Trabecular Bone Failure Research Articles

Failure of trabecular bone: XFEM modelling of multiple crack growth

Trabecular bone plays an important role in structural integrity of bone tissues. Its complex microstructure characterised by high porosity and intricate composition with multiple trabeculae is a challenge for analysis of fracture initiation and propagation in it. This work investigates mechanical behaviour and failure of representative volume elements (RVEs) of porous structure of trabecular bone using numerical simulations. The extended finite-element method (XFEM) is used together with an original algorithm for the growth of multiple cracks in individual trabeculae of the structure. The obtained results are presented in comparison with the model of degradation of elastic properties. The effect of morphology on accumulation of damage and crack growth - both on the scale of a RVE and in individual ligaments - was investigated using the developed approach for estimation of a relative crack-surface area. The results are presented for five RVEs, obtained with high-resolution computed tomography of human trabecular bone, subjected to applied tensile and compressive loads.

Finite Element Evaluation of the Femoral Neck System as Prophylactic Fixation to Prevent Contralateral Hip Fractures.

Hip fractures cause significant morbidity and mortality for geriatric patients, and incidence is increasing as the population ages. Following a primary hip fracture, up to 20% may suffer a contralateral hip fracture within 5years despite fracture risk reduction measures, including fall prevention and osteoporosis pharmacologic treatment. The aim of this study is to assess whether insertion of the Femoral Neck System (Depuy Synthes, West Chester, PA) into the contralateral proximal femur may strengthen the bone and decrease the incidence of contralateral hip fractures. ScanIP, an image processing software was used to produce 3-dimensional models of a cadaver femur with the implanted device. Models were meshed and exported to Abaqus for finite element analysis to evaluate the device's ability to reduce stress in the proximal femur. Results were analyzed for element-wise volume and von-Mises stresses. The implant reduced peak stress and bone failure at all levels of bone quality. Specifically in osteoporotic bone, the implant decreased peak stress by 27%, proximal femur trabecular bone failure by 5% and cortical bone failure by 100% in the femoral neck. Our results from computer generated finite element analyses indicate that the Femoral Neck System may strengthen an osteoporotic proximal femur in the event of a lateral fall. Further investigation with expanded finite element analysis and cadaveric biomechanical studies are needed to validate these results.

Effect of osteoporosis-related reduction in the mechanical properties of bone on the acetabular fracture during a sideways fall: A parametric finite element approach.

The incidence of acetabular fractures due to low-energy falls is increasing among the geriatric population. Studies have shown that several biomechanical factors such as body configuration, impact velocity, and trochanteric soft-tissue thickness contribute to the severity and type of acetabular fracture. The effect of reduction in apparent density and elastic modulus of bone as well as other bone mechanical properties due to osteoporosis on low-energy acetabular fractures has not been investigated. The current comprehensive finite element study aimed to study the effect of reduction in bone mechanical properties (trabecular, cortical, and trabecular + cortical) on the risk and type of acetabular fracture. Also, the effect of reduction in the mechanical properties of bone on the load-transferring mechanism within the pelvic girdle was examined. We observed that while the reduction in the mechanical properties of trabecular bone considerably affects the severity and area of trabecular bone failure, reduction in mechanical properties of cortical bone moderately influences both cortical and trabecular bone failure. The results also indicated that by reducing bone mechanical properties, the type of acetabular fracture turns from elementary to associated, which requires a more extensive intervention and rehabilitation period. Finally, we observed that the cortical bone plays a substantial role in load transfer, and by increasing reduction in the mechanical properties of cortical bone, a greater share of load is transmitted toward the pubic symphysis. This study increases our understanding of the effect of osteoporosis progression on the incidence of low-energy acetabular fractures. The osteoporosis-related reduction in the mechanical properties of cortical bone appears to affect both the cortical and trabecular bones. Also, during the extreme reduction in the mechanical properties of bone, the acetabular fracture type will be more complicated. Finally, during the final stages of osteoporosis (high reduction in mechanical properties of bone) a smaller share of impact load is transferred by impact-side hemipelvis to the sacrum, therefore, an osteoporotic pelvis might mitigate the risk of sacral fracture.

Ratcheting-fatigue behavior of trabecular bone under cyclic tensile-compressive loading

This study aims to investigate the ratcheting-fatigue behaviors of trabecular bone under cyclic tension-compression, which are produced due to the accumulations of residual strain in trabecular bone. Simultaneously, the effects of different loading conditions on ratcheting behaviors of trabecular bone were probed. It is found that the gap between ratcheting strains under three stress amplitudes will gradually widen. As the stress amplitude increases, the ratcheting strain also increases. Mean stress has a significant effect on the ratcheