The Effect of Regional Variations of the Trabecular Bone Properties on the Compressive Strength of Human Vertebral Bodies

A concise gradient tensor model in quantitatively describing the anisotropic properties of lumbar trabecular bone

OBJECTIVE

This study aimed to evaluate the feasibility of image gradient methods for quantifying directional heterogeneity in lumbar trabecular bone.

METHODS

A total of 326 male patients' lumbar CT images were collected and grouped by age (20-39 years, 40-59 years, and ≥ 60 years). The tangential gradient calculation was performed on the mid-sagittal plane of the L4 vertebra, and the ratio of the longitudinal to transverse gradient (ratio_σ) was computed to construct a gradient tensor model. Statistical analysis was conducted to assess the differences in ratio_σ among the groups. Individuals with the same bone mineral density were selected to construct finite element models to validate the value of different tensor models for fracture risk assessment.

RESULTS

Our study results indicate that there is significant directional heterogeneity in the lumbar trabecular core across all age groups, which becomes more pronounced with advancing age, as evidenced by the gradual increase in ratio_σ values (1.44±0.29 for 20-39 years group, 1.86±0.19 for 40-59 years group, and 2.10±0.33 for ≥ 60 years group). Finite element analysis results at the same bone mineral density show that the high tensor group has a higher proportion of fracture risk elements compared to the low tensor group.

CONCLUSION

The trabecular core shows marked directional heterogeneity with age-dependent variations. Using directional gradient decomposition, we developed gradient tensor models to quantify direction-specific remodeling states in bone microstructures. This tensor-based approach also enables fracture risk assessment at comparable bone mineral density levels.

Risk of bony endplate failure during vertebral fracture

The endplate region of the vertebra, which includes the bony endplate (BEP) and underlying subchondral trabecular bone (STB), is critically involved in vertebral fracture (VF). While evidence abounds that failure initiates in the endplate region, the relative risk of failure of the BEP vs. STB has not been established. In this study, micro-finite element models were constructed of L1 vertebrae (n = 21) that were mechanically tested in a prior study and given experimentally matched boundary conditions corresponding to the vertebra's yield point. Volumes of interest (VOIs) were defined corresponding to the BEP and STB; the remainder was defined as the mid-vertebral body (MVB). The proportion of elements within each VOI that yielded was defined as the VOI yield fraction, and this value divided by the yield fraction of the entire model was defined as the normalized yield fraction. While yield fraction did not differ across VOIs (p = 0.179), normalized yield fraction was greater in the BEP than STB and MVB (p < 0.001), indicating a higher risk of yield in the BEP compared to the other two VOIs. None of the yield fractions was correlated with BEP or STB microstructure, and tension (rather than compression) was the dominant mode of tissue level yield. These findings indicate that the BEP, more so than the STB, is likely the site of VF initiation and that current methods of screening for VF risk, because they omit specific analysis of the BEP, are missing the region that matters the most. The endplate region of the vertebra, which includes the bony endplate (BEP) and underlying subchondral bone (SB), is critically involved in vertebral fracture (VF). While evidence abounds that failure initiates in the endplate region, the relative risk of failure of the BEP vs. SB has not been established. In this study, micro-finite element models were constructed of L1 vertebrae (n = 21) that had been mechanically tested in a prior study, and they were given experimentally matched boundary conditions corresponding to the vertebra's yield point. Volumes of interest (VOIs) were defined corresponding to the BEP and SB; the remainder was defined as the mid-vertebral body (MVB). The proportion of yielded elements within each VOI was defined as the VOI yield fraction, and this value divided by the yield fraction of the entire model was defined as the normalized yield fraction. While yield fraction did not differ across VOIs (p = 0.179), normalized yield fraction was greater in the BEP than SB and MVB (p < 0.001), indicating a higher risk of yield in the BEP compared to the other two VOIs. None of the yield fractions was correlated with BEP or SB microstructure, and tension (rather than compression) was the dominant mode of tissue level yield. These findings indicate that the BEP, more so than the SB, is likely the site of VF initiation and that current methods of screening for VF risk, because they omit specific analysis of the BEP, are missing the region that matters the most.

The Relationship Between the Heterogeneity of Lumbar Vertebral Trabecular Bone Mineral Density Distribution and Osteoporotic Vertebral Fractures

This study aims to investigate the relationship between the spatial distribution and heterogeneity of lumbar vertebral trabecular volumetric bone mineral density (vBMD) and osteoporotic vertebral fractures(OVF). This retrospective study included the L1 and L2 vertebrae of 143 participants with osteoporotic vertebral fractures and 429 age- and sex-matched no-fractured controls. Spatial distribution was assessed using the superior/middle and inferior/middle ratios, while heterogeneity was indicated by the quartile coefficient of variation (QCV) and interquartile range (IQR). We used QCT to measure the integral vBMD of the vertebra and the regional vBMD in the superior, middle, and inferior subregions. QCV and IQR were computed for both integral vertebrae and three subregions using voxel values from CT images. Differences between fracture and control groups were analyzed after stratification by age and sex. T-tests and Wilcoxon rank-sum tests assessed differences in spatial distribution and heterogeneity between fracture and control groups. Conditional logistic regression was employed to evaluate the associations between spatial distribution and heterogeneity with osteoporotic vertebral fractures. Trabecular vBMD was higher in the middle subregion of the vertebrae than the superior and inferior subregions. The fracture group had lower mean integral vBMD than controls. In terms of the spatial distribution, significant differences in the superior/middle and inferior/middle ratios of the L1 vertebra were observed between the fracture and control groups in the female 40-60 years group. The superior/middle ratio of the L1 vertebra in males was positively correlated with the fracture risk. Regarding heterogeneity, the fracture group had a higher QCV than the control group. QCV was positively correlated with fracture risk, with no significant variation between sexes. The spatial distribution and heterogeneity of trabecular vBMD are crucial for predicting vertebral fracture risk. These indicators are essential for fracture risk assessment and may inform prevention and treatment strategies.

Comparative study of lumbar bone mineral content using DXA and CT Hounsfield unit values in chest CT

BACKGROUND

Bone mineral content (BMC) values in certain bones and changes in BMC over time are key features for diagnosing osteoporosis. This study examined those features using morphometric texture analysis in chest computational tomography (CT) by comparing a dual-energy X-ray absorptiometry (DXA)-based BMC. An accessible approach for screening osteoporosis was suggested by accessing BMC using only Hounsfield units (HU).

METHODOLOGY

The study included a total of 510 cases (255 patients) acquired between May 6, 2012, and June 30, 2020, at a single institution. Two cases were associated with two chest CT scans from one patient with a scan interval of over two years, and each scan was followed soon after by a DXA scan. Axial cuts of the first lumbar vertebra in CT and DXA-based L1 BMC values were corrected for each case. The maximum trabecular area was selected from the L1 spine body, and 45 texture features were extracted from the region using gray-level co-occurrence matrices. A regression model was employed to estimate the absolute BMC value in each case using 45 features. Also, an additional regression model was used to estimate the change in BMC between two scans for each patient using 90 features from the corresponding cases.

RESULTS

The correlation coefficient (CC) and mean absolute error (MAE) between estimates and DXA references were obtained for the evaluation of regressors. In the case of the BMC estimation, CC and MAE were 0.754 and 1.641 (g). In the case of the estimation of change in BMC, CC and MAE were 0.680 and 0.528 (g).

CONCLUSION

The modality using morphometric texture analysis with CT HUs can indirectly help screening osteoporosis because it provides estimates of BMC and BMC change that show moderate positive correlations with DXA measures.

Density and mechanical properties of vertebral trabecular bone-A review

Being able to predict the mechanical properties of vertebrae in patients with osteoporosis and other relevant pathologies is essential to prevent fractures and to develop the most favorable fracture treatments. Furthermore, a reliable prediction is important for developing more patient- and pathology-specific biomaterials. A plethora of studies correlating bone density to mechanical properties has been reported; however, the results are variable, due to a variety of factors, including anatomical site and methodological differences. The aim of this study was to provide a comprehensive literature review on density and mechanical properties of human vertebral trabecular bone as well as relationships found between these properties. A literature search was performed to include studies, which investigated mechanical properties and bone density of trabecular bone. Only studies on vertebral trabecular bone tissue, reporting bone density or mechanical properties, were kept. A large variation in reported vertebral trabecular bone densities, mechanical properties, and relationships between the two was found, as exemplified by values varying between 0.09 and 0.35 g/cm3 for the wet apparent density and from 0.1 to 976 MPa for the elastic modulus. The differences were found to reflect variations in experimental and analytical processes that had been used, including testing protocol and specimen geometry. The variability in the data decreased in studies where bone tissue testing occurred in a standardized manner (eg, the reported differences in average elastic modulus decreased from 400% to 10%). It is important to take this variability into account when analyzing the predictions found in the literature, for example, to calculate fracture risk, and it is recommended to use the models suggested in the present review to reduce data variability.

Pharmaceutical electrospinning and 3D printing scaffold design for bone regeneration

Bone regenerative engineering provides a great platform for bone tissue regeneration covering cells, growth factors and other dynamic forces for fabricating scaffolds. Diversified biomaterials and their fabrication methods have emerged for fabricating patient specific bioactive scaffolds with controlled microstructures for bridging complex bone defects. The goal of this review is to summarize the points of scaffold design as well as applications for bone regeneration based on both electrospinning and 3D bioprinting. It first briefly introduces biological characteristics of bone regeneration and summarizes the applications of different types of material and the considerations for bone regeneration including polymers, ceramics, metals and composites. We then discuss electrospinning nanofibrous scaffold applied for the bone regenerative engineering with various properties, components and structures. Meanwhile, diverse design in the 3D bioprinting scaffolds for osteogenesis especially in the role of drug and bioactive factors delivery are assembled. Finally, we discuss challenges and future prospects in the development of electrospinning and 3D bioprinting for osteogenesis and prominent strategies and directions in future.

Trabecular Architecture and Mechanical Heterogeneity Effects on Vertebral Body Strength

PURPOSE OF REVIEW

We aimed to synthesize the recent work on the intra-vertebral heterogeneity in density, trabecular architecture and mechanical properties, its implications for fracture risk, its association with degeneration of the intervertebral discs, and its implications for implant design.

RECENT FINDINGS

As compared to the peripheral regions of the centrum, the central region of the vertebral body exhibits lower density and more sparse microstructure. As compared to the anterior region, the posterior region shows higher density. These variations are more pronounced in vertebrae from older persons and in those adjacent to degenerated discs. Mixed results have been reported in regard to variation along the superior-inferior axis and to relationships between the heterogeneity in density and vertebral strength and fracture risk. These discrepancies highlight that, first, despite the large amount of study of the intra-vertebral heterogeneity in microstructure, direct study of that in mechanical properties has lagged, and second, more measurements of vertebral loading are needed to understand how the heterogeneity affects distributions of stress and strain in the vertebra. These future areas of study are relevant not only to the question of spine fractures but also to the design and selection of implants for spine fusion and disc replacement. The intra-vertebral heterogeneity in microstructure and mechanical properties may be a product of mechanical adaptation as well as a key determinant of the ability of the vertebral body to withstand a given type of loading.

The micro-structural analysis of lumbar vertebrae in alcoholic liver cirrhosis

Although vertebral fracture is more common among alcoholic liver cirrhosis patients when compared to general population, current data on three-dimensional micro-architecture are scarce. Our study showed significant trabecular deterioration in lumbar vertebrae obtained from alcoholic liver cirrhosis donors, suggesting that they should be advised to undergo early-stage screening for osteoporosis.

PURPOSE

Recent studies showed an increased incidence of vertebral fractures in alcoholic liver cirrhosis (ALC) patients, while data about vertebral micro-structure are still limited. The aim of this study was to compare trabecular and cortical micro-architecture of lumbar vertebrae between ALC patients and healthy age- and sex-matched controls.

METHODS

Our study included lumbar vertebral samples of male cadaveric donors, divided into ALC (n = 20, age: 59 ± 6 years) and control group (n = 20, age: 59 ± 8 years). Following pathohistological verification of liver cirrhosis, trabecular and cortical bone micro-architecture was analyzed by micro-computed tomography (micro-CT).

RESULTS

Micro-CT evaluation of the trabecular bone in lumbar vertebrae showed a significant decrease in bone volume fraction, trabecular thickness, trabecular number, and connectivity (p < 0.01). In contrast to trabecular deterioration, prominent alteration in cortical parameters was not observed in lumbar vertebrae of ALC patients (p > 0.05).

CONCLUSIONS

Our data indicate that susceptibility to non-traumatic fractures in ALC patients could be explained by alterations in trabecular bone micro-architecture. Thus, we genuinely recommend osteological screening of the lumbar spine for all ALC patients in order to evaluate individual fracture risk. Graphical abstract.

Heterogeneity and Spatial Distribution of Intravertebral Trabecular Bone Mineral Density in the Lumbar Spine Is Associated With Prevalent Vertebral Fracture

The spatial heterogeneity in trabecular bone density within the vertebral centrum is associated with vertebral strength and could explain why volumetric bone mineral density (vBMD) exhibits low sensitivity in identifying fracture risk. This study evaluated whether the heterogeneity and spatial distribution of trabecular vBMD are associated with prevalent vertebral fracture. We examined the volumetric quantitative computed tomography (QCT) scans of the L3 vertebra in 148 participants in the Framingham Heart Study Multidetector CT study. Of these individuals, 37 were identified as cases of prevalent fracture, and 111 were controls, matched on sex and age with three controls per case. vBMD was calculated within 5-mm contiguous cubic regions of the centrum. Two measures of heterogeneity were calculated: (i) interquartile range (IQR); and (ii) quartile coefficient of variation (QCV). Ratios in the spatial distributions of the trabecular vBMD were also calculated: anterior/posterior, central/outer, superior/mid-transverse, and inferior/mid-transverse. Heterogeneity and spatial distributions were compared between cases and controls using Wilcoxon rank sum tests and t tests and tested for association with prevalent fractures with conditional logistic regressions independent of integral vBMD. Prevalent fracture cases had lower mean ± SD integral vBMD (134 ± 38 versus165 ± 42 mg/cm3 , p < .001), higher QCV (0.22 ± 0.13 versus 0.17 ± 0.09, p = .003), and lower anterior/posterior rBMD (0.65 ± 0.13 versus 0.78 ± 0.16, p < .001) than controls. QCV was positively associated with increased odds of prevalent fracture (OR 1.61; 95% CI, 1.04 to 2.49; p = .034), but this association was not independent of integral vBMD (p = .598). Increased anterior/posterior trabecular vBMD ratio was associated with decreased odds of prevalent fracture independent of integral vBMD (OR 0.38; 95% CI, 0.20 to 0.71; p = .003). In conclusion, increased trabecular vBMD in the anterior versus posterior centrum, but not trabecular vBMD heterogeneity, was associated with decreased risk of prevalent fracture independent of integral vBMD. Regional measurements of trabecular vBMD could aid in determining the risk and underlying mechanisms of vertebral fracture. © 2019 American Society for Bone and Mineral Research.

Association of vertebral endplate microstructure with bone strength in men and women

Epidemiological and biomechanical evidence indicates that the risk of vertebral fracture differs between men and women, and that vertebral fracture frequently involves failure of the endplate region. The goal of this study was to compare the bone microstructure of the endplate region-defined as the (bony) vertebral endplate and underlying subchondral trabecular bone-between sexes and to determine whether any such sex differences are associated with vertebral strength. The bone density (volume fraction, apparent density and tissue mineral density) of the superior-most 2 mm of the vertebra, and the bone density and trabecular architecture of the next 5 mm were quantified using micro-computed tomography in human T8 (12 female, 16 male) and L1 (13 female, 12 male) vertebrae. Average density of the vertebra (integral bone mineral density (BMD)) was determined by quantitative computed tomography and compressive strength by mechanical testing. Few differences were found between male and female vertebrae in the density of the endplate region; none were found in trabecular architecture. However, whereas endplate volume fraction was positively correlated with integral BMD in male vertebrae (r = 0.654, p < .001), no correlation was found in the female vertebrae (r = 0.157, p = .455). Accounting for the density of the endplate region improved predictions of vertebral strength (p < .034) and eliminated sex-specificity in the strength prediction that was based on integral BMD alone. These results suggest that the density of the endplate region influences vertebral fracture and that non-invasive assessment of this region's density can contribute to predictions of vertebral strength in men and women.

Material properties of human lumbar intervertebral discs across strain rates

BACKGROUND CONTEXT

The use of finite element (FE) methods to study the biomechanics of the intervertebral disc (IVD) has increased over recent decades due to their ability to quantify internal stresses and strains throughout the tissue. Their accuracy is dependent upon realistic, strain-rate dependent material properties, which are challenging to acquire.

PURPOSE

The aim of this study was to use the inverse FE technique to characterize the material properties of human lumbar IVDs across strain rates.

STUDY DESIGN

A human cadaveric experimental study coupled with an inverse finite element study.

METHODS

To predict the structural response of the IVD accurately, the material response of the constituent structures was required. Therefore, compressive experiments were conducted on 16 lumbar IVDs (39±19 years) to obtain the structural response. An FE model of each of these experiments was developed and then run through an inverse FE algorithm to obtain subject-specific constituent material properties, such that the structural response was accurate.

RESULTS

Experimentally, a log-linear relationship between IVD stiffness and strain rate was observed. The material properties obtained through the subject-specific inverse FE optimization of the annulus fibrosus (AF) fiber and AF fiber ground matrix allowed a good match between the experimental and FE response. This resulted in a Young modulus of AF fibers (-MPa) to strain rate (ε˙, /s) relationship of YMAF=31.5ln(ε˙)+435.5, and the C₁₀ parameter of the Neo-Hookean material model of the AF ground matrix was found to be strain-rate independent with an average value of 0.68 MPa.

CONCLUSIONS

These material properties can be used to improve the accuracy, and therefore predictive ability of FE models of the spine that are used in a wide range of research areas and clinical applications.

CLINICAL SIGNIFICANCE

Finite element models can be used for many applications including investigating low back pain, spinal deformities, injury biomechanics, implant design, design of protective systems, and degenerative disc disease. The accurate material properties obtained in this study will improve the predictive ability, and therefore clinical significance of these models.

Variation in human vertebral body strength for vertebral body samples from different locations in segments L1-L5

BACKGROUND

The human spine, in particular the lumbar spine, is subject to significant compressive and bending stresses, which affect the structure of the bone tissue of the vertebrae. The more heterogeneous the structure of the spongy bone tissue, the less resistant the whole vertebral body. It is therefore necessary to establish variations in bone strength parameters within one particular vertebral body.

METHODS

The research material comprised human L1-L5 lumbar vertebrae sampled from 15 donors aged 29-35. A total of 975 samples prepared from the collected material were subjected to compressive and bending strength tests. The samples for the tests were collected from carefully selected locations in order to discover the strength properties of various parts of the vertebral body.

FINDINGS

In the case of sample 2 (located in the posterior part of the vertebra, at mid-height) the stress values were the lowest and there were statistically significant differences compared to other samples. Moreover the value of compressive force in this case was lower for vertebrae with higher numbers. Top and bottom samples demonstrated statistically significant higher mean values of destructive stress. In terms of the bending strength test, the mean value of destructive stress in all lumbar vertebrae for all samples increased for vertebrae with higher numbers.

INTERPRETATION

The spongy tissue in healthy vertebral bodies has a very heterogeneous structure. This may be due to the presence of the nutrient canal and the arc structure allowing more springy movement and improved transfer of loads by the vertebral body.

Influence of the shape of the micro-finite element model on the mechanical properties calculated from micro-finite element analysis

Assessing the biomechanical properties of trabecular bone is of major biological and clinical significance for the research of bone diseases, fractures and their treatments. Micro-finite element (µFE) models are becoming increasingly popular for investigating the biomechanical properties of trabecular bone. The shapes of µFE models typically include cube and cylinder. Whether there are differences between cubic and cylindrical µFE models has not yet been studied. In the present study, cubic and cylindrical µFE models of human vertebral trabecular bone were constructed. A 1% strain was prescribed to the model along the superior-inferior direction. E values were calculated from these models, and paired t-tests were performed to determine whether these were any differences between E values obtained from cubic and cylindrical models. The results demonstrated that there were no statistically significant differences in the E values between cubic and cylindrical models, and there were no significant differences in Von Mises stress distributions between the two models. These findings indicated that, to construct µFE models of vertebral trabecular bone, cubic or cylindrical models were both feasible. Choosing between the cubic or cylindrical µFE model is dependent upon the specific study design.

A New Ensemble Classification System For Fracture Zone Prediction Using Imbalanced Micro-CT Bone Morphometrical Data

Trabecular bone fractures constitute a major health issue for the modern societies, with the currently established prediction methods of fracture risk, such as bone mineral density (BMD), resulting in errors up to 40%. Fracture-zone prediction based on bone's microstructure has been recently proposed as an alternative prediction method of fracture risk. In this paper, a classification system (CS) for the automatic fracture-zone prediction based on an Ensemble of Imbalanced Learning methods is proposed, following the observation that the percentage of the actual fractured bone area is significantly smaller than the intact bone in the case of a fracture event. The sample is divided into Volumes of Interest (VOIs) of specific size and 29 morphometrical parameters are calculated from each VOI, which serve as input features for the CS in order for it to separate the input patterns in to two classes: fractured and nonfractured. To this end, two well-established Imbalanced Learning methods, namely Random Undersampling and Synthetic Minority Oversampling, and two popular classification algorithms, namely Multilayer Perceptrons and Support Vector Machines, are tested and combined accordingly, to provide the best possible performance on a dataset that contains 45 specimens' pre- and postfailure scans. The best combination is then compared with three well-established Ensembles of Imbalanced Learning methods, namely RUSBoost, UnderBagging and SMOTEBagging. The experimental results clearly show that the proposed CS outperforms the competition, scoring in some occasions more than 90% in G-Mean and Area under Curve metrics. Finally, an investigation on the significance of the various trabecular bone's biomechanical parameters is made using the sequential forward floating selection technique, in order to identify possible biomarkers for fracture-zone prediction.

Bone mechanical properties and changes with osteoporosis

This review will define the role of collagen and within-bone heterogeneity and elaborate the importance of trabecular and cortical architecture with regard to their effect on the mechanical strength of bone. For each of these factors, the changes seen with osteoporosis and ageing will be described and how they can compromise strength and eventually lead to bone fragility.

Relationship between sample volumes and modulus of human vertebral trabecular bone in micro-finite element analysis

Micro-finite element (μFE) models have been widely used to assess the biomechanical properties of trabecular bone. How to choose a proper sample volume of trabecular bone, which could predict the real bone biomechanical properties and reduce the calculation time, was an interesting problem. Therefore, the purpose of this study was to investigate the relationship between different sample volumes and apparent elastic modulus (E) calculated from μFE model. 5 Human lumbar vertebral bodies (L1-L5) were scanned by micro-CT. Cubic concentric samples of different lengths were constructed as the experimental groups and the largest possible volumes of interest (VOI) were constructed as the control group. A direct voxel-to-element approach was used to generate μFE models and steel layers were added to the superior and inferior surface to mimic axial compression tests. A 1% axial strain was prescribed to the top surface of the model to obtain the E values. ANOVA tests were performed to compare the E values from the different VOIs against that of the control group. Nonlinear function curve fitting was performed to study the relationship between volumes and E values. The larger cubic VOI included more nodes and elements, and more CPU times were needed for calculations. E values showed a descending tendency as the length of cubic VOI decreased. When the volume of VOI was smaller than (7.34mm(3)), E values were significantly different from the control group. The fit function showed that E values approached an asymptotic values with increasing length of VOI. Our study demonstrated that apparent elastic modulus calculated from μFE models were affected by the sample volumes. There was a descending tendency of E values as the length of cubic VOI decreased. Sample volume which was not smaller than (7.34mm(3)) was efficient enough and timesaving for the calculation of E.

Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra

Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (μFE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age = 81.17 ± 7.7 yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin's fabric-based constitutive model (Cowin, 1985, "The Relationship Between the Elasticity Tensor and the Fabric Tensor," Mech. Mater., 4(2), pp. 137-147.) and the orientation of the principal axes of the fabric tensor, respectively. Deviations from orthotropy were quantified by the "orthotropic error" (van Rietbergen et al., 1996, "Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture," J. Biomech., 29(12), pp. 1653-1657), and deviations from transverse isotropy were determined by statistical comparison of the secondary and tertiary elastic moduli. The orthotropic error was greater than 50% for nearly half of the cubes, and the secondary and tertiary moduli differed from one another (p < 0.0001). Both the orthotropic error and the difference between secondary and tertiary moduli decreased with increasing bone volume fraction (BV/TV; p ≤ 0.007). Considering only the cubes with an orthotropic error less than 50%, only moderate correlations were observed between the fabric-based and the μFE-computed elastic moduli (R2 ≥ 0.337; p < 0.0001). These results indicate that when using a criterion of 5 mm for a representative volume element (RVE), transverse isotropy or orthotropy cannot be assumed for elderly human vertebral trabecular bone. Particularly at low values of BV/TV, this criterion does not ensure applicability of theories of continuous media. In light of the very sparse and inhomogeneous microstructure found in the specimens analyzed in this study, further work is needed to establish guidelines for selecting a RVE within the aged vertebral centrum.

Stochastic predictors from the DXA scans of human lumbar vertebrae are correlated with the microarchitecture parameters of trabecular bone

The purpose of this study was to provide a novel stochastic assessment of inhomogeneous distribution of bone mineral density (BMD) from the Dual-energy X-ray Absorptiometry (DXA) scans of human lumbar vertebrae and identify the stochastic predictors that were correlated with the microarchitecture parameters of trabecular bone. Eighteen human lumbar vertebrae with intact posterior elements from 5 cadaveric spines were scanned in the posterior-anterior projection using a Hologic densitometer. The BMD map of human vertebrae was obtained from the raw data of DXA scans by directly operating on the transmission measurements of low- and high-energy X-ray beams. Stochastic predictors were calculated by fitting theoretical models onto the experimental variogram of the BMD map, rather than grayscale images, from DXA scans. In addition, microarchitecture parameters of trabecular bone were measured from the 3D images of human vertebrae acquired using a Micro-CT scanner. Significant correlations were observed between stochastic predictors and microarchitecture parameters. The sill variance, representing the standard deviation of the BMD map to some extent, had significantly positive correlations with bone volume, trabecular thickness, trabecular number and connectivity density. The sill variance was also negatively associated with bone surface to volume ratio and trabecular separation. This study demonstrates that the stochastic assessment of the inhomogeneous distribution of BMD from DXA scans of human lumbar vertebrae can reveal microarchitecture information of trabecular bone. However, future studies are needed to examine the potential of stochastic predictors from routine clinical DXA scans in providing bone fragility information complementary to BMD.

Subregional DXA-derived vertebral bone mineral measures are stronger predictors of failure load in specimens with lower areal bone mineral density, compared to those with higher areal bone mineral density

Measurement of areal bone mineral density (aBMD) in intravertebral subregions may increase the diagnostic sensitivity of dual-energy X-ray absorptiometry (DXA)-derived parameters for vertebral fragility. This study investigated whether DXA-derived bone parameters in vertebral subregions were better predictors of vertebral bone strength in specimens with low aBMD, compared to those with higher aBMD. Twenty-five lumbar vertebrae (15 embalmed and 10 fresh-frozen) were scanned with posteroanterior- (PA) and lateral-projection DXA, and then mechanically tested in compression to ultimate failure. Whole-vertebral aBMD and bone mineral content (BMC) were measured from the PA- and lateral-projection scans and within 6 intravertebral subregions. Multivariate regression was used to predict ultimate failure load by BMC, adjusted for vertebral size and specimen fixation status across the whole specimen set, and when subgrouped into specimens with low aBMD and high aBMD. Adjusted BMC explained a substantial proportion of variance in ultimate vertebral load, when measured over the whole vertebral area in lateral projection (adjusted R (2) 0.84) and across the six subregions (ROIs 2-7) (adjusted R (2) range 0.58-0.78). The association between adjusted BMC, either measured subregionally or across the whole vertebral area, and vertebral failure load, was increased for the subgroup of specimens with identified 'low aBMD', compared to those with 'high aBMD', particularly in the anterior subregion where the adjusted R (2) differed by 0.44. The relative contribution of BMC measured in vertebral subregions to ultimate failure load is greater among specimens with lower aBMD, compared to those with higher aBMD, particularly in the anterior subregion of the vertebral body.

Modic (endplate) changes in the lumbar spine: bone micro-architecture and remodelling

PURPOSE

In the literature, inter-vertebral MRI signal intensity changes (Modic changes) were associated with corresponding histological observations on endplate biopsies. However, tissue-level studies were limited. No quantitative histomorphometric study on bone biopsies has yet been conducted for Modic changes. The aim of this study was to characterise the bone micro-architectural parameters and bone remodelling indices associated with Modic changes.

METHODS

Forty patients suffering from disabling low back pain, undergoing elective spinal surgery, and exhibiting Modic changes on MRI (Modic 1, n = 9; Modic 2, n = 25; Modic 3, n = 6), had a transpedicular vertebral body biopsy taken of subchondral bone. Biopsies were first examined by micro-CT, for 3D morphometric analysis of bone volume fraction (BV/TV), trabecular thickness (Tb.Th), trabecular separation, trabecular number, and structure model index. Then, samples underwent histological analysis, for determination of bone remodelling indices: osteoid surface to bone surface ratio (OS/BS), eroded surface to bone surface (ES/BS) and osteoid surface to eroded surface ratio (OS/ES).

RESULTS

Micro-CT analysis revealed significantly higher BV/TV (up to 70% increase, p < 0.01) and Tb.Th (up to +57%, p < 0.01) in Modic 3 biopsies, compared to Modic 1 and 2. Histological analysis showed significantly lower OS/BS in Modic 2 biopsies (more than 28% decrease, p < 0.05) compared to 1 and 3. ES/BS progressively decreased from Modic 1 to 2 to 3, whereas OS/ES progressively increased with significantly higher values in Modic 3 (up to 159% increase, p < 0.05) than in Modic 1 and 2.

CONCLUSIONS

Significant differences were found in bone micro-architectural parameters and remodelling indices among Modic types. Modic 1 biopsies had evidence of highest bone turnover, possibly due to an inflammatory process; Modic 2 biopsies were consistent with a reduced bone formation/remodelling stage; Modic 3 biopsies suggested a more stable sclerotic phase, with significantly increased BV/TV and Tb.Th compared to Modic 1 and 2, linked to increased bone formation and reduced resorption.

The micro-structure of bone trabecular fracture: an inter-site study

Trabecular bone fracture represents a major health problem, therefore the improvement of its assessment is mandatory for the reduction of the economic and social burden. The micro-structure of the trabecular bone was found to have an important effect on trabecular mechanical behavior. Nonetheless, the high variability of the trabecular micro-structure suggests a search for the local characteristics leading to the fracture. This work concerns the study of the local trabecular fracture zone and its morphometrical characterization, aiming to prediction of the probable fracture zone. Ninety micro-CT datasets acquired before and after the mechanical compression of 45 trabecular specimens were analyzed. Specimens were extracted from the lower limbs of two donors: 4 femora and 4 tibiae. A previously validated tool for the identification of the 3D fracture zone was applied and the local fracture zone was identified and analyzed in all the specimens. Fifteen morphometrical parameters were extracted for each local fracture zone. Standard statistical non-parametric analysis was performed to compare fractured and un-fractured zones together with a classification analysis for the prediction of the fracture zone. The statistical analysis showed strong statistical difference in the micro-structure of the trabecular fractured zone compared to the un-fractured one. Ten out of 15 measured parameters, like SMI, Tb.Th, BV/TV, off-axis angle, BS/BV and others, showed a statistical difference between full 3D fractured and un-fractured zones. Nonetheless, a satisfactory classification of the fractured zone was possible with none of the identified parameters. On the other hand, a total classification accuracy of 95.5% was presented by the application of a linear classifier based on a combination of the most representative parameters, like BS/BV and the off-axis angle. The study points out the local essence and peculiar characteristics of the fracture zone, it highlights the weakness of some parameters in discriminate between fractured and un-fractured zones and encourage focussing the future studies over the local fracture zone itself with the aim to identify objective differences that could one day lead to the improvement of clinical assessment of fracture risk.

Principal trabecular structural orientation predicted by quantitative ultrasound is strongly correlated with μFEA determined anisotropic apparent stiffness

The microarchitecture and alignment of trabecular bone adapts to the particular mechanical milieu applied to it. Due to this anisotropic mechanical property, measurement orientation has to be taken into consideration when assessing trabecular bone quality and fracture risk prediction. Quantitative ultrasound (QUS) has demonstrated the ability in predicting the principal structural orientation (PSO) of trabecular bone. Although the QUS prediction for PSO is very close to that of μCT, certain angle differences still exist. It remains unknown whether this angle difference can induce significant differences in mechanical properties or not. The objective of this study was to evaluate the mechanical properties in different PSOs predicted using different methods, QUS and μCT, thus to investigate the ability of QUS as a means to predict the PSO of trabecular bone noninvasively. By validating the ability of QUS to predict the PSO of trabecular bone, it is beneficial for future QUS applications because QUS measurements in the PSO can provide information more correlated with the mechanical properties than with other orientations. In this study, seven trabecular bone balls from distal bovine femurs were used to generate finite element models based on the 3-dimensional μCT images. Uniaxial compressive loading was performed on the bone ball models in the finite element analysis (FEA) in six different orientations (three anatomical orientations, two PSOs predicted by QUS and the longest vector of mean intercept length (MIL) tensor calculated by μCT). The stiffness was calculated based on the reaction force of the bone balls under loading, and the von Mises stress results showed that both the mechanical properties in the PSOs predicted by QUS are significantly higher than the anatomical orientations and comparatively close to the longest vector of MIL tensor. The stiffness in the PSOs predicted by QUS is also highly correlated with the stiffness in the MIL tensor orientation (ATTmax vs. MIL, R(2) = 0.98, p < 001; UVmax vs. MIL, R(2) = 0.92, p < 001). These results were validated by in vitro mechanical testing on the bone ball samples. This study demonstrates that the PSO of trabecular bone predicted by QUS has an equally strong apparent stiffness with the orientation predicted by μCT.

The intravertebral distribution of bone density: correspondence to intervertebral disc health and implications for vertebral strength

This study's goal was to determine associations among the intravertebral heterogeneity in bone density, bone strength, and intervertebral disc (IVD) health. Results indicated that predictions of vertebral strength can benefit from considering the magnitude of the density heterogeneity and the congruence between the spatial distribution of density and IVD health.

INTRODUCTION

This study aims to determine associations among the intravertebral heterogeneity in bone density, bone strength, and IVD health

METHODS

Regional measurements of bone density were performed throughout 30 L1 vertebral bodies using micro-computed tomography (μCT) and quantitative computed tomography (QCT). The magnitude of the intravertebral heterogeneity in density was defined as the interquartile range and quartile coefficient of variation in regional densities. The spatial distribution of density was quantified using ratios of regional densities representing different anatomical zones (e.g., anterior to posterior regional densities). Cluster analysis was used to identify groups of vertebrae with similar spatial distributions of density. Vertebral strength was measured in compression. IVD health was assessed using two scoring systems.

RESULTS

QCT- and μCT-based measures of the magnitude of the intravertebral heterogeneity in density were strongly correlated with each other (p < 0.005). Accounting for the interquartile range in regional densities improved predictions of vertebral strength as compared to predictions based only on mean density (R (2) = 0.59 vs. 0.43; F-test p-value = 0.018). Specifically, after adjustment for mean density, vertebral bodies with greater heterogeneity in density exhibited higher strength. No single spatial distribution of density was associated with high vertebral strength. Analyses of IVD scores suggested that the health of the adjacent IVDs may modulate the effect of a particular spatial distribution of density on vertebral strength.

CONCLUSIONS

Noninvasive measurements of the intravertebral distribution of bone density, in conjunction with assessments of IVD health, can aid in predictions of bone strength and in elucidating biomechanical mechanisms of vertebral fracture.

Presence of intervertebral discs alters observed stiffness and failure mechanisms in the vertebra

Ex vivo mechanical testing is an essential tool for study of vertebral mechanics. However, the common method of testing vertebral bodies in the absence of adjacent intervertebral discs (IVDs) may limit the physiological relevance of the results. The goal of this study was to determine the influence of IVDs on vertebral mechanical properties and failure mechanisms. Rabbit thoracic vertebral bodies were tested with and without IVDs in a stepwise fashion that incorporated a micro-computed tomography scan at each loading step. The image sequences were analyzed using digital volume correlation to quantify deformations throughout the vertebral body. The observed deformation patterns differed substantially between the groups. Specimens tested with IVDs exhibited a slow increase in strain in the inferior and posterior regions, followed by a sudden increase in strain in the anterior cortex right at the yield point. In contrast, the highest strains in the isolated vertebral bodies were in the posterior regions throughout the test. Specimens tested with IVDs had lower stiffness (507.49±184.73N/mm vs. 845.61±296.09N/mm; p=0.044), higher ultimate displacement (2.00±0.68mm vs. 1.17±0.54mm; p=0.043), and higher maximum shear strains (e.g. top 25th percentile: 0.19±0.11 vs. 0.06±0.07mm/mm; p<0.0458), and tended to have lower ultimate force (690.28±160.25N vs. 873.81±131.48N; p=0.056). Similar work to failure (648.15±317.86N-mm vs. 603.49±437.95 N-mm; p=0.844) was observed between the two groups. These results indicate that testing vertebral bodies in the absence of IVDs can elicit artifactual failure mechanisms. These artifacts may be more prominent than the effects on vertebral strength and toughness.

Heterogeneity of bone mineral density and fatigue failure of human vertebrae

There is increasing interest in using the heterogeneity of tissue properties in a bone for predicting its fracture risk. Heterogeneity of volumetric bone mineral density (BMD) as measured from quantitative computed tomography (QCT) is of particular interest as these measurements are clinically feasible. Previous examinations of the relationship between the BMD heterogeneity and the mechanical behavior of human vertebrae only considered quasistatic strength and were with limited number of samples. McCubbrey et al. (1995) studied the value of regional BMDs for predicting vertebral fatigue life, determined from short-cycle tests at force levels scaled with the estimated strength of the vertebra, but the focus of that work was in best predictor subsets without a specific focus on the heterogeneity of BMD or the positive vs negative direction of the relationships. The previous analysis also did not take into account the censored nature of the fatigue life data. As such, whether BMD heterogeneity is positively or negatively associated with fatigue life and whether this is independent of the average or minimum BMD are not clear. In the present work, we revisited the McCubbrey data for a preliminary examination of the relationship between BMD heterogeneity and fatigue life using survival analysis. The analysis suggests that BMD heterogeneity measured as the intra-vertebral standard deviation of BMDs in a vertebra is negatively associated with short cycle (high-amplitude) fatigue life independent of the average BMD. The results motivate further studies on the role of BMD heterogeneity in fatigue failure and clinical fracture risk of human vertebrae.

The effect of intravertebral heterogeneity in microstructure on vertebral strength and failure patterns

The goal of this study was to determine the influence of intravertebral heterogeneity in microstructure on vertebral failure. Results show that noninvasive assessments of the intravertebral heterogeneity in density improve predictions of vertebral strength and that local variations in microstructure are associated with locations of failure in the vertebral body.

INTRODUCTION

The overall goal of this study was to determine the influence of intravertebral 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 4.81 mm, contiguous cubes throughout the centrum. Intravertebral heterogeneity in density was defined as the interquartile 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 midtransverse plane with concomitant endplate biconcavity and were linked to the intravertebral 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 midtransverse 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 intravertebral heterogeneity in density improved predictions of strength and stiffness as compared to predictions based only on mean density (strength: R(2) = 0.75 vs. 0.61, p < 0.001; stiffness: R(2) = 0.44 vs. 0.26, p = 0.001).

CONCLUSIONS

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

Increased variability of bone tissue mineral density resulting from estrogen deficiency influences creep behavior in a rat vertebral body

Progressive vertebral deformation increases the fracture risk of a vertebral body in the postmenopausal patient. Many studies have observed that bone can demonstrate creep behavior, defined as continued time-dependent deformation even when mechanical loading is held constant. Creep is a characteristic of viscoelastic behavior, which is common in biological materials. We hypothesized that estrogen deficiency-dependent alteration of the mineral distribution of bone at the tissue level could influence the progressive postmenopausal vertebral deformity that is observed as the creep response at the organ level. The objective of this study was thus to examine whether the creep behavior of vertebral bone is changed by estrogen deficiency, and to determine which bone property parameters are responsible for the creep response of vertebral bone at physiological loading levels using an ovariectomized (OVX) rat model. Correlations of creep parameters with bone mineral density (BMD), tissue mineral density (TMD) and architectural parameters of both OVX and sham surgery vertebral bone were tested. As the vertebral creep was not fully recovered during the post-creep unloading period, there was substantial residual displacement for both the sham and OVX groups. A strong positive correlation between loading creep and residual displacement was found (r=0.868, p<0.001). Of the various parameters studied, TMD variability was the parameter that best predicted the creep behavior of the OVX group (p<0.038). The current results indicated that creep caused progressive, permanent reduction in vertebral height for both the sham and OVX groups. In addition, estrogen deficiency-induced active bone remodeling increased variability of trabecular TMD in the OVX group. Taken together, these results suggest that increased variability of trabecular TMD resulting from high bone turnover influences creep behavior of the OVX vertebrae.

Failure strength of human vertebrae: prediction using bone mineral density measured by DXA and bone volume by micro-CT

Significant relationships exist between areal bone mineral density (BMD) derived from dual energy X-ray absorptiometry (DXA) and bone strength. However, the predictive validity of BMD for osteoporotic vertebral fractures remains suboptimal. The diagnostic sensitivity of DXA in the lumbar spine may be improved by assessing BMD from lateral-projection scans, as these might better approximate the objective of measuring the trabecular-rich bone in the vertebral body, compared to the commonly-used posterior-anterior (PA) projections. Nowadays, X-ray micro-computed tomography (μCT) allows non-destructive three-dimensional structural characterization of entire bone segments at high resolution. In this study, human lumbar cadaver spines were examined ex situ by DXA in lateral and PA projections, as well as by μCT, with the aims (1) to investigate the ability of bone quantity measurements obtained by DXA in the lateral projection and in the PA projection, to predict variations in bone quantity measurements obtained by μCT, and (2) to assess their respective capabilities to predict whole vertebral body strength, determined experimentally. Human cadaver spines were scanned by DXA in PA projections and lateral projections. Bone mineral content (BMC) and BMD for L2 and L3 vertebrae were determined. The L2 and L3 vertebrae were then dissected and entirely scanned by μCT. Total bone volume (BV(tot)=cortical+trabecular), trabecular bone volume (BV), and trabecular bone volume fraction (BV/TV) were calculated over the entire vertebrae. The vertebral bodies were then mechanically tested to failure in compression, to determine ultimate load. The variables BV(tot), BV, and BV/TV measured by μCT were better predicted by BMC and BMD measured by lateral-projection DXA, with higher R(2) values and smaller standard errors of the estimate (R(2)=0.65-0.90, SEE=11%-18%), compared to PA-projection DXA (R(2)=0.33-0.53, SEE=22%-34%). The best predictors of ultimate load were BV(tot) and BV assessed by μCT (R(2)=0.88 and R(2)=0.81, respectively), and BMC and BMD from lateral-projection DXA (R(2)=0.82 and R(2)=0.70, respectively). Conversely, BMC and BMD from PA-projection DXA were lower predictors of ultimate load (R(2)=0.49 and R(2)=0.37, respectively). This ex vivo study highlights greater capabilities of lateral-projection DXA to predict variations in vertebral body bone quantity as measured by μCT, and to predict vertebral strength as assessed experimentally, compared to PA-projection DXA. This provides basis for further exploring the clinical application of lateral-projection DXA analysis.

Measurement of subregional vertebral bone mineral density in vitro using lateral projection dual-energy X-ray absorptiometry: validation with peripheral quantitative computed tomography

Although a strong relationship exists between areal bone mineral density (aBMD) derived from dual-energy X-ray absorptiometry (DXA) and bone strength, the predictive validity of aBMD for osteoporotic vertebral fractures remains suboptimal. The diagnostic sensitivity of DXA may be improved by assessing aBMD within vertebral subregions, rather than relying on an estimate derived from the total area of the vertebra. The objective of this study was to validate a method of measuring subregional vertebral aBMD in vitro using lateral-projection DXA against subregional volumetric BMD (vBMD) measured with peripheral quantitative computed tomography (pQCT). A mixed set of 49 lumbar and thoracic vertebrae from 25 donors were scanned using lateral-projection DXA and pQCT. aBMD and apparent vBMD were measured in 7 vertebral regions (1 total area and 6 subregions) from the lateral DXA scan. vBMD was calculated in anatomically equivalent regions from pQCT scan data, using a customised software program designed to increase efficiency of the analysis process. Significant differences in densitometric parameters between subregions were observed by DXA and pQCT (P < 0.01). Subregional vBMD derived from pQCT was explained by a significant proportion of the variance in DXA-derived aBMD (R (2) = 0.51-0.67, P < 0.05) and apparent vBMD (R (2) = 0.64-0.75, P < 0.05). These results confirm the validity of measuring aBMD in vertebral subregions using lateral-projection DXA. The clinical significance should now be explored.

Variability of trabecular microstructure is age-, gender-, race- and anatomic site-dependent and affects stiffness and stress distribution properties of human vertebral cancellous bone

Cancellous bone microstructure is an important determinant of the mechanical integrity of vertebrae. The numerous microstructural parameters that have been studied extensively are generally represented as a single value obtained as an average over a sample. The range of the intra-sample variability of cancellous microstructure and its effect on the mechanical properties of bone are less well-understood. The objectives of this study were to investigate the extent to which human cancellous bone microstructure within a vertebra i) is related to bone modulus and stress distribution properties and ii) changes along with age, gender and locations thoracic 12 (T12) vs lumbar 1 (L1). Vertebrae were collected from 15 male (66±15 years) and 25 female (54±16 years) 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. The current results collectively demonstrate that microstructural variability has a significant effect on mechanical properties and tissue stress of human vertebral cancellous bone. Considering microstructural variability could improve the understanding of bone fragility and improve assessment of vertebral fracture risk.

Stiffness of the endplate boundary layer and endplate surface topography are associated with brittleness of human whole vertebral bodies

Stress magnitude and variability as estimated from large scale finite element (FE) analyses have been associated with compressive strength of human vertebral cancellous cores but these relationships have not been explored for whole vertebral bodies. In this study, the objectives were to investigate the relationship of FE-calculated stress distribution parameters with experimentally determined strength, stiffness, and displacement based ductility measures in human whole vertebral bodies, investigate the effect of endplate loading conditions on vertebral stiffness, strength, and ductility and test the hypothesis that endplate topography affects vertebral ductility and stress distributions. Eighteen vertebral bodies (T6-L3 levels; 4 female and 5 male cadavers, aged 40-98 years) were scanned using a flat-panel CT system and followed with axial compression testing with Wood's metal as filler material to maintain flat boundaries between load plates and specimens. FE models were constructed using reconstructed CT images and filler material was added digitally. Two different FE models with different filler material modulus simulating Wood's metal and intervertebral disc (W-layer and D-layer models) were used. Element material modulus to cancellous bone was based on image gray value. Average, standard deviation, and coefficient of variation of von Mises stress in vertebral bone for W-layer and D-layer models and also the ratios of FE parameters from the two models (W/D) were calculated. Inferior and superior endplate surface topographical distribution parameters were calculated. Experimental stiffness, maximum load and work to fracture had the highest correlation with FE-calculated stiffness while experimental ductility measures had highest correlations with FE-calculated average von Mises stress and W-layer to D-layer stiffness ratio. Endplate topography of the vertebra was also associated with its structural ductility and the distribution parameter that best explained this association was kurtosis of inferior endplate topography. Our results indicate that endplate topography variations may provide insight into the mechanisms responsible for vertebral fractures.

Novel assessment of subregional bone mineral density using DXA and pQCT and subregional microarchitecture using micro-CT in whole human vertebrae: applications, methods, and correspondence between technologies

In the clinical environment dual-energy X-ray absorptiometry (DXA) is the current tool of first choice for assessing and monitoring skeletal integrity. A major drawback of standard DXA is that the bone mineral density (BMD) data cannot be used with certainty to predict who will sustain a vertebral fracture. However, measurement of BMD within vertebral subregions, instead of relying on a gross estimate of vertebral BMD, may improve diagnostic sensitivity. The aim of this article was to describe a validation study for subregional BMD measurement using lateral-projection DXA and to present preliminary data. Concurrent validity of measuring subregional BMD with DXA was established against measures of volumetric subregional BMD from peripheral quantitative computed tomography (pQCT) and subregional bone volume fraction from microCT at the L2 vertebral body in 8 cadaver spine specimens. The novel approaches for measuring subregional parameters with each imaging modality are described. Significant differences in bone parameters between vertebral subregions were observed for each imaging modality (p<0.05). Correspondence ranged from R(2)=0.01-0.79 and R(2)=0.06-0.80 between "DXA vs. pQCT" and "DXA vs. micro-CT," respectively. For both imaging modalities, correspondence with DXA was high for centrally and anteriorly positioned subregions. These data provide a basis for larger studies to examine the biological significance of heterogeneity in vertebral BMD.

Increased microstructural variability is associated with decreased structural strength but with increased measures of structural ductility in human vertebrae

The lack of accuracy in the prediction of vertebral fracture risk from average density measurements, all external factors being equal, may not just be because bone mineral density (BMD) is less than a perfect surrogate for bone strength but also because strength alone may not be sufficient to fully characterize the structural failure of a vertebra. Apart from bone quantity, the regional variation of cancellous architecture would have a role in governing the mechanical properties of vertebrae. In this study, we estimated various microstructural parameters of the vertebral cancellous centrum based on stereological analysis. An earlier study indicated that within-vertebra variability, measured as the coefficient of variation (COV) of bone volume fraction (BV/TV) or as COV of finite element-estimated apparent modulus (E(FE)) correlated well with vertebral strength. Therefore, as an extension to our earlier study, we investigated (i) whether the relationships of vertebral strength found with COV of BV/TV and COV of E(FE) could be extended to the COV of other microstructural parameters and microcomputed tomography-estimated BMD and (ii) whether COV of microstructural parameters were associated with structural ductility measures. COV-based measures were more strongly associated with vertebral strength and ductility measures than average microstructural measures. Moreover, our results support a hypothesis that decreased microstructural variability, while associated with increased strength, may result in decreased structural toughness and ductility. The current findings suggest that variability-based measures could provide an improvement, as a supplement to clinical BMD, in screening for fracture risk through an improved prediction of bone strength and ductility. Further understanding of the biological mechanisms underlying microstructural variability may help develop new treatment strategies for improved structural ductility.

Relative strength of thoracic vertebrae in axial compression versus flexion

BACKGROUND CONTEXT

Noninvasive strength assessment techniques are the clinical standard in the diagnosis and treatment of osteoporotic vertebral fractures, and the efficacy of these protocols depends on their ability to predict vertebral strength at all at-risk spinal levels under multiple physiological loading conditions.

PURPOSE

To assess differences in vertebral strength between loading modes and across spinal levels.

STUDY DESIGN/SETTING

This study examined the relative strength of isolated vertebral bodies in compression versus flexion.

METHODS

Destructive biomechanical tests were conducted on 30 pairs of donor-matched, isolated thoracic vertebral bodies (T9 and T10; F=19, M=11; 87+5 years old, max=97 years old, min=80 years old) in both uniform axial compression and flexion using previously described protocols. Quantitative computed tomography (QCT) scans were taken before mechanical testing and used to obtain bone mineral density (BMD) and "mechanics of solids" (MOS) measures, such as axial and bending rigidities.

RESULTS

Compressive strength was higher than flexion strength for each donor by 940+152N (p<.001, paired t test), and vertebral strengths in the two loading modes were moderately correlated (adjusted R(2)=0.50, p<.001). For both compression and flexion loading modes, adjacent-level BMD and MOS metrics had approximately half the predictive capacity as same-level measurements, and BMD and MOS values were only moderately correlated across spinal levels.

CONCLUSIONS

The results of this study are important in designing clinical test protocols for assessing vertebral fracture risk. Because vertebral body flexion and compressive strength are not strongly correlated and flexion strength is significantly less than compressive strength, it is imperative to investigate a patient's spinal structural capacity under bending loading conditions. Furthermore, our work suggests that clinicians using QCT-based measures should perform site-specific strength assessments on each at-risk spinal level. Future work should focus on improving the accuracy of densitometric measures in predicting vertebral strength in flexion and also on examining same- versus adjacent-level strength assessment for radiographic techniques with lower X-ray dosage, such as dual-energy X-ray absorptiometry.

Biomechanical properties across trabeculae from the proximal femur of normal and ovariectomised sheep

The elastic behaviour of trabecular bone is a function not only of bone volume and architecture, but also of tissue material properties. Variation in tissue modulus can have a substantial effect on the biomechanical properties of trabecular bone. However, the nature of tissue property variation within a single trabecula is poorly understood. This study uses nanoindentation to determine the mechanical properties of bone tissue in individual trabeculae. Using an ovariectomised ovine model, the modulus and hardness distribution across trabeculae were measured. In both normal and ovariectomised bone, the modulus and hardness were found to increase towards the core of the trabeculae. Across the width of the trabeculae, the modulus was significantly less in the ovariectomised bone than in the control bone. However, in contrast to this hardness was found not to differ significantly between the two groups. This study provides valuable information on the variation of mechanical material properties in healthy and diseased trabecular bone tissue. The results of the current study will be useful in finite element modelling where more accurate values of trabecular bone modulus will enable the prediction of the macroscale behaviour of trabecular bone.

Human cancellous bone from T12-L1 vertebrae has unique microstructural and trabecular shear stress properties

Increase of trabecular stress variability with loss of bone mass has been implicated as a mechanism for increased cancellous bone fragility with age and disease. In the current study, a previous observation that trabecular shear stress estimates vary along the human spine such that the cancellous tissue from the thoracic 12 (T12)-lumbar 1 (L1) junction experiences the highest trabecular stresses for a given load was tested as a formal hypothesis using multiple human spines. Thoracic 4, T5, T7, T9, T10, T12, L1, L2, L4 and L5 vertebrae from 10 human cadaver spines were examined. One specimen in the central anterior region was cored in the supero-inferior (SI) direction and another in the postero-lateral region was cored in the transverse (TR) direction from each vertebra. Micro-CT-based large-scale finite element models were constructed for each specimen and compression in the long axis of the cylindrical specimens was simulated. Cancellous bone modulus and the mean, the standard deviation, variability and amplification of trabecular von Mises stresses were computed. Bone volume fraction, trabecular number, trabecular thickness, trabecular separation, connectivity density and degree of anisotropy were calculated using 3D stereology. The results were analyzed using a mixed model in which spine level was modeled using a quadratic polynomial. The maximum of trabecular shear stress amplification and minimum of bone volume fraction were found in the cancellous tissue from the T12-L1 location when results from the samples of the same vertebra were averaged. When groups were separated, microstructure and trabecular stresses varied with spine level, extrema being at the T12-L1 levels, for the TR specimens only. SI/TR ratio of measured parameters also had quadratic relationships with spine level, the extrema being located at T12-L1 levels for most parameters. For microstructural parameters, these ratios approached to a value of one at the T12-L1 level, suggesting that T12-L1 vertebrae have more uniform cancellous tissue properties than other levels. The mean intercept length in the secondary principal direction of trabecular orientation could account for the variation of all mechanical parameters with spine level. Our results support that cancellous tissue from T12-L1 levels is unique and may explain, in part, the higher incidence of vertebral fractures at these levels.

Bone volume fraction explains the variation in strength and stiffness of cancellous bone affected by metastatic cancer and osteoporosis

Preventing nontraumatic fractures in millions of patients with osteoporosis or metastatic cancer may significantly reduce the associated morbidity and reduce health-care expenditures incurred by these fractures. Predicting fracture occurrence requires an accurate understanding of the relationship between bone structure and the mechanical properties governing bone fracture that can be readily measured. The aim of this study was to test the hypothesis that a single analytic relationship with either bone tissue mineral density or bone volume fraction (BV/TV) as independent variables could predict the strength and stiffness of normal and pathologic cancellous bone affected by osteoporosis or metastatic cancer. After obtaining institutional review board approval and informed consent, 15 patients underwent excisional biopsy of metastatic prostate, breast, lung, ovarian, or colon cancer from the spine and/or femur to obtain 41 metastatic cancer specimens. In addition, 96 noncancer specimens were excised from 43 age- and site-matched cadavers. All specimens were imaged using micro-computed tomography (micro-CT) and backscatter emission imaging and tested mechanically by uniaxial compression and nanoindentation. The minimum BV/TV, measured using quantitative micro-CT, accounted for 84% of the variation in bone stiffness and strength for all cancellous bone specimens. While relationships relating bone density to strength and stiffness have been derived empirically for normal and osteoporotic bone, these relationships have not been applied to skeletal metastases. This simple analytic relationship will facilitate large-scale screening and prediction of fracture risk for normal and pathologic cancellous bone using clinical CT systems to determine the load capacity of bones altered by metastatic cancer, osteoporosis, or both.

Bone mass and architecture determination: state of the art

Bone fracture occurs when the bone strength (i.e. the ability of the bone to resist a force) is less than the force applied to the bone. In the elderly, falls represent the more severe forces applied to bone. Bone density is a good marker of bone strength, and has been used widely in this respect. Nevertheless, many aspects of bone strength cannot be explained by bone density alone. For this reason there has been increasing interest in studying architectural parameters of bone, beyond bone density, which may affect bone strength. Macro-architectural parameters include e.g. bone size and geometry assessed with techniques such as radiography, dual-energy x-ray absorptiometry (DXA), peripheral quantitative computed tomography (QCT), computed tomography (CT) and magnetic resonance imaging (MRI). Micro-architectural parameters include fine cortical and trabecular structural detail which can be evaluated using high-resolution imaging techniques such as multidetector CT, MRI, and high-resolution peripheral QCT. These techniques are providing a great deal of new information on the physiological architectural responses of bone to aging, weightlessness, and treatment. This will ultimately lead to the prediction of fracture risk being improved through a combined assessment of bone density and architectural parameters.

Trabecular shear stress amplification and variability in human vertebral cancellous bone: relationship with age, gender, spine level and trabecular architecture

Trabecular shear stress magnitude and variability have been implicated in damage formation and reduced bone strength associated with bone loss for human vertebral bone. This study addresses the issue of whether these parameters change with age, gender or anatomical location, and if so whether this is independent of bone mass. Additionally, 3D-stereology-based architectural parameters were examined in order to establish the relationship between stress distribution parameters and trabecular architecture. Eighty cancellous bone specimens were cored from the anterior region of thoracic 12 and donor-matched lumbar 1 vertebrae from a randomly selected population of 40 cadavers. The specimens were scanned at 21-microm voxel size using microcomputed tomography (microCT) and reconstructed at 50microm. Bone volume fraction (BV/TV), trabecular number (Tb.N), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), bone surface-to-volume ratio (BS/BV), degree of anisotropy (MIL1/MIL3), and connectivity density (-#Euler/Vol) were calculated directly from micro-CT images. Large-scale finite element models were constructed and superoinferior compressive loading was simulated. Apparent cancellous modulus (EFEM) was calculated. The average trabecular von Mises stress generated per uniaxial apparent stress (sigma (-)VM / sigmaapp) and coefficient of variation of trabecular von Mises stresses (COV) were calculated as measures of the magnitude and variability of shear stresses in the trabeculae. Mixed-models and regression were used for analysis. sigma(-)VM / sigmaapp and COV were not different between genders and vertebrae. Both sigma(-)VM / sigmaapp and COV increased with age accompanied by a decrease in BV/TV. Strong relationship of sigma(-)VM / sigmaapp with BV/TV was found whereas COV was strongly related to EFEM/(BV/TV). The results from T12 and L1 were not different and highly correlated with each other. The relationship of sigma(-)VM / sigmaapp with COV was observed to be different between males and females. This difference could not be explained by architectural parameters considered in this study. Our results support the relevance of trabecular shear stress amplification and variability in age-related vertebral bone fragility. The relationships found are expected to help understand the micro-mechanisms by which cancellous bone mass and mechanical properties are modulated through a collection of local stress parameters.