The influence of boundary conditions and loading mode on high-resolution finite element-computed trabecular tissue properties

The Role of Vertebral Porosity and Implant Loading Mode on Bone-Tissue Stress in the Human Vertebral Body Following Lumbar Total Disc Arthroplasty

STUDY DESIGN

Micro-computed tomography- (micro-CT-) based finite element analysis of cadaveric human lumbar vertebrae virtually implanted with total disc arthroplasty (TDA) implants.

OBJECTIVE

(1) Assess the relationship between vertebral porosity and maximum levels of bone-tissue stress following TDA; (2) determine whether the implant's loading mode (axial compression vs. sagittal bending) alters the relationship between vertebral porosity and bone-tissue stress.

SUMMARY OF BACKGROUND DATA

Implant subsidence may be related to the bone biomechanics in the underlying vertebral body, which are poorly understood. For example, it remains unclear how the stresses that develop in the supporting bone tissue depend on the implant's loading mode or on typical inter-individual variations in vertebral morphology.

METHODS

Data from micro-CT scans from 12 human lumbar vertebrae (8 males, 4 females; 51-89 years of age; bone volume fraction [BV/TV] = 0.060-0.145) were used to construct high-resolution finite element models (37 μm element edge length) comprising disc-vertebra-implant motion segments. Implants were loaded to 800 N of force in axial compression, flexion-, and extension-induced impingement. For comparison, the same net loads were applied via an intact disc without an implant. Linear regression was used to assess the relationship between BV/TV, loading mode, and the specimen-specific change in stress caused by implantation.

RESULTS

The increase in maximum bone-tissue stress caused by implantation depended on loading mode (P < 0.001), increasing more in bending-induced impingement than axial compression (for the same applied force). The change in maximum stress was significantly associated with BV/TV (P = 0.002): higher porosity vertebrae experienced a disproportionate increase in stress compared with lower porosity vertebrae. There was a significant interaction between loading mode and BV/TV (P = 0.002), indicating that loading mode altered the relationship between BV/TV and the change in maximum bone-tissue stress.

CONCLUSION

Typically-sized TDA implants disproportionately increase the bone-tissue stress in more porous vertebrae; this affect is accentuated when the implant impinges in sagittal bending.Level of Evidence: N/A.

Opportunistic application of phantom-less calibration methods for fracture risk prediction using QCT/FEA

OBJECTIVES

Quantitative computed tomography (QCT)-based finite element analysis (FEA) implements a calibration phantom to estimate bone mineral density (BMD) and assign material properties to the models. The objectives of this study were to (1) propose robust phantom-less calibration methods, using subject-specific tissues, to obtain vertebral fracture properties estimations using QCT/FEA; and (2) correlate QCT/FEA predictions to DXA values of areal BMD.

METHODS

Eighty of a cohort of 111 clinical QCT scans were used to obtain subject-specific parameters using a phantom calibration approach and for the development of the phantom-less calibration equations. Equations were developed based on the HU measured from various soft tissues and regions, and using multiple linear regression analyses. Thirty-one additional QCT scans were used for cross-validation of QCT/FEA estimated fracture loads from the L₃ vertebrae based on the phantom and phantom-less equations. Finally, QCT/FEA-predicted fracture loads were correlated with aBMD obtained from DXA.

RESULTS

Overall, 217 QCT/FEA models from 31 subjects (20 females, 11 men) with mean ages of 69.6 (13.1) and 67.3 (14) were used to cross-validate the phantom-less equations and assess bone strength. The proposed phantom-less equations showed high correlations with phantom-based estimates of BMD (99%). Cross-validation of QCT/FEA-predicted fracture loads from phantom-less equations and phantom-specific outcomes resulted in high correlations for all proposed methods (0.94-0.99). QCT/FEA correlation outcomes from the phantom-less equations and DXA-aBMD were moderately high (0.64-0.68).

CONCLUSIONS

The proposed QCT/FEA subject-specific phantom-less calibration methods demonstrated the potential to be applied to both prospective and retrospective applications in the clinical setting.

KEY POINTS

• QCT/FEA overcomes the disadvantages of DXA and improves fracture properties predictions of vertebrae. • QCT/FEA fracture estimates using the phantom-less approach highly correlated to values obtained using a calibration phantom. • QCT/FEA prediction using a phantom-less approach is an accurate alternative over phantom-based methods.

Density-Dependent Material and Failure Criteria Equations Highly Affect the Accuracy and Precision of QCT/FEA-Based Predictions of Osteoporotic Vertebral Fracture Properties

About 700,000 vertebral fractures occur in the US as a result of bone loss. Quantitative computed tomography (QCT)-based finite element analysis (FEA) is a promising tool for fracture risk prediction that is becoming attractive in the clinical setting. The goals of this study were (1) to perform individual and pooled specimen optimization using inverse QCT/FEA modeling to obtain ash density-elastic modulus equations incorporating the whole vertebral body and accounting for all variables used during FE modeling, and (2) to determine the effect of material equations and failure criteria on the accuracy and precision of mechanical properties. Fifty-four (54) human vertebrae were used to optimize material equations based on experimental outcomes and, together with a previously proposed material equation, were implemented in our models using three different failure criteria to obtain fracture loads. Our robust QCT/FEA approach predicted 78% of the failure loads. Material equations resulted in poor accuracy in the predicted stiffness, yet yielded good precision and, more importantly, strong correlations with fracture loads. Both material and fracture criterion equations are equally important in estimating accurate and precise QCT/FEA predictions. Results suggest that both elastic modulus and fracture criterion equations should be validated against experimental outcomes to better explain the response of the tissue under various conditions.

Estimating tissue-level properties of porcine talar subchondral bone

Tissue-level properties of bone play an important role when characterising apparent-level bone biomechanical behaviour and yet little is known about its effect at this hierarchical level. In combination with trabecular morphological data these properties can be used to predict bone strength, which becomes an invaluable tool for clinicians in patient treatment planning. This study developed specimen-specific micro-finite element (μFE) models using validated continuum-level models, containing grayscale-derived material properties, to indirectly establish tissue-level properties of porcine talar subchondral bone. Specimen-specific continuum finite element (hFE) models of subchondral trabecular bone were setup using μCT data of ten cylindrical specimens extracted from juvenile porcine tali. The models were validated using quasi-static uniaxial compression testing. Validated hFE models were used to calibrate the tissue modulus of corresponding μFE models by minimising the difference between the μFE and hFE stiffness values. Key trabecular morphological indices (BV/TV, DA, Conn.D, Tb.Th, EF) were evaluated. Good agreement was observed between hFE models and experiment (CCC = 0.66). Calibrated E_tiss was 504 ± 37.65 MPa. Average BV/TV and DA for μFE specimens were 0.37 ± 0.05 and 0.68 ± 0.11, respectively. BV/TV (r² = 0.667) correlated highly with μFE stiffness. The small intra-specimen variation to tissue-level properties suggests that variations to apparent-level stiffness originate from variations to microarchitecture rather than tissue mechanical properties.

Effect of variations in tissue-level ductility on human vertebral strength

Although the ductility of bone tissue is a unique element of bone quality and varies with age and across the population, the extent to which and mechanisms by which typical population-variations in tissue-level ductility can alter whole-bone strength remains unclear. To provide insight, we conducted a finite element analysis parameter study of whole-vertebral (monotonic) compressive strength on six human L1 vertebrae. Each model was generated from micro-CT scans, capturing the trabecular micro-architecture in detail, and included a non-linear constitutive model for the bone tissue that allowed for plastic yielding, different strengths in tension and compression, large deformations, and, uniquely, localized damage once a specified limit in tissue-level ultimate strain was exceeded. Those strain limits were based on reported (mean ± SD) values from cadaver experiments (8.8 ± 3.7% strain for trabecular tissue and 2.2 ± 0.9% for cortical tissue). In the parameter study, the strain limits were varied by ±1 SD from their mean values, for a combination of nine analyses per specimen; bounding values of zero and unlimited post-yield strain were also modeled. The main outcomes from the finite element analysis were the vertebral compressive strength and the amount of failed (yielded or damaged) tissue at the overall structure-level failure. Compared to a reference case of using the mean values of ultimate strain, we found that varying both trabecular and cortical tissue ultimate strains by ±1 SD changed the computed vertebral strength by (mean ± SD) ±6.9 ± 1.1% on average. Mechanistically, that modest effect arose because the proportion of yielded tissue (without damage) was 0.9 ± 0.3% of all the bone tissue across the nine cases and the proportion of damaged tissue (i.e. tissue exceeding the prescribed tissue-level ultimate strain) was 0.2 ± 0.1%. If the types of variations in tissue-level ductility investigated here accurately represent real typical variations in the population, the consistency of our results across specimens and the modest effect size together suggest that typical variations in tissue-level ductility only have a modest impact on vertebral compressive strength, in large part because so few trabeculae are damaged at the load capacity of the bone.

Effect of fabric on the accuracy of computed tomography-based finite element analyses of the vertebra

Quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra are widely used in studying spine biomechanics and mechanobiology, but their accuracy has not been fully established. Although the models typically assign material properties based only on local bone mineral density (BMD), the mechanical behavior of trabecular bone also depends on fabric. The goal of this study was to determine the effect of incorporating measurements of fabric on the accuracy of FE predictions of vertebral deformation. Accuracy was assessed by using displacement fields measured via digital volume correlation-applied to time-lapse microcomputed tomography (μCT)-as the gold standard. Two QCT-based FE models were generated from human L1 vertebrae (n = 11): the entire vertebral body and a cuboid-shaped portion of the trabecular centrum [dimensions: (20-30) × (15-20) × (15-20) mm3]. For axial compression boundary conditions, there was no difference (p = 0.40) in the accuracy of the FE-computed displacements for models using material properties based on local values of BMD versus those using material properties based on local values of fabric and volume fraction. However, when using BMD-based material properties, errors were higher for the vertebral-body models (8.4-50.1%) than cuboid models (1.5-19.6%), suggesting that these properties are inaccurate in the peripheral regions of the centrum. Errors also increased when assuming that the cuboid region experienced uniaxial loading during axial compression of the vertebra. These findings indicate that a BMD-based constitutive model is not sufficient for the peripheral region of the vertebral body when seeking accurate QCT-based FE modeling of the vertebra.

Mechanisms of Interaction of Ultrasound With Cancellous Bone: A Review

Ultrasound is now a clinically accepted modality in the management of osteoporosis. The most common commercial clinical devices assess fracture risk from measurements of attenuation and sound speed in cancellous bone. This review discusses fundamental mechanisms underlying the interaction between ultrasound and cancellous bone. Because of its two-phase structure (mineralized trabecular network embedded in soft tissue-marrow), its anisotropy, and its inhomogeneity, cancellous bone is more difficult to characterize than most soft tissues. Experimental data for the dependencies of attenuation, sound speed, dispersion, and scattering on ultrasound frequency, bone mineral density, composition, microstructure, and mechanical properties are presented. The relative roles of absorption, scattering, and phase cancellation in determining attenuation measurements in vitro and in vivo are delineated. Common speed of sound metrics, which entail measurements of transit times of pulse leading edges (to avoid multipath interference), are greatly influenced by attenuation, dispersion, and system properties, including center frequency and bandwidth. However, a theoretical model has been shown to be effective for correction for these confounding factors in vitro and in vivo. Theoretical and phantom models are presented to elucidate why cancellous bone exhibits negative dispersion, unlike soft tissue, which exhibits positive dispersion. Signal processing methods are presented for separating "fast" and "slow" waves (predicted by poroelasticity theory and supported in cancellous bone) even when the two waves overlap in time and frequency domains. Models to explain dependencies of scattering on frequency and mean trabecular thickness are presented and compared with measurements. Anisotropy, the effect of the fluid filler medium (marrow in vivo or water in vitro), phantoms, computational modeling of ultrasound propagation, acoustic microscopy, and nonlinear properties in cancellous bone are also discussed.

Load-transfer in the human vertebral body following lumbar total disc arthroplasty: Effects of implant size and stiffness in axial compression and forward flexion

Adverse clinical outcomes for total disc arthroplasty (TDA), including subsidence, heterotopic ossification, and adjacent-level vertebral fracture, suggest problems with the underlying biomechanics. To gain insight, we investigated the role of size and stiffness of TDA implants on load-transfer within a vertebral body. Uniquely, we accounted for the realistic multi-scale geometric features of the trabecular micro-architecture and cortical shell. Using voxel-based finite element analysis derived from a micro-computed tomography scan of one human L1 vertebral body (74-μm-sized elements), a series of generic elliptically shaped implants were analyzed. We parametrically modeled three implant sizes (small, medium [a typical clinical size], and large) and three implant materials (metallic, E = 100 GPa; polymeric, E = 1 GPa; and tissue-engineered, E = 0.01 GPa). Analyses were run for two load cases: 800 N in uniform compression and flexion-induced anterior impingement. Results were compared to those of an intact model without an implant and loaded instead via a disc-like material. We found that TDA implantation increased stress in the bone tissue by over 50% in large portions of the vertebra. These changes depended more on implant size than material, and there was an interaction between implant size and loading condition. For the small implant, flexion increased the 98th-percentile of stress by 32 ± 24% relative to compression, but the overall stress distribution and trabecular-cortical load-sharing were relatively insensitive to loading mode. In contrast, for the medium and large implants, flexion increased the 98th-percentile of stress by 42 ± 9% and 87 ± 29%, respectively, and substantially re-distributed stress within the vertebra; in particular overloading the anterior trabecular centrum and cortex. We conclude that TDA implants can substantially alter stress deep within the lumbar vertebra, depending primarily on implant size. For implants of typical clinical size, bending-induced impingement can substantially increase stress in local regions and may therefore be one factor driving subsidence in vivo.

Dual-energy estimates of volumetric bone mineral densities in the lumbar spine using quantitative computed tomography better correlate with fracture properties when compared to single-energy BMD outcomes

It is estimated that over 200 million people worldwide are affected by osteoporosis. Vertebral fracture risk prediction using dual energy x-ray absorptiometry (DXA) is confounded by limitations of the technology, such as 2D measurements of bone mineral density (BMD), inability to measure bone distribution and heterogeneity, and potential overestimations of BMD due to degenerative diseases. To overcome these shortcomings, single energy (SE) quantitative computed tomography (QCT) imaging estimates of Hounsfield units (HU) and volumetric BMD have been implemented as alternative methodologies for assessing fracture risk. However, marrow fat within the vertebrae can highly affect the vBMD and fracture properties estimations. To address this issue, 54 vertebrae were dissected from nine cadaveric spines and scanned using SE-QCT (120kVp) and dual energy (DE)-QCT (80/140 kVp), with the latter accounting for marrow fat within the vertebrae. The vertebrae were then scanned using DXA and subjected to mechanical testing to obtain fracture properties. aBMD outcomes from DXA showed a better correlation with DE-QCT vBMD versus SE outcomes [DE: aBMD vs. vBMD (R²: 0.61); SE: aBMD vs. vBMD (R²: 0.27)]. SE-QCT underestimated vertebral vBMD by -56% (p<0.0001) when compared to DE-QCT. vBMD estimates from SE-QCT could predict 45% and 37% of the vertebral failure loads and stiffness, respectively, compared to 67% and 46% from DE-QCT. DE-QCT vBMD outcomes highly correlated with fracture properties of vertebrae as compared to SE-QCT metrics. As DE scanning has the ability to correct for the effects of bone marrow fat, estimated vBMD from SE-QCT were significantly underestimated compared to DE-QCT. Dual energy CT scanning has the potential to more accurately predict vertebral failure and aid the clinician in the evaluation of appropriate interventions. Future studies should consider implementing DE-QCT in their fracture assessment.

The Implantation of Bioactive Glass Granules Can Contribute the Load-Bearing Capacity of Bones Weakened by Large Cortical Defects

Bioactive glass (BAG) granules (S53P4) have shown good clinical results in one-stage treatment of osteomyelitis. During this treatment, a cortical window is created, and infected bone is debrided, which results in large defects that affect the mechanical properties of the bone. This study aimed to evaluate the role of BAG granules in load-bearing bone defect grafting. First, the influence of the geometry of the cortical window on the bone bending stiffness and estimated failure moments was evaluated using micro finite element analysis (µFE). This resulted in significant differences between the variations in width and length. In addition, µFE analysis showed that BAG granules contribute to bearing loads in simulated compression of a tibia with a defect grafted with BAG and a BAG and bone morsel mixture. These mixtures potentially can unload the cortical bone that is weakened by a large defect directly after the operation by up to approximately 25%, but only in case of optimal load transfer through the mixture.

Young's modulus of trabecular bone at the tissue level: A review

The tissue-level Young's modulus of trabecular bone is important for detailed mechanical analysis of bone and bone-implant mechanical interactions. However, the heterogeneity and small size of the trabecular struts complicate an accurate determination. Methods such as micro-mechanical testing of single trabeculae, ultrasonic testing, and nanoindentation have been used to estimate the trabecular Young's modulus. This review summarizes and classifies the trabecular Young's moduli reported in the literature. Information on species, anatomic site, and test condition of the samples has also been gathered. Advantages and disadvantages of the different methods together with recent developments are discussed, followed by some suggestions for potential improvement for future work. In summary, this review provides a thorough introduction to the approaches used for determining trabecular Young's modulus, highlights important considerations when applying these methods and summarizes the reported Young's modulus for follow-up studies on trabecular properties.

STATEMENT OF SIGNIFICANCE

The spongy trabecular bone provides mechanical support while maintaining a low weight. A correct measure of its mechanical properties at the tissue level, i.e. at a single-trabecula level, is crucial for analysis of interactions between bone and implants, necessary for understanding e.g. bone healing mechanisms. In this study, we comprehensively summarize the Young's moduli of trabecular bone estimated by currently available methods, and report their dependency on different factors. The critical review of different methods with recent updates is intended to inspire improvements in estimating trabecular Young's modulus. It is strongly suggested to report detailed information on the tested bone to enable statistical analysis in the future.

Standardizing compression testing for measuring the stiffness of human bone

Objectives

The ability to determine human bone stiffness is of clinical relevance in many fields, including bone quality assessment and orthopaedic prosthesis design. Stiffness can be measured using compression testing, an experimental technique commonly used to test bone specimens in vitro. This systematic review aims to determine how best to perform compression testing of human bone.

Methods

A keyword search of all English language articles up until December 2017 of compression testing of bone was undertaken in Medline, Embase, PubMed, and Scopus databases. Studies using bulk tissue, animal tissue, whole bone, or testing techniques other than compression testing were excluded.

Results

A total of 4712 abstracts were retrieved, with 177 papers included in the analysis; 20 studies directly analyzed the compression testing technique to improve the accuracy of testing. Several influencing factors should be considered when testing bone samples in compression. These include the method of data analysis, specimen storage, specimen preparation, testing configuration, and loading protocol.

Conclusion

Compression testing is a widely used technique for measuring the stiffness of bone but there is a great deal of inter-study variation in experimental techniques across the literature. Based on best evidence from the literature, suggestions for bone compression testing are made in this review, although further studies are needed to establish standardized bone testing techniques in order to increase the comparability and reliability of bone stiffness studies.

Cite this article: S. Zhao, M. Arnold, S. Ma, R. L. Abel, J. P. Cobb, U. Hansen, O. Boughton. Standardizing compression testing for measuring the stiffness of human bone. Bone Joint Res 2018;7:524–538. DOI: 10.1302/2046-3758.78.BJR-2018-0025.R1.

Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level

OBJECTIVE OF THE STUDY

The objective of the present study is to assess the mechanical behavior of trabecular bone based on microCT imaging and micro-finite-element analysis. In this way two methods are detailed: (i) direct determination of macroscopic elastic property of trabecular bone; (ii) inverse approach to assess mechanical properties of trabecular bone tissue.

PATIENTS

Thirty-five females and seven males (forty-two subjects) mean aged (±SD) 80±11.7 years from hospitals of Assistance publique-Hôpitaux de Paris (AP-HP) diagnosed with osteoporosis following a femoral neck fracture due to a fall from standing were included in this study.

MATERIALS AND METHODS

Fractured heads were collected during hip replacement surgery. Standardized bone cores were removed from the femoral head's equator by a trephine in a water bath. MicroCT images acquisition and analysis were performed with CTan^® software and bone volume fraction was then determined. Micro-finite-element simulations were per-formed using Abaqus 6.9-2^® software in order to determine the macroscopic mechanical behaviour of the trabecular bone. After microCT acquisition, a longitudinal compression test was performed and the experimental macroscopic Young's Modulus was extracted. An inverse approach based on the whole trabecular bone's mechanical response and micro-finite-element analysis was performed to determine microscopic mechanical properties of trabecular bone.

RESULTS

In the present study, elasticity of the tissue was shown to be similar to that of healthy tissue but with a lower yield stress.

CONCLUSION

Classical histomorphometric analysis form microCT imaging associated with an inverse micro-finite-element method allowed to assess microscopic mechanical trabecular bone parameters.

Relationships among ultrasonic and mechanical properties of cancellous bone in human calcaneus in vitro

Clinical bone sonometers applied at the calcaneus measure broadband ultrasound attenuation and speed of sound. However, the relation of ultrasound measurements to bone strength is not well-characterized. Addressing this issue, we assessed the extent to which ultrasonic measurements convey in vitro mechanical properties in 25 human calcaneal cancellous bone specimens (approximately 2×4×2cm). Normalized broadband ultrasound attenuation, speed of sound, and broadband ultrasound backscatter were measured with 500kHz transducers. To assess mechanical properties, non-linear finite element analysis, based on micro-computed tomography images (34-micron cubic voxel), was used to estimate apparent elastic modulus, overall specimen stiffness, and apparent yield stress, with models typically having approximately 25-30 million elements. We found that ultrasound parameters were correlated with mechanical properties with R=0.70-0.82 (p<0.001). Multiple regression analysis indicated that ultrasound measurements provide additional information regarding mechanical properties beyond that provided by bone quantity alone (p≤0.05). Adding ultrasound variables to linear regression models based on bone quantity improved adjusted squared correlation coefficients from 0.65 to 0.77 (stiffness), 0.76 to 0.81 (apparent modulus), and 0.67 to 0.73 (yield stress). These results indicate that ultrasound can provide complementary (to bone quantity) information regarding mechanical behavior of cancellous bone.

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.

Long-term treatment with odanacatib maintains normal trabecular biomechanical properties in ovariectomized adult monkeys as demonstrated by micro-CT-based finite element analysis

The cathepsin K inhibitor odanacatib (ODN) is a potent and reversible inhibitor of osteoclastic resorption activity. This drug is currently under development for the treatment of postmenopausal osteoporosis. Previously, we described data on the treatment efficacy of ODN in a preclinical estrogen-deficient model of an ovariectomized (OVX) rhesus monkey using HR-pQCT based finite element analysis (FEA) in vivo estimates of bone strength on the distal radius. To support the bone safety profile of ODN, we report ex vivo data on the apparent and hard tissue biomechanical properties of the trabecular bone of vertebrae of animals after 20 months of dosing in three treatment groups: Vehicle (VEH), ODN (2 mg/kg/day), and ALN (30 μg/kg/week). Biomechanical axial compression tests were performed on cylindrical trabecular samples cored out of the third lumbar vertebra of each animal at the end of the study. The biomechanical test results demonstrated that a normal (positive correlation between bone mineral density and bone strength) apparent material property relationship was maintained in the lumbar spine of ODN and ALN treated non-human primates (NHP). Trabecular bone hard tissue Young's modulus value was estimated using experimentally measured stiffness combined with FEA. The FEA and experimental results demonstrated that ODN treatment for 20 months maintained normal trabecular bone material hard tissue properties in the OVX-monkeys and was comparable to ALN.

Effect of intraspecimen spatial variation in tissue mineral density on the apparent stiffness of trabecular bone

This study investigated the effects of intraspecimen variations in tissue mineral density(TMD) on the apparent-level stiffness of human trabecular bone. High-resolution finite element (FE) models were created for each of 12 human trabecular bone specimens,using both microcomputed tomography (lCT) and “gold-standard” synchrotron radiation lCT (SRlCT) data. Our results confirm that incorporating TMD spatial variation reduces the calculated apparent stiffness compared to homogeneous TMD models. This effect exists for both lCT- and SRlCT-based FE models, but is exaggerated in lCT based models. This study provides a direct comparison of lCT to SRlCT data and is thereby able to conclude that the influence of including TMD heterogeneity is overestimated in lCT-based models.

Finite element models predict the location of microdamage in cancellous bone following uniaxial loading

High-resolution finite element models derived from micro-computed tomography images are often used to study the effects of trabecular microarchitecture and loading mode on tissue stress, but the degree to which existing finite element methods correctly predict the location of tissue failure is not well characterized. In the current study, we determined the relationship between the location of highly strained tissue, as determined from high-resolution finite element models, and the location of tissue microdamage, as determined from three-dimensional fluoroscopy imaging, which was performed after the microdamage was generated in-vitro by mechanical testing. Fourteen specimens of human vertebral cancellous bone were assessed (8 male donors, 2 female donors, 47-78 years of age). Regions of stained microdamage, were 50-75% more likely to form in highly strained tissue (principal strains exceeding 0.4%) than elsewhere, and generally the locations of the regions of microdamage were significantly correlated (p<0.05) with the locations of highly strained tissue. This spatial correlation was stronger for the largest regions of microdamage (≥1,000,000μm(3) in volume); 87% of large regions of microdamage were located near highly strained tissue. Together, these findings demonstrate that there is a strong correlation between regions of microdamage and regions of high strain in human cancellous bone, particularly for the biomechanically more important large instances of microdamage.

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.

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

As in clinical studies, finite element analysis (FEA) developed from computed tomography (CT) images of bones are useful in pre-clinical rodent studies assessing treatment effects on vertebral body (VB) strength. Since strength predictions from microCT-derived FEAs (μFEA) have not been validated against experimental measurements of mouse VB strength, a parametric analysis exploring material and failure definitions was performed to determine whether elastic μFEAs with linear failure criteria could reasonably assess VB strength in two studies, treatment and genetic, with differences in bone volume fraction between the control and the experimental groups. VBs were scanned with a 12-μm voxel size, and voxels were directly converted to 8-node, hexahedral elements. The coefficient of determination or R (2) between predicted VB strength and experimental VB strength, as determined from compression tests, was 62.3% for the treatment study and 85.3% for the genetic study when using a homogenous tissue modulus (E t) of 18 GPa for all elements, a failure volume of 2%, and an equivalent failure strain of 0.007. The difference between prediction and measurement (that is, error) increased when lowering the failure volume to 0.1% or increasing it to 4%. Using inhomogeneous tissue density-specific moduli improved the R (2) between predicted and experimental strength when compared with uniform E t=18 GPa. Also, the optimum failure volume is higher for the inhomogeneous than for the homogeneous material definition. Regardless of model assumptions, μFEA can assess differences in murine VB strength between experimental groups when the expected difference in strength is at least 20%.

A survey of micro-finite element analysis for clinical assessment of bone strength: the first decade

Micro-Finite Element (micro-FE) analysis is now widely used in biomedical research as a tool to derive bone mechanical properties as they relate to its microstructure. With the development of in vivo high-resolution peripheral quantitative CT (HR-pQCT) scanners, it can now be applied to analyze bone in-vivo in the peripheral skeleton. In this survey, the results of several experimental and clinical studies are summarized that addressed the feasibility of this approach to predict bone strength in-vivo. Specific questions that will be addressed are: how accurate are strength predictions based on micro-FE; how reproducible are the results; and, is it a better predictor of bone fracture risk than DXA based measures? Based on results of experimental studies, it is first concluded that micro-FE based on HR-pQCT images can accurately predict the strength of the distal radius during a fall on the outstretched hand using either linear elastic analysis, implementing a 'Pistoia criterion' or similar criterion in combination with an 'effective' Young's modulus or using non-linear analyses. When evaluating results of clinical reproducibility studies, it is concluded that for single-center studies, errors at the radius are less than 4.4% and 3.7% and at the tibia less than 3.6% and 2.3% for stiffness and strength, respectively. In multicenter trials, however, these errors can be increased by some 1.8% and 1.4% for stiffness and strength, respectively. Finally, based on the results of large cohort studies, it is concluded that micro-FE calculated stiffness better separates cases from controls than bone density parameters for subjects with fragility fractures at any site, but not for subjects with only radius fractures. In this latter case, however, combinations of micro-FE derived parameters can significantly improve the separation.

Effect of specimen-specific anisotropic material properties in quantitative computed tomography-based finite element analysis of the vertebra

Intra- and inter-specimen variations in trabecular anisotropy are often ignored in quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra. The material properties are typically estimated solely from local variations in bone mineral density (BMD), and a fixed representation of elastic anisotropy ("generic anisotropy") is assumed. This study evaluated the effect of incorporating specimen-specific, trabecular anisotropy on QCT-based FE predictions of vertebral stiffness and deformation patterns. Orthotropic material properties estimated from microcomputed tomography data ("specimen-specific anisotropy"), were assigned to a large, columnar region of the L1 centrum (n = 12), and generic-anisotropic material properties were assigned to the remainder of the vertebral body. Results were compared to FE analyses in which generic-anisotropic properties were used throughout. FE analyses were also performed on only the columnar regions. For the columnar regions, the axial stiffnesses obtained from the two categories of material properties were uncorrelated with each other (p = 0.604), and the distributions of minimum principal strain were distinctly different (p ≤ 0.022). In contrast, for the whole vertebral bodies in both axial and flexural loading, the stiffnesses obtained using the two categories of material properties were highly correlated (R2 > 0.82, p < 0.001) with, and were no different (p > 0.359) from, each other. Only moderate variations in strain distributions were observed between the two categories of material properties. The contrasting results for the columns versus vertebrae indicate a large contribution of the peripheral regions of the vertebral body to the mechanical behavior of this bone. In companion analyses on the effect of the degree of anisotropy (DA), the axial stiffnesses of the trabecular column (p < 0.001) and vertebra (p = 0.007) increased with increasing DA. These findings demonstrate the need for accurate modeling of the peripheral regions of the vertebral body in analyses of the mechanical behavior of the vertebra.

Seeing double: a comparison of microstructure, biomechanical function, and adjacent disc health between double- and single-layer vertebral endplates

STUDY DESIGN

Experimental and computational assessment of thickness, porosity, biomechanical behavior, and adjacent disc glycosaminoglycan content in double- and single-layer bony endplate samples harvested from human cadaver spines.

OBJECTIVE

To determine if the second layer of bone in double-layer vertebral endplates allows the superficial layer to achieve a more optimal balance between its biomechanical and nutritional functions.

SUMMARY OF BACKGROUND DATA

Proper disc health requires the endplate to balance opposing biomechanical and nutritional functions. Previous studies investigating endplate function report seeing double: some endplates have a second layer of bone. However, it remains unclear whether the second layer of bone has any functional advantage. Such information could shed light on the factors that protect against disc degeneration.

METHODS

Six lumbar spines were obtained from human cadavers (32-84 yr) and scanned with magnetic resonance imaging. Cylindrical cores that included the endplate and underlying trabecular bone were harvested from the center of the superior vertebral endplates (6 double- and 12 single-layer endplates) and imaged using micro-computed tomography. The thickness and porosity of the bony endplate layers were measured for each core. High-resolution finite element analysis was performed to assess biomechanical behavior. Glycosaminoglycan content within the adjacent nucleus tissue was quantified using the dimethylmethylene blue technique.

RESULTS

The superficial layer of the double-layer endplates was 50% thinner (P = 0.009) and tended also to be more porous than single-layer endplates. Strains were higher in thinner endplates; however, the second layer of bone in the double-layer endplates had a stiffening effect so that despite being thinner than single-layer endplates, the superficial layer of the double-layer endplates had a similar risk of damage. After adjusting for age, glycosaminoglycan content was significantly higher in the nucleus tissue adjacent to the double-layer endplates (P = 0.01).

CONCLUSION

Compared with single-layer endplates, double-layer endplates seem to permit a more optimal balance between endplate biomechanical and nutritional functions, and may therefore offer a significant protective factor against disc degeneration.

Irradiation does not modify mechanical properties of cancellous bone under compression

BACKGROUND

Gamma radiation sterilization can make cortical bone allograft more brittle, but whether it influences mechanical properties and propensity to form microscopic cracks in structurally intact cancellous bone allograft is unknown.

QUESTIONS/PURPOSES

We therefore determined the effects of gamma radiation sterilization on structurally intact cancellous bone mechanical properties and damage formation in both low- and high-density femoral cancellous bone (volume fraction 9%-44%).

METHODS

We studied 26 cancellous bone cores from the proximal and distal femurs of 10 human female cadavers (49-82 years of age) submitted to a single compressive load beyond yield. Mechanical properties and the formation of microscopic cracks and other tissue damage (identified through fluorochrome staining) were compared between irradiated and control specimens.

RESULTS

We observed no alterations in mechanical properties with gamma radiation sterilization after taking into account variation in specimen porosity. No differences in microscopic tissue damage were observed between the groups.

CONCLUSIONS

Although gamma radiation sterilization influences the mechanical properties and failure processes in cortical bone, it does not appear to influence the performance of cancellous bone under uniaxial loading.

