD) were not used in this study due to insufficient image resolution. The ratio of average trabecular thickness (153.6 μm) to voxel size (37 μm) was less than five, indicating that measurements of Tb.Th* and TMD would not be reliable.

To examine whether measures of intra-vertebral heterogeneity in density depend on the cube size, a subset of the samples (n =14) were each divided successively into contiguous cubes of different sizes: 4.44mm (120 pixels), 5.55mm (150 pixels), 5.92mm (160 pixels), and 8.14mm (220 pixels) contiguous cubes. The data from these cubes were analyzed in the same manner as the 4.81mm (130 pixels) cubes.

Analyses of Failure Patterns

Digital volume correlation (DVC) was used to obtain direct, 3-D experimental measurements of the failure patterns in the vertebra, as defined by the distribution of residual strains throughout the centrum [28]. DVC is an extension of digital image correlation, a standard method in experimental mechanics to quantify heterogeneous surface strains [29], to measure strains throughout a 3-D volume. For the application of DVC in this study, the pre- and post-test μCT images were analyzed in an automated fashion to track the movement and deformation of multiple, individual sub-regions throughout the entire centrum. In this analysis, the grayscale variations, or image “texture”, that the μCT images contain as a result of the porous, irregular trabecular structure enable the automated tracking.

The pre- and post-test images were aligned using image registration (Scanco Medical). To define sub-regions within the vertebral body for DVC analysis, an irregular mesh that conforms to the geometry of the vertebral body was generated using IA-FEMesh modeling software (The University of Iowa, Iowa City, IA). The vertebrae were divided into irregularly shaped hexahedral sub-regions with side length ~4.8 mm. The sub-regions from pre- and post-test images were then analyzed using a custom, DVC algorithm [28,30] to determine the continuum-level displacement and strain fields throughout the entire vertebral body (Figure 2). The measured strain fields correspond to residual strain experienced by the fractured vertebra. The magnitudes of the principal strains and maximum shear strain, and the directions of these strains were computed. The displacement and strain errors from this DVC algorithm were calculated using an approach similar to that of Liu et al. [30] and were found to be 0.43 voxels and 0.0007 mm/mm, respectively.

Fig. 2.

Schematic for using DVC to calculate residual strains (minimum principal strain is shown) in the vertebra using pre- and post-test scans

Axial Rigidity

In addition to quantifying the statistical distribution of density in the vertebra, as captured by the IQR and QCV, the spatial distribution of density was examined by computing an estimate of the axial rigidity. A mechanistic approach that estimates the axial rigidity (EA) of each transverse cross section (i.e. each slice of the pre-test scan) of the vertebra was adopted from previously published methods [31,32], which compute this estimate as

$$EA=\sum _{i=1}^N{E}_{i}dA$$ (Eq. 2)

where EA is the axial rigidity, E_i is theYoung’s modulus for the i^th pixel, dA is the area of one pixel, and N is number of pixels in the cross-section. For each pixel, E_i was estimated based on the pixel intensity (I) according to

$$E={cI}^b$$ (Eq. 3)

where b = 7.4 [33] and c was determined by setting the 97^th percentile of the pixel intensities within the vertebra to have a Young’s modulus of 17 GPa [34], i.e., by assuming that pixels with intensity equal to the 97^th percentile were occupied by mature, lamellar tissue. A sensitivity analysis was performed to examine the effect of setting 17 GPa as the modulus corresponding to the 100^th through the 95^th percentile in intensity values. For some specimens, the 100^th percentile corresponded to bright pixels from a few particles of metal dust that became attached to the surface of the vertebra during sample preparation. The 97^th percentile fell in the middle of the range of percentile values over which the resulting value of EA was insensitive to the percentile value and for which the few pixels corresponding to the metal had minimum contribution to EA.

The minimum value of EA over all transverse cross-sections (EA_min) was identified for each vertebra since it has been hypothesized that fracture load is correlated with minimum structural rigidity [31]. Predicted vertebral strength was then defined using the yield strain of trabecular bone (0.0077mm/mm) [35] and the minimum axial rigidity:

$$F_{\mathit{ult}}=0.0077\left({EA}_{min}\right)$$ (Eq. 4)

Statistics

Repeated-measures analyses of variance (ANOVAs) (JMP 9.0, SAS Institute Inc., Cary, NC) were used to determine the dependence of each of the microstructural properties and the components of residual strain on anatomic location and sex. The data from the 4.81mm, contiguous cubes were grouped by anatomic locations: 1) superior, middle or inferior transverse plane; 2) posterior, middle, or anterior coronal plane; and 3) left, middle, or right sagittal plane. For each outcome variable, a repeated-measures ANOVA was carried out for each of these three groupings and was followed by Wilcoxon signed-rank test for pairwise comparisons. Subsequently, analyses of covariance (ANCOVAs) were used to examine the dependence of residual strains on microstructural properties (the covariate) and anatomic location and sex (the two grouping factors). These ANCOVAs were used to examine whether the regions of high residual strain occurred preferentially in certain anatomic locations within the vertebra and/or in locations with certain microstructural characteristics (e.g., low volume fraction). For each microstructural variable and type of strain (compressive or shear), one ANCOVA was performed for each of the three anatomic groupings. The ANCOVAs allowed assessment of associations between strains and microstructure, and of interactions between microstructure and either or both grouping factors (e.g., whether and how the association between strain and volume fraction differed among transverse planes). All of these statistical analyses accounted for inclusion of multiple cubes and vertebrae (T10 and T11) from each donor, and the Bonferroni correction was used when applicable.

Linear-regression analyses (JMP 9.0, SAS Institute Inc., Cary, NC) were used to determine the dependence of ultimate force, stiffness and toughness on each of the following combinations of explanatory variables: 1) ρ_app*CSA and QCV_app; 2) ρ_app*CSA; 3) BV/TV*CSA and QCV_BV/TV; 4) BV/TV*CSA; and 5) EA_min. Restricted vs. full F-tests were used to compare regression models 1 and 2 and models 3 and 4 to examine the additional, predictive effect of accounting for intra-vertebral heterogeneity in density. J-tests [36] were used to compare model 5 to models 1 and 2 and also to models 3 and 4. Forward-stepwise regression analyses were used to test the dependence of ultimate force on the architectural parameters, using models 1 and 3 as the baseline. Finally, the effect of accounting for intra-vertebral variation in density in addition to donor age and sex was analyzed using linear-regression analyses. A significance level of 0.05 was used for all statistical analyses.

Four vertebrae were excluded from the study. One vertebra had a pre-existing fracture (T11, female, age 86), and a second suffered an operator error in mechanical testing (T10, male, age 87). Two additional vertebrae, which were both from one donor (male, age 86), were excluded because they had extremely low values of BV/TV and ρ_app and very thick shells compared to other vertebrae. The mean density of the elliptical VOI, the IQR in the cube densities, and the QCV in cube densities were either higher or lower than the median, elliptical-VOI density of all 32 vertebrae by two-to-four times the inter-quartile range (e.g., the inter-quartile range of the elliptical-VOI densities of the 32 vertebrae), and these two vertebrae were considered as outliers.

Results

Distributions of trabecular microstructure and residual strain

Substantial intra-vertebral heterogeneity in density and trabecular microstructure was observed. When the three transverse planes—superior, middle and inferior—were compared using a repeated-measures ANOVA, the middle plane was found to have high ρ_app and BV/TV, and low DA and SMI, while the superior plane had low ConnD and high DA (p<0.013) (Figure 3A–C). The inferior transverse plane had the highest Tb.N* and lowest Tb.Sp* (p<0.001). Among coronal planes, the posterior plane had the highest ρ_app, BV/TV, ConnD, and Tb.N*, and the lowest Tb.Sp*, DA, and SMI (p<0.001). The middle sagittal plane had low ConnD and high SMI as compared to the left and right sagittal planes (p<0.033). The regional variations in microstructure exhibited a mild dependence on sex. Whereas men had higher ConnD and Tb.N* but lower Tb.Sp* than women overall (p<0.051), these sex-dependent differences were more pronounced for some regions than others. For example, the differences between sexes in Tb.N* and Tb.Sp* were larger in the superior and middle transverse planes as compared to the inferior plane.

Fig. 3.

Distributions of: (A) Volume fraction; (B) Apparent mineral density; (C) Connectivity density; (D) Minimum principal strain (large compressive strains shown in red); (E) Maximum shear strain (large shear strains shown in red). The color of each of the nine regions corresponds to the median value over all vertebrae. *: Significantly different transverse planes; #: Significantly different coronal planes

Residual strains were also non-uniformly distributed throughout the vertebra (Figure 2D–E). The minimum principal strain (maximal compressive strain) was most compressive in the middle transverse plane (p=0.004). Near the superior endplate, larger compressive strains occurred in the center as compared to the periphery; a similar, though milder, trend was found near the inferior endplate, indicating overall a development of endplate biconcavity. No differences in minimum principal strain were found among coronal or sagittal planes (p>0.248). The maximum shear strain was higher in the middle transverse plane than in the inferior plane (p=0.008). High shear strains were distributed throughout the superior transverse plane; a trend that was different from the inferior plane, in which high shear strain occurred in the center. The middle sagittal plane had higher maximum shear strain than the left sagittal plane (p=0.047). No differences in maximum shear strain were found among the coronal planes (p>0.480). Similar patterns of residual strain were found for both sexes; however, vertebrae from female donors tended to have higher shear strains in all transverse (p=0.071), coronal (p=0.087) and sagittal (p=0.019) planes. Neither the directions of the principal strains nor those of the maximum shear strain were uniformly aligned with the loading axis (superior-inferior direction) or the other two anatomical axes of the vertebrae.

Relationships between Failure Patterns and Spatial Distributions of Trabecular Microstructure

Failure patterns, as defined by the distributions of residual strain, were associated with the spatial distributions of multiple features of the trabecular microstructure. When the grouping of cubes was done according to coronal plane, the ANCOVAs indicated that small values of ConnD and Tb.N*, and high values Tb.Sp* were associated with large compressive (p<0.050) and large shear (p<0.025) strains, and low values DA were associated with large shear strains only (p=0.039). When the grouping was done according to sagittal plane, high values of Tb.Sp* were associated with large shear strains (p=0.015).

Interaction terms in many of the ANCOVAs were also significant, meaning that the association between microstructure and strain differed depending on anatomic location and/or sex. For example, in the superior and middle transverse planes, large compressive strains were associated with low SMI, low Tb.N*, and high DA, and large shear strains were associated with low SMI, yet the opposite associations were found for the inferior transverse plane (p<0.049). High values of Tb.Sp* were associated with large compressive and shear strains in the superior and inferior planes, yet the opposite association was found for the middle layer (p<0.016). With regards to sex, high DA was associated with low shear strains for women yet high shear strains for men (p<0.039). All other sex-dependent differences were coupled with differences between T10 and T11. For example, for T10, high BV/TV was associated with large strains for women and small strains for men, while the opposite result was found for T11 (p<0.003).

Predictions of Mechanical Properties

Accounting for the intra-vertebral variation in density in addition to mean density significantly improved predictions of vertebral strength. Including QCV_BV/TV in addition to BV/TV*CSA in the regression model improved the coefficient of determination (R²) from 0.61 to 0.75 (p<0.001) (Table 1 and Figure 4A). Including QCV_app in addition to ρ_app*CSA in the regression model produced a trend towards improved predictions (R² = 0.73 vs. 0.76; p=0.096) (Table 1). Using IQR as a measure of heterogeneity produced similar results to those obtained with QCV, but with higher p-values from the F-tests (p=0.019 for the models with BV/TV and p=0.127 for the models with ρ_app). Regression models with stiffness as a dependent variable were also improved when intra-vertebral heterogeneity was included, though the coefficients of determination were lower than those for the regressions with strength as the dependent variable (Table 1). None of the regression models with toughness as a dependent variable were significant (p>0.3; Table 1). Although the minimum axial rigidity (EA_min) was a significant predictor of vertebral strength (p=0.003; Figure 4B), the results of the J-tests indicated that models based on EA_min did not perform as well as those based on the mean density and intra-vertebral heterogeneity in density (Table 2). For the stepwise regressions, including ConnD in addition to QCV_BV/TV and BV/TV*CSA improved predictions of vertebral strength (R² = 0.75 vs. 0.76; p<0.001). However, none of the architectural parameters were found to improve the strength prediction when ρ_app was used instead of volume fraction as the measure of density.

Table 1.

Regressions of mechanical properties against measures of average density (either BV/TV or ρ_app), with and without the QCV in density (n=28).

Explanatory variable(s)	Volume Fraction (BV/TV)		Apparent Mineral Density (ρapp)
	R2	F-test p-value	R2	F-test p-value
Ultimate Force
QCVDensity	0.13		0.00
Density* CSA	0.61*	0.001+	0.73*	0.096
Density* CSA, QCVDensity	0.75*		0.76*
Stiffness
QCVDensity	0.18*		0.02
Density* CSA	0.26*	0.008+	0.27*	0.189
Density* CSA, QCVDensity	0.44*		0.32*
Toughness
QCVDensity	0.03		0.00
Density* CSA	0.03	0.403	0.04	0.883
Density* CSA, QCVDensity	0.05		0.04

^*: Regression is significant (p<0.05).

⁺: F-test indicates an improvement in the R² value when QCV is added to the regression model (p<0.05).

Fig. 4.

Measured ultimate force vs. the ultimate force predicted from: (A) BV/TV*CSA and QCV_BV/TV (B) EA_min. RMSE: root mean square error. In (A), the regression result for the model without QCV_BV/TV is shown for comparison.

Table 2.

Regression models ranked using J-tests from best to worst predictions of vertebral strength (n=28). EA_min is not computed using BV/TV or ρ_app, so the results for this model are the same for both of the sets of columns.

Explanatory variable(s)	Apparent Mineral Density (ρapp)			Volume Fraction (BV/TV)
	Rank	R2	RMSE (kN)	Rank	R2	RMSE (kN)
Density*CSA, QCVDensity	1	0.76	0.50	1	0.75	0.51
Density*CSA	1	0.73	0.52	2	0.61	0.63
EAmin	3	0.29	0.85	3	0.29	0.85

Accounting for the intra-vertebral variation in density also tended to improve the coefficient of determination when donor age and sex were considered. For example, including QCV_BV/TV in addition to BV/TV*CSA, age, and sex as explanatory variables improved the R² value from 0.72 to 0.80 (p=0.005). However, for this expanded set of explanatory variables, no improvement in the model prediction was found when ρ_app was used as the density measure (p=0.231). In these expanded models, sex was not a significant variable (p<0.116), and age showed a trend towards significance (p<0.094).

The above findings regarding the predictive power of measures of intra-vertebral heterogeneity were not specific to the 4.81mm-cube size. The measures of heterogeneity computed for the different cube sizes were correlated with each other (BV/TV: p<0.019 for all cube sizes; ρ_app: p<0.043 for cubes sizes >4.44 mm). Regression models of vertebral strength with intra-vertebral variation in density in addition to mean density were significant for all cube sizes (p<0.004). However, the contribution of heterogeneity measures to the models was only significant for cube sizes 4.81mm and 5.55 mm (F-tests: p<0.03).

Discussion

In light of the growing attention on the potential biomechanical consequences of spatial inhomogeneity in bone structure within the vertebra and the possibilities of measuring this inhomogeneity in the clinical setting, our focus in this study was to examine the influence of intra-vertebral heterogeneity in density and microarchitecture on vertebral failure. We found multiple associations between the observed failure patterns and the spatial variations in density and microarchitecture. Interestingly, the middle transverse plane of the vertebrae had the highest density, lowest SMI (i.e., less rod-like trabeculae), and lowest degree of anisotropy, yet this plane experienced the highest compressive and shear strains. In contrast, the endplate concavity was more pronounced in the superior than inferior plane, and the superior plane had the lowest connectivity density and highest degree of anisotropy. When the interplay among anatomic location, sex, and microstructure was investigated via the ANCOVAs, low values of connectivity density and trabecular number, and high values of trabecular separation, were found to be associated with regions of high strain. Links between the other microarchitectural metrics and strain magnitudes differed depending on anatomic location and sex. These collective results indicate that the locations of failure in the vertebra are influenced, but not determined purely, by local variations in density and microarchitecture.

This association between the intra-vertebral distribution of bone tissue and vertebral failure patterns was also found to extend to vertebral strength and stiffness. Predictions of strength and stiffness based on average density and cross-sectional area were improved when the regression models also incorporated a numerical measure of the intra-vertebral heterogeneity in density. Though similar results were found whether the quartile coefficient of variation or the inter-quartile range was used as the measure of heterogeneity, the former may be preferred since it is independent of the mean (p>0.259). The regression models that incorporated intra-vertebral heterogeneity in density along with average density were further improved, albeit slightly, by including connectivity density. The fact that connectivity density was the lone microarchitectural property that enhanced the strength predictions, combined with our findings regarding the association between connectivity density and failure patterns, and with those of prior studies [14,37], suggests a key role for this property in vertebral failure. Given that the intra-vertebral variance in density and trabecular connectivity can be measured clinically using multi-detector-row computed tomography (MDCT) [38], these results have immediate bearing on current clinical approaches to estimating vertebral strength and fracture risk.

While our results regarding the predictive role of intra-vertebral heterogeneity appear consistent with prior studies [8,9,22,10], there is an important contradiction. Prior studies have shown a decrease in strength with increasing heterogeneity [10,22], yet our data show the opposite. The two likely sources of this difference are that we quantified heterogeneity using regional density measures throughout the entire vertebral centrum, rather than in only a small sampling of regions, and that we used different statistical measures of heterogeneity. The distributions of density obtained from the contiguous cubes were non-Gaussian, prompting us to use the quartile coefficient of variation and inter-quartile range instead of the coefficient of variation and standard deviation as the heterogeneity measures. Moreover, the distributions were positively skewed (long right-hand tail), indicating that, for a given average density, increased heterogeneity arose from a larger number of cubes with high density (Figure 1D), thus producing the positive correlation between heterogeneity and strength and stiffness. We revisited our data to sample regions of the vertebra that matched the regions defined by Kim et al. [22,10] and to use the coefficient of variation as the heterogeneity measure, and we obtained similar results to those prior two studies. However, when we sampled our data to match the regions analyzed by Wegryzn et al. and used their heterogeneity measure (the ratio of the posterior to anterior volume fraction), we found no correlation with strength, perhaps due to differences in vertebral level (T10/T11 vs. L3) and scan resolution. These ancillary analyses indicate above all that how one defines the intra-vertebral heterogeneity in density can have a major effect on the results. We also examined heterogeneity by computing an estimate of the axial rigidity, and similar to previous findings [39] found a comparatively poor correlation. Although CT-derived estimates of the structural rigidity of vertebrae provided reasonable predictions of strength fracture risk in vertebrae with metastases or simulated lytic lesions [32,40], this method may be less effective for the comparatively subtle changes in vertebral trabecular bone due to aging.

A novel aspect of this study was the use digital volume correlation to obtain direct, 3-D, experimental measurements of the failure patterns in the vertebral bodies. As compared to qualitative examination of plain-film X-rays, the DVC results provide more detailed descriptions of the deformations throughout the vertebral body. These results revealed that even though the vertebrae were loaded in axial compression, large shear deformations occurred, both in the mid-transverse plane and underlying the central region of the inferior endplate, and the directions of greatest compressive strain were not always axial. The results also revealed more pronounced endplate concavity near the superior vs. inferior endplate, which could be attributed to endplate fracture. The DVC results were also essential for identifying the role of local variations in apparent mineral density, connectivity density, and other features of the microarchitecture in vertebral failure. This role appears to be complex, in that the influence of structure on the locations of failure was often mediated by anatomic location. Indeed, in contrast to prior hypotheses that regions of sparse, rod-like trabeculae in the vertebra are those at greatest risk for failure [14], we found that the residual deformations were highest in the comparatively dense, less rod-like, and less anisotropic, mid-transverse plane of the vertebra.

The limitations of this study relate mainly to the experimental procedures. First, the vertebrae used for this study were from lower thoracic spine and may not be applicable to other vertebral levels. Second, the need for high-resolution scans for the DVC analyses and regional measurements of microstructure precluded the use of a clinical CT scanner. Further work is required to determine if the utility of the intra-vertebral heterogeneity holds for clinical CT images and, possibly, dual-energy X-ray absorptiometry, which would involve lower radiation exposure. Third, we examined the effect of cube size for only a subset (n =14) of the vertebrae, and it is possible that we might have found a significant contribution of the intra-vertebral heterogeneity in density for additional cube sizes if we had enlarged that subset. However, we believe that it is unlikely that the contribution would be significant for cube sizes much different from approximately five millimeters on a side, because for regions much larger and much smaller, the trabecular structure within each region becomes very heterogeneous [27]. Fourth, we tested isolated vertebrae to avoid the confounding influence of the varying quality of the intervertebral discs, and the nature of the load application was necessarily less physiological as a result. The load distribution on the endplates is thought to be relatively uniform in healthy intervertebral discs and to become more non-uniform with disc degeneration [41]. In our experiments, we subjected all vertebrae to uniform loading and hence we are not able to examine how the intra-vertebral heterogeneity in density and microarchitecture might result from disc degeneration or how the influence of this heterogeneity on vertebral failure might be altered by the presence of a degenerated disc. Finally, the deformations that we quantified were only the residual strains. The patterns of initial failure may be different. Prior studies that have quantified initial failure events in excised specimens of trabecular bone have found that the regions of initial failure tend to be those of low volume fraction and connectivity density [18,19], whereas our results for whole vertebral bodies show a more pronounced interaction between microstructure and anatomic location. At present, we cannot determine if this discrepancy is due to possible differences between initial and final failure patterns or to differences in failure mechanics between isolated specimens of trabecular bone and whole bones. Future work that involves μCT imaging while the compressive load is applied on the vertebra is necessary to obtain real-time, 3-D, strain measurements.

In summary, we have found that non-invasive assessments of the intra-vertebral heterogeneity in density can improve predictions of vertebral strength and stiffness and that local variations in microstructure are associated with failure patterns in the vertebra. Among the many microarchitectural parameters, connectivity density emerged as the most consistently associated with vertebral failure. These findings suggest the potential clinical utility of measurements of connectivity density and the intra-vertebral heterogeneity in bone density for enhanced prediction of vertebral strength and fracture risk.