Heterogeneity of yield strain in low-density versus high-density human trabecular bone

Understanding the off-axis behavior of trabecular yield strains may lend unique insight into the etiology of fractures since yield strains provide measures of failure independent of elastic behavior. We sought to address anisotropy of trabecular yield strains while accounting for variations in both density and anatomic site and to determine the mechanisms governing this behavior. Cylindrical specimens were cored from vertebral bodies (n=22, BV/TV=0.11±0.02) and femoral necks (n=28, BV/TV=0.22±0.06) with the principal trabecular orientation either aligned along the cylinder axis (on-axis, n=22) or at an oblique angle of 15° or 45° (off-axis, n=28). Each specimen was scanned with micro-CT, mechanically compressed to failure, and analysed with nonlinear micro-CT-based finite element analysis. Yield strains depended on anatomic site (p=0.03, ANOVA), and the effect of off-axis loading was different for the two sites (p=0.04)—yield strains increased for off-axis loading of the vertebral bone (p=0.04), but were isotropic for the femoral bone (p=0.66). With sites pooled together, yield strains were positively correlated with BV/TV for on-axis loading (R²=58%, p<0.0001), but no such correlation existed for off-axis loading (p=0.79). Analysis of the modulus-BV/TV and strength-BV/TV relationships indicated that, for the femoral bone, the reduction in strength associated with off-axis loading was greater than that for modulus, while the opposite trend occurred for the vertebral bone. The micro-FE analyses indicated that these trends were due to different failure mechanisms for the two types of bone and the different loading modes. Taken together, these results provide unique insight into the failure behavior of human trabecular bone and highlight the need for a multiaxial failure criterion that accounts for anatomic site and bone volume fraction.     

Gender specific LRP5 influences on trabecular bone structure and strength

A mutation in LRP5 (low-density lipoprotein receptor-related protein 5) has been shown to increase bone mass and density in humans and animals. Transgenic mice expressing the LRP5 mutation (G171V) demonstrate an increase in bone mass as compared to non-transgenic (NTG) littermates. This study evaluated LRP5 gene and gender-related influences on the structural and biomechanical strength properties of trabecular and cortical bone in femurs and vertebrae (L5) of 17-week-old mice. Micro-computed tomography was used to evaluate the trabecular bone structure of distal femurs and vertebrae ex vivo. Mechanical testing of the trabecular bone in the distal femur was done to determine biomechanical strength. Differences due to genotype and gender were tested using two-way ANOVA at a significance level of p<0.05. Trabecular bone structural parameters (BV/TV, trabecular thickness, number, etc.) at the distal femur, femoral neck, and vertebral body sites were greater in the transgenic as compared to the NTG mice. In addition, vertebral cortical thickness and trabecular strength parameters (ultimate and yield loads, stiffness, ultimate and yield stresses) in the distal femur were greater in the transgenic mice as compared to NTG. The increasing trends of cortical thickness were also noted in the transgenic mice as compared to NTG. Within LRP5 (G171V) mutant mice, there were significant gender-related differences in some of the trabecular bone structural parameters at all the sites (distal femur, femoral neck, and vertebral body). However, unlike trabecular structural parameters, the gender-specific differences were not found in the trabecular strength of LRP5 transgenic mice. In summary, these findings suggest that the LRP5 (G171V) mutation results in greater trabecular bone structure and strength at both the distal femurs and vertebral bodies as compared to NTG. In addition, only the trabecular structure parameters were affected by gender within the LRP5 (G171V) mutation.     

The effect of resorption cavities on bone stiffness is site dependent

Resorption cavities formed during the bone remodelling cycle change the structure and thus the mechanical properties of trabecular bone. We tested the hypotheses that bone stiffness loss due to resorption cavities depends on anatomical location, and that for identical eroded bone volumes, cavities would cause more stiffness loss than homogeneous erosion. For this purpose, we used beam–shell finite element models. This new approach was validated against voxel-based FE models. We found an excellent agreement for the elastic stiffness behaviour of individual trabeculae in axial compression (R² = 1.00) and in bending (R²>0.98), as well as for entire trabecular bone samples to which resorption cavities were digitally added (R² = 0.96, RMSE = 5.2%). After validation, this new method was used to model discrete cavities, with dimensions taken from a statistical distribution, on a dataset of 120 trabecular bone samples from three anatomical sites (4th lumbar vertebra, femoral head, iliac crest). Resorption cavities led to significant reductions in bone stiffness. The largest stiffness loss was found for samples from the 4th lumbar vertebra, the lowest for femoral head samples. For all anatomical sites, resorption cavities caused significantly more stiffness loss than homogeneous erosion did. This novel technique can be used further to evaluate the impact of resorption cavities, which are known to change in several metabolic bone diseases and due to treatment, on bone competence.     

Bone morphogenetic protein signaling through ACVR1 and BMPR1A negatively regulates bone mass along with alterations in bone composition

Bone quantity and bone quality are important factors in determining the properties and the mechanical functions of bone. This study examined the effects of disrupting bone morphogenetic protein (BMP) signaling through BMP receptors on bone quantity and bone quality. More specifically, we disrupted two BMP receptors, Acvr1 and Bmpr1a, respectively, in Osterix-expressing osteogenic progenitor cells in mice. We examined the structural changes to the femora from 3-month old male and female conditional knockout (cKO) mice using micro-computed tomography (micro-CT) and histology, as well as compositional changes to both cortical and trabecular compartments of bone using Raman spectroscopy. We found that the deletion of Acvr1 and Bmpr1a, respectively, in an osteoblast-specific manner resulted in higher bone mass in the trabecular compartment. Disruption of Bmpr1a resulted in a more significantly increased bone mass in the trabecular compartment. We also found that these cKO mice showed lower mineral-to-matrix ratio, while tissue mineral density was lower in the cortical compartment. Collagen crosslink ratio was higher in both cortical and trabecular compartments of male cKO mice. Our study suggested that BMP signaling in osteoblast mediated by BMP receptors, namely ACVR1 and BMPR1A, is critical in regulating bone quantity and bone quality.     

A Comparison of Micro-CT and Dental CT in Assessing Cortical Bone Morphology and Trabecular Bone Microarchitecture

Objective

The objective of this study was to evaluate the relationship between the trabecular bone microarchitecture and cortical bone morphology by using micro-computed tomography (micro-CT) and dental cone-beam computed tomography (dental CT).

Materials and Methods

Sixteen femurs and eight fifth lumbar vertebrae were collected from eight male Sprague Dawley rats. Four trabecular bone microarchitecture parameters related to the fifth lumbar vertebral body (percent bone volume [BV/TV], trabecular thickness [TbTh], trabecular separation [TbSp], and trabecular number [TbN]) were calculated using micro-CT. In addition, the volumetric cancellous bone grayscale value (vCanGrayscale) of the fifth lumbar vertebral body was measured using dental CT. Furthermore, four cortical bone morphology parameters of the femoral diaphysis (total cross-sectional area [TtAr], cortical area [CtAr], cortical bone area fraction [CtAr/TtAr], and cortical thickness [CtTh]) were calculated using both micro-CT and dental CT. Pearson analysis was conducted to calculate the correlation coefficients (r) of the micro-CT and dental CT measurements. Paired-sample t tests were used to compare the differences between the measurements of the four cortical bone morphology parameters obtained using micro-CT and dental CT.

Results

High correlations between the vCanGrayscale measured using dental CT and the trabecular bone microarchitecture parameters (BV/TV [r = 0.84] and TbTh [r = 0.84]) measured using micro-CT were observed. The absolute value of the four cortical bone morphology parameters may be different between the dental CT and micro-CT approaches. However, high correlations (r ranged from 0.71 to 0.90) among these four cortical bone morphology parameters measured using the two approaches were obtained.

Conclusion

We observed high correlations between the vCanGrayscale measured using dental CT and the trabecular bone microarchitecture parameters (BV/TV and TbTh) measured using micro-CT, in addition to high correlations between the cortical bone morphology measured using micro-CT and dental CT. Further experiments are necessary to validate the use of dental CT on human bone.     

Bone microarchitecture in ankylosing spondylitis and the association with bone mineral density,fractures, and syndesmophytes

Introduction

Osteoporosis of the axial skeleton is a known complication of ankylosing spondylitis (AS), but bone loss affecting the peripheral skeleton is less studied. This study on volumetric bone mineral density (vBMD) and bone microarchitecture in AS was conducted to compare peripheral vBMD in AS patients with that in healthy controls, to study vBMD in axial compared with peripheral bone, and to explore the relation between vertebral fractures, spinal osteoproliferation, and peripheral bone microarchitecture and density.

Methods

High-resolution peripheral quantitative computed tomography (HRpQCT) of ultradistal radius and tibia and QCT and dual-energy x-ray absorptiometry (DXA) of lumbar spine were performed in 69 male AS patients (NY criteria). Spinal radiographs were assessed for vertebral fractures and syndesmophyte formation (mSASSS). The HRpQCT measurements were compared with the measurements of healthy controls.

Results

The AS patients had lower cortical vBMD in radius (P = 0.004) and lower trabecular vBMD in tibia (P = 0.033), than did the controls. Strong correlations were found between trabecular vBMD in lumbar spine, radius (r_S = 0.762; P < 0.001), and tibia (r_S = 0.712; P < 0.001).When compared with age-matched AS controls, patients with vertebral fractures had lower lumbar cortical vBMD (-22%; P = 0.019), lower cortical cross-sectional area in radius (-28.3%; P = 0.001) and tibia (-24.0%; P = 0.013), and thinner cortical bone in radius (-28.3%; P = 0.001) and tibia (-26.9%; P = 0.016).mSASSS correlated negatively with trabecular vBMD in lumbar spine (r_S = -0.620; P < 0.001), radius (r_S = -0.400; p = 0.001) and tibia (r_S = -0.475; p < 0.001) and also with trabecular thickness in radius (r_S = -0.528; P < 0.001) and tibia (r_S = -0.488; P < 0.001).Adjusted for age, syndesmophytes were significantly associated with decreasing trabecular vBMD, but increasing cortical vBMD in lumbar spine, but not with increasing cortical thickness or density in peripheral bone. Estimated lumbar vBMD by DXA correlated with trabecular vBMD measured by QCT (r_S = 0.636; P < 0.001).

Conclusions

Lumbar osteoporosis, syndesmophytes, and vertebral fractures were associated with both lower vBMD and deteriorated microarchitecture in peripheral bone. The results indicate that trabecular bone loss is general, whereas osteoproliferation is local in AS.     

Distal skeletal tibia assessed by HR-pQCT is highly correlated with femoral and lumbar vertebra failure loads

Dual energy X-ray absorptiometry (DXA) is the standard for assessing fragility fracture risk using areal bone mineral density (aBMD), but only explains 60–70% of the variation in bone strength. High-resolution peripheral quantitative computed tomography (HR-pQCT) provides 3D-measures of bone microarchitecture and volumetric bone mineral density (vBMD), but only at the wrist and ankle. Finite element (FE) models can estimate bone strength with 86–95% precision. The purpose of this study is to determine how well vBMD and FE bone strength at the wrist and ankle relate to fracture strength at the hip and spine, and to compare these relationships with DXA measured directly at those axial sites. Cadaveric samples (radius, tibia, femur and L4 vertebra) were compared within the same body. The radius and tibia specimens were assessed using HR-pQCT to determine vBMD and FE failure load. aBMD from DXA was measured at the femur and L4 vertebra. The femur and L4 vertebra specimens were biomechanically tested to determine failure load. aBMD measures of the axial skeletal sites strongly correlated with the biomechanical strength for the L4 vertebra (r = 0.77) and proximal femur (r = 0.89). The radius correlated significantly with biomechanical strength of the L4 vertebra for vBMD (r = 0.85) and FE-derived strength (r = 0.72), but not with femur strength. vBMD at the tibia correlated significantly with femoral biomechanical strength (r = 0.74) and FE-estimated strength (r = 0.83), and vertebral biomechanical strength for vBMD (r = 0.97) and FE-estimated strength (r = 0.91). The higher correlations at the tibia compared to radius are likely due to the tibia’s weight-bearing function.     

Finite element analysis of vertebral body mechanics with a nonlinear microstructural model for the trabecular core.

In this study, a finite element model of a vertebral body was used to study the load-bearing role of the two components (shell and core) under compression. The model of the vertebral body has the characteristic kidney shape transverse cross section with concave lateral surfaces and flat superior and inferior surfaces. A nonlinear unit cell based foam model was used for the trabecular core, where nonlinearity was introduced as coupled elastoplastic beam behavior of individual trabeculae. The advantage of the foam model is that architecture and material properties are separated, thus facilitating studies of the effects of architecture on the apparent behavior. Age-related changes in the trabecular architecture were considered in order to address the effects of osteoporosis on the load-sharing behavior. Stiffness changes with age (architecture and porosity changes) for the trabecular bone model were shown to follow trends in published experimental results. Elastic analyses showed that the relative contribution of the shell to the load-bearing ability of the vertebra decreases with increasing age and lateral wall curvature. Elasto-plastic (non-linear) analyses showed that failure regions were concentrated in the upper posterior region of the vertebra in both the shell and core components. The ultimate load of the vertebral body model varied from 2800 N to 5600 N, depending on age (architecture and porosity of the trabecular core) and shell thickness. The model predictions lie within the range of experimental results. The results provide an understanding of the relative role of the core and shell in vertebral body mechanics and shed light on the yield and post-yield behavior of the vertebral body.     

Experimental and finite element analysis of the mouse caudal vertebrae loading model: prediction of cortical and trabecular bone adaptation

In this study, we attempt to predict cortical and trabecular bone adaptation in the mouse caudal vertebrae loading model using knowledge of bone’s local mechanical environment at the onset of loading. In a previous study, we demonstrated appreciable 25.9 and 11% increases in both trabecular and cortical bone volume density, respectively, when subjecting the fifth caudal vertebrae (C5) of C57BL/6 (B6) mice to an acute loading regime (amplitude of 8N, 3000 cycles, 10 Hz, 3 times a week for 4 weeks). We have also established a validated finite element (FE) model of the C5 vertebra using micro-computed tomography (micro-CT), which characterizes, in 3D, the micro-mechanical strains present in both cortical and trabecular compartments due to the applied loads. To investigate the relationship between load-induced bone adaptation and mechanical strains in-vivo and in-silico data sets were compared. Using data from the previous cross-sectional study, we divided cortical and trabecular compartments into 15 subregions and determined, for each region, a bone formation parameter ΔBV/BS (a cross-sectional measure of the bone volume added to cortical and trabecular surfaces following the described loading regime). Linear regression was then used to correlate mean regional values of ΔBV/BS with mean values of mechanical strains derived from the FE models which were similarly regionalized. The mechanical parameters investigated were strain energy density (SED), the orthogonal strains (e _x , e _y , e _z ) and the three shear strains (e _xy , e _yz , e _zx ). For cortical regions, regression analysis showed SED to correlate extremely well with ΔBV/BS (R ² =?0.82) and e _z (R ²?=?0.89). Furthermore, SED was found to predict expansion of the cortical shell correlating significantly with the regional percentage increases in cortical tissue volume (R ² = 0.92), cortical marrow volume (R ² =?0.91) and cortical thickness (R ² = 0.56). For trabecular regions, FE parameters were found not to correlate with load-induced trabecular bone morphology. These results indicate that load-induced cortical morphology can be predicted from population data, whereas the prediction of trabecular morphology requires subject-specific micro- architecture.     

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

IntroductionPreviously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R² = 0.77, normalized root mean squared error (RMSE%) = 16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia.MethodsLocal stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin’s fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R² and RMSE%.ResultsThe uniform anisotropic FE model explained 53–74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76–79% of the variance in stiffness with RMSE% being 11.2–11.5%.ConclusionsOf the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin’s fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.     

Noninvasive prediction of vertebral body compressive strength using nonlinear finite element method and an image based technique

Noninvasive prediction of vertebral body strength under compressive loading condition is a valuable tool for the assessment of clinical fractures. This paper presents an effective specimen-specific approach for noninvasive prediction of human vertebral strength using a nonlinear finite element (FE) model and an image based parameter based on the quantitative computed tomography (QCT). Nine thoracolumbar vertebrae excised from three cadavers with an average age of 42 years old were used as the samples. The samples were scanned using the QCT. Then, a segmentation technique was performed on each QCT sectional image. The segmented images were then converted into three-dimensional FE models for linear and nonlinear analyses. A new material model was implemented in our nonlinear model being more compatible with real mechanical behavior of trabecular bone. A new image based MOS (Mechanic of Solids) parameter named minimum sectional strength ((σ_uA)_min) was used for the ultimate compressive strength prediction. Subsequently, the samples were destructively tested under uniaxial compression and their experimental ultimate compressive strengths were obtained. Results indicated that our new implemented FE model can predict ultimate compressive strength of human vertebra with a correlation coefficient (R² = 0.94) better than usual linear and nonlinear FE models (R² = 0.83 and 0.85 respectively). The image based parameter introduced in this study ((σ_uA)_min) was also correlated well with the experimental results (R² = 0.86). Although nonlinear FE method with new implemented material model predicts compressive strength better than the (σ_uA)_min, this parameter is clinically more feasible due to its simplicity and lower computational costs. This can make future applications of the (σ_uA)_min more justified for human vertebral body compressive strength prediction.     

Effect of239Pu on mouse hemopoietic stem cells in different types of bone marrow cavities

Summary Repopulative activity of hemopoietic stem cells of mice given i.v. 5 kBq²³⁹Pu/mouse (166.5 kBq/kg) was followed. The activity retained was measured in the whole mouse, the skeleton and the liver. Simultaneously average cumulative skeletal dose was calculated. Quantitative parameters of the stem cell compartment and the marrow cellularity were studied in variously arranged bones (femur, pelvis, lumbar vertebra) using the exocolonizing test and cytological techniques. The effects of radiation were most marked in lumbar vertebra, less serious changes were found in pelvis and only a moderate response was present in femur. The bone marrow hemopoiesis is damaged in various bone sites to different degrees and the percentage of cells at risk appears higher in trabecular than in cortical bone.     

Dietary supplementation with dried plum prevents ovariectomy-induced bone loss while modulating the immune response in C57BL/6J mice

This study was designed to investigate the effects of dried plum on the changes in bone metabolism and the immune response associated with ovarian hormone deficiency. Adult female C57BL/6J mice were either sham-operated (Sham) and fed AIN-93 diet (control) or ovariectomized (OVX) and fed a control diet with 0%, 5%, 15% or 25% dried plum (w/w), corresponding to control, low- (LDP), medium- (MDP) and high (HDP)-dose dried plum. Four weeks of HDP supplementation prevented the decrease in spine bone mineral density and content induced by OVX. The OVX compromise in trabecular bone of the vertebra and proximal tibia was prevented by the higher doses of dried plum, and in the vertebra these effects resulted in greater (P<.05) bone strength and stiffness. In the bone marrow, OVX suppressed granulocyte and committed monocyte populations and increased the lymphoblast population, but the MDP and HDP restored these myeloid and lymphoid populations to the level of the Sham. Dried plum also suppressed lymphocyte tumor necrosis factor (TNF)-α production ex vivo by splenocytes, in response to concanavalin (Con) A stimulation. These data indicate that dried plum's positive effects on bone structural and biomechanical properties coincide with the restoration of certain bone marrow myeloid and lymphoid populations, and suppressed splenocyte activation occurring with ovarian hormone deficiency.     

The effects of tensile-compressive loading mode and microarchitecture on microdamage in human vertebral cancellous bone

The amount of microdamage in bone tissue impairs mechanical performance and may act as a stimulus for bone remodeling. Here we determine how loading mode (tension vs. compression) and microstructure (trabecular microarchitecture, local trabecular thickness, and presence of resorption cavities) influence the number and volume of microdamage sites generated in cancellous bone following a single overload. Twenty paired cylindrical specimens of human vertebral cancellous bone from 10 donors (47–78 years) were mechanically loaded to apparent yield in either compression or tension, and imaged in three dimensions for microarchitecture and microdamage (voxel size 0.7×0.7×5.0 μm³). We found that the overall proportion of damaged tissue was greater (p=0.01) for apparent tension loading (3.9±2.4%, mean±SD) than for apparent compression loading (1.9±1.3%). Individual microdamage sites generated in tension were larger in volume (p<0.001) but not more numerous (p=0.64) than sites in compression. For both loading modes, the proportion of damaged tissue varied more across donors than with bone volume fraction, traditional measures of microarchitecture (trabecular thickness, trabecular separation, etc.), apparent Young?s modulus, or strength. Microdamage tended to occur in regions of greater trabecular thickness but not near observable resorption cavities. Taken together, these findings indicate that, regardless of loading mode, accumulation of microdamage in cancellous bone after monotonic loading to yield is influenced by donor characteristics other than traditional measures of microarchitecture, suggesting a possible role for tissue material properties.     

Dependence of mechanical properties of trabecular bone on plate–rod microstructure determined by individual trabecula segmentation (ITS)

Individual trabecula segmentation (ITS) technique can decompose the trabecular bone network into individual trabecular plates and rods and is capable of quantifying the plate/rod-related microstructural characteristics of trabecular bone. This novel technique has been shown to be able to provide in-depth insights into micromechanics and failure mechanisms of human trabecular bone, as well as to distinguish the fracture status independent of area bone mineral density in clinical applications. However, the plate/rod microstructural parameters from ITS have never been correlated to experimentally determined mechanical properties of human trabecular bone. In this study, on-axis cylindrical trabecular bone samples from human proximal tibia (n=22), vertebral body (n=10), and proximal femur (n=21) were harvested, prepared, scanned using micro computed-tomography (µCT), analyzed with ITS and mechanically tested. Regression analyses showed that the plate bone volume fraction (pBV/TV) and axial bone volume fraction (aBV/TV) calculated by ITS analysis correlated the best with elastic modulus (R²=0.96–0.97) and yield strength (R²=0.95–0.96). Trabecular plate-related microstructural parameters correlated highly with elastic modulus and yield strength, while most rod-related parameters were found inversely and only moderately correlated with the mechanical properties. In addition, ITS analysis also identified that trabecular bone at human femoral neck had the highest trabecular plate-related parameters while the other sites were similar with each other in terms of plate–rod microstructure.     

Volume to density relation in adult human bone tissue

Uniformity of tissue mineralisation is a strongly debated issue, due to its relation with bone mechanical behaviour. Bone mineral density (BMD) is measured in the clinical practice and is applied in computational application to derive material proprieties of bone tissue. However, BMD cannot identify if the variation in bone density is related to a modification of tissue mineral density (TMD), a change in bone volume or a combination of the two. This study was aimed to investigate whether TMD can be assumed as a constant in adult human bone (trabecular and cortical).A total number of 115 cylindrical bone specimens were collected. An inter-site analysis (96 specimens, 2 donors) was performed on cortical and trabecular specimens extracted from different anatomical sites. An intra-site study (19 specimens, 19 donors) was performed on specimens extracted from femoral heads. Bone volume fraction (BV/TV) was computed by means of a micro-computed tomography. Furthermore, ash density (ρ_ash) was measured. TMD was computed as the ratio between ρ_ash and BV/TV.It was found that the TMD of trabecular (1.24±0.16 g/cm³) and cortical (1.19±0.06 g/cm³) bone were not statistically different (p=0.31). Furthermore, the linear regression between ρ_ash and BV/TV was statistically significant (r²=0.99, p<0.001). Intra- and inter-site analyses demonstrated that the mineral distribution was independent of the extraction site.The present study suggests that TMD can be assumed reasonably constant in non-pathological adult bone tissue. Consequently, it is suggested that TMD can be managed as a constant in computational models, varying only BV in relation to clinical densitometric analysis.     

A patient-specific finite element methodology to predict damage accumulation in vertebral bodies under axial compression, sagittal flexion and combined loads

Due to the inherent limitations of DXA, assessment of the biomechanical properties of vertebral bodies relies increasingly on CT-based finite element (FE) models, but these often use simplistic material behaviour and/or single loading cases. In this study, we applied a novel constitutive law for bone elasticity, plasticity and damage to FE models created from coarsened pQCT images of human vertebrae, and compared vertebral stiffness, strength and damage accumulation for axial compression, anterior flexion and a combination of these two cases. FE axial stiffness and strength correlated with experiments and were linearly related to flexion properties. In all loading modes, damage localised preferentially in the trabecular compartment. Damage for the combined loading was higher than cumulated damage produced by individual compression and flexion. In conclusion, this FE method predicts stiffness and strength of vertebral bodies from CT images with clinical resolution and provides insight into damage accumulation in various loading modes.     

Validation of composite finite elements efficiently simulating elasticity of trabecular bone

Patient-specific analyses of the mechanical properties of bones become increasingly important for the management of patients with osteoporosis. The potential of composite finite elements (CFEs), a novel FE technique, to assess the apparent stiffness of vertebral trabecular bone is investigated in this study. Segmented volumes of cylindrical specimens of trabecular bone are compared to measured volumes. Elasticity under uniaxial loading conditions is simulated; apparent stiffnesses are compared to experimentally determined values. Computational efficiency is assessed and recommendations for simulation parameters are given. Validating apparent uniaxial stiffnesses results in concordance correlation coefficients 0.69 ≤ r_𝒸 ≤ 0.92 for resolutions finer than 168 μm, and an average error of 5.8% between experimental and numerical results at 24 μm resolution. As an application, the code was used to compute local, macroscopic stiffness tensors for the trabecular structure of a lumbar vertebra. The presented technique allows for computing stiffness using smooth FE meshes at resolutions that are well achievable in peripheral high resolution quantitative CT. Therefore, CFEs could be a valuable tool for the patient-specific assessment of bone stiffness.     

Quantification of a rat tail vertebra model for trabecular bone adaptation studies

A feedback controlled loading apparatus for the rat tail vertebra was developed to deliver precise mechanical loads to the eighth caudal vertebra (C8) via pins inserted into adjacent vertebrae. Cortical bone strains were recorded using strain gages while subjecting the C8 in four cadaveric rats to mechanical loads ranging from 25 to 100 N at 1 Hz with a sinusoidal waveform. Finite element (FE) models, based on micro computed tomography, were constructed for all four C8 for calculations of cortical and trabecular bone tissue strains. The cortical bone strains predicted by FE models agreed with strain gage measurements, thus validating the FE models. The average measured cortical bone strain during 25-100 N loading was between 298 +/- 105 and 1210 +/- 297 microstrain (muepsilon). The models predicted average trabecular bone tissue strains ranging between 135 +/- 35 and 538 +/- 138 mu epsilon in the proximal region, 77 +/- 23-307 +/- 91 muepsilon in the central region, and 155 +/- 36-621 +/- 143 muepsilon in the distal region for 25-100 N loading range. Although these average strains were compressive, it is also interesting that the trabecular bone tissue strain can range from compressive to tensile strains (-1994 to 380 mu epsilon for a 100 N load). With this novel approach that combines an animal model with computational techniques, it could be possible to establish a quantitative relationship between the microscopic stress/strain environment in trabecular bone tissue, and the biosynthetic response and gene expression of bone cells, thereby study bone adaptation.