Biomechanical effects of simulated resorption cavities in cancellous bone across a wide range of bone volume fractions

Resorption cavities formed during bone remodeling may act as "stress risers" and impair cancellous bone strength, but biomechanical analyses of the effects of stress risers have been limited. To provide further insight, we assessed the theoretical biomechanical effects of virtually-added resorption cavities in cancellous bone specimens spanning a wide range of bone volume fraction (BV/TV = 0.05-0.36) and across different anatomic sites (hip and spine) and species (human and canine). Micro-CT scans of 40 cubes of cancellous bone were converted into nonlinear finite element models (voxel element size ∼ 20 µm) for strength assessment. In each model, uniform trench-like resorption cavities with nominal dimensions 500 µm (length) × 200 µm (width) × 40 µm (depth), were virtually added either at random locations throughout the specimen, or, preferentially at locations of high tissue-level strain. We found that cancellous bone strength (p < 0.0001) and its relation with BV/TV (p < 0.001) were both altered by the virtual addition of the resorption cavities. When the resorption cavities were added at random locations throughout the specimen, the reduction in strength did not depend on BV/TV or anatomic site or species. When the resorption cavities were instead added preferentially at locations of high tissue-level strain, the effect was accentuated and was greatest in low-BV/TV bone. We conclude that, in theory, uniform-sized resorption cavities can reduce cancellous bone strength over the full range of BV/TV and across species, and the effect is larger if the cavities occur at highly strained locations in low-BV/TV bone.

Shear strength behavior of human trabecular bone

The shear strength of human trabecular bone may influence overall bone strength under fall loading conditions and failure at bone-implant interfaces. Here, we sought to compare shear and compressive yield strengths of human trabecular bone and elucidate the underlying failure mechanisms. We analyzed 54 specimens (5-mm cubes), all aligned with the main trabecular orientation and spanning four anatomic sites, 44 different cadavers, and a wide range of bone volume fraction (0.06-0.38). Micro-CT-based non-linear finite element analysis was used to assess the compressive and shear strengths and the spatial distribution of yielded tissue; the tissue-level constitutive model allowed for kinematic non-linearity and yielding with strength asymmetry. We found that the computed values of both the shear and compressive strengths depended on bone volume fraction via power law relations having an exponent of 1.7 (R(2)=0.95 shear; R(2)=0.97 compression). The ratio of shear to compressive strengths (mean±SD, 0.44±0.16) did not depend on bone volume fraction (p=0.24) but did depend on microarchitecture, most notably the intra-trabecular standard deviation in trabecular spacing (R(2)=0.23, p<0.005). For shear, the main tissue-level failure mode was tensile yield of the obliquely oriented trabeculae. By contrast, for compression, specimens having low bone volume fraction failed primarily by large-deformation-related tensile yield of horizontal trabeculae and those having high bone volume failed primarily by compressive yield of vertical trabeculae. We conclude that human trabecular bone is generally much weaker in shear than compression at the apparent level, reflecting different failure mechanisms at the tissue level.

Mechanical failure begins preferentially near resorption cavities in human vertebral cancellous bone under compression

The amount of bone turnover in the body has been implicated as a factor that can influence fracture risk and bone strength. Here we test the idea that remodeling cavities promote local tissue failure by determining if microscopic tissue damage (microdamage) caused by controlled loading in vitro is more likely to form near resorption cavities. Specimens of human vertebral cancellous bone (L4, 7 male and 2 female, age 70±10, mean±SD) were loaded in compression to the yield point, stained for microscopic tissue damage and submitted to three-dimensional fluorescent imaging using serial milling (image voxel size 0.7×0.7×5.0 μm). We found the resulting damage volume per bone volume (DV/BV) was correlated with percent eroded surface (p<0.01, r(2)=0.65), demonstrating that whole specimen measures of resorption cavities and microdamage are related. Locations of microdamage were more than two times as likely to have a neighboring resorption cavity than randomly selected sites without microdamage (relative risk 2.39, 95% confidence interval of relative risk: 2.09-2.73), indicating a spatial association between resorption cavities and microdamage at the local level. Individual microdamage sites were 48,700 (40,100; 62,700) μm(3) in size (median, 25th and 75th percentiles). That microdamage was associated with resorption cavities when measured at the whole specimen level as well as at the local level provides strong evidence that resorption cavities play a role in mechanical failure processes of cancellous bone and therefore have the potential to influence resistance to clinical fracture.

Mechanisms of initial endplate failure in the human vertebral body

Endplate failure occurs frequently in osteoporotic vertebral fractures and may be related to the development of high tensile strain. To determine whether the highest tensile strains in the vertebra occur in the endplates, and whether such high tensile strains are associated with the material behavior of the intervertebral disc, we used micro-CT-based finite element analysis to assess tissue-level strains in 22 elderly human vertebrae (81.5 ± 9.6 years) that were compressed through simulated intervertebral discs. In each vertebra, we compared the highest tensile and compressive strains across the different compartments: endplates, cortical shell, and trabecular bone. The influence of Poisson-type expansion of the disc on the results was determined by compressing the vertebrae a second time in which we suppressed the Poisson expansion. We found that the highest tensile strains occurred within the endplates whereas the highest compressive strains occurred within the trabecular bone. The ratio of strain to assumed tissue-level yield strain was the highest for the endplates, indicating that the endplates had the greatest risk of initial failure. Suppressing the Poisson expansion of the disc decreased the amount of highly tensile-strained tissue in the endplates by 79.4 ± 11.3%. These results indicate that the endplates are at the greatest risk of initial failure due to the development of high tensile strains, and that such high tensile strains are associated with the Poisson expansion of the disc. We conclude that initial failure of the vertebra is associated with high tensile strains in the endplates, which in turn are influenced by the material behavior of the disc.

Influence of vertical trabeculae on the compressive strength of the human vertebra

Vertebral strength, a key etiologic factor of osteoporotic fracture, may be affected by the relative amount of vertically oriented trabeculae. To better understand this issue, we performed experimental compression testing, high-resolution micro-computed tomography (µCT), and micro-finite-element analysis on 16 elderly human thoracic ninth (T(9)) whole vertebral bodies (ages 77.5 ± 10.1 years). Individual trabeculae segmentation of the µCT images was used to classify the trabeculae by their orientation. We found that the bone volume fraction (BV/TV) of just the vertical trabeculae accounted for substantially more of the observed variation in measured vertebral strength than did the bone volume fraction of all trabeculae (r(2) = 0.83 versus 0.59, p < .005). The bone volume fraction of the oblique or horizontal trabeculae was not associated with vertebral strength. Finite-element analysis indicated that removal of the cortical shell did not appreciably alter these trends; it also revealed that the major load paths occur through parallel columns of vertically oriented bone. Taken together, these findings suggest that variation in vertebral strength across individuals is due primarily to variations in the bone volume fraction of vertical trabeculae. The vertical tissue fraction, a new bone quality parameter that we introduced to reflect these findings, was both a significant predictor of vertebral strength alone (r(2) = 0.81) and after accounting for variations in total bone volume fraction in multiple regression (total R(2) = 0.93). We conclude that the vertical tissue fraction is a potentially powerful microarchitectural determinant of vertebral strength.

Specimen diameter and "side artifacts" in cancellous bone evaluated using end-constrained elastic tension

In cancellous bone testing of cored samples, side artifacts are the underestimation of the true (i.e. in situ) mechanical properties due to the severing of the trabecular network during specimen preparation. Although other researchers have suggested correction factors derived from finite element method (FEM) models, it is proposed that side effects can be minimized by increasing the specimen diameter. Six different diameter specimens (3.1-10.6 mm), from two different anatomic sites (bovine femoral condyle and bovine lumbar vertebrae), were mechanically tested in elastic tension using an epoxy endcap protocol to eliminate end artifacts. Elastic modulus was found to be significantly affected by diameter in both sites. For example, the 5.1 mm samples underestimated the elastic modulus of the 10.6 mm samples by an average of roughly 20%. Yet no statistical difference was detected between the 8.3 and 10.6 mm samples in either anatomic site, suggesting that 8.3 mm diameter specimens were sufficiently large to avoid side artifacts. FEM models created from micro-CT images reveal that modulus approaches an asymptotic value with increasing diameter, and demonstrate an architecture-dependent drop in modulus at decreasing diameters. These results confirm, both experimentally and numerically, that side effects can be ignored given a suitably large specimen diameter and that this minimum diameter will be dependent on the cancellous architecture. An important implication of the latter result is that specimen diameters must be chosen appropriately when comparing test groups with different architectures (e.g. normal versus osteoporotic) to ensure that the magnitude of side artifacts does not confound the true differences between the groups.

Contribution of the intra-specimen variations in tissue mineralization to PTH- and raloxifene-induced changes in stiffness of rat vertebrae

The intra-specimen spatial variation in mineralization of bone tissue can be changed by drug treatments that alter bone remodeling. However, the contribution of such changes to the overall biomechanical effect of a treatment on bone strength is not known. To provide insight into this issue, we used a rat model to determine the effects of ovariectomy, parathyroid hormone, and raloxifene (vs. sham) on the contribution of spatial variations in mineralization to treatment-induced changes in vertebral stiffness. Mineral density was measured from 6-microm voxel-sized quantitative micro-CT scans. Whole-vertebral and trabecular stiffness values were estimated using finite element analysis of these micro-CT scans, first including all intra-specimen variations in mineral density in the model and then excluding such variations by using a specimen-specific average density throughout each specimen. As expected, we found appreciable effects of treatment on overall bone stiffness, the effect being greater for the trabecular compartment (up to 52% reduction vs. sham, p<0.0001) than the whole vertebra (p=0.055). Intra-specimen mean mineralization was not changed with treatment but the intra-specimen variation in mineralization was, although the effect was small (4%). Intra-specimen spatial variations in mineralization accounted for 10-12% and 5-6% of overall stiffness of the trabecular compartment and whole vertebral body, respectively. However, after accounting for all treatment effects on bone geometry and trabecular microstructure, any treatment effects due to changes in mineralization were negligible (<2%), although statistically detectable (p<0.02). We conclude that, despite a role in the general biomechanical behavior of bone, the spatial variations in tissue mineralization, as measured by quantitative micro-CT, did not appreciably contribute to ovariectomy-, PTH-, or raloxifene-induced changes in stiffness of the whole bone or the trabecular compartment in these rat vertebrae.

Valid micro finite element models of vertebral trabecular bone can be obtained using tissue properties measured with nanoindentation under wet conditions

Osteoporosis-related vertebral fractures represent a major public health problem. Anatomy-specific CT-based finite element (FE) simulations could help in identifying which vertebrae have the highest risk of fracture and thus help to decide upon the need for vertebroplasty or other surgical intervention. Continuum level FE simulations require effective macroscopic material properties of the vertebra. Micro finite element (microFE) models can be used to circumvent the difficult experiments that are necessary to determine these effective properties. From a quantitative point of view, these microFE models depend critically on the chosen trabecular tissue properties. The question remains whether linear elastic microFE models of vertebral trabecular bone with and without specimen-specific tissue properties yield similar results as non-destructive macroscopic experiments under moist conditions. microFE models were set up from microCT scans with specimen-specific or average tissue moduli measured by nanoindentation under dry and wet testing conditions. Non-destructive macroscopic mechanical compression, tension and torsion tests were performed. Experimentally obtained and simulated apparent stiffnesses were compared. No significant difference was found when comparing microFE simulations with wet tissue properties and experiments for tension, compression and torsion (p>0.05). Concordance correlation coefficients were high for tension and compression (r(c)(wet)>or=0.96,p<0.05) but moderate for torsion (r(c)(wet)=0.81,p<0.05). The agreement between simulation and experiment was confirmed by Bland-Altman plots which showed mean differences <or=10MPa. Surprisingly, the agreement between simulation and experiment was not reduced by using an average tissue modulus. The results indicate that valid microFE models can be set up using average tissue properties obtained under wet indentation conditions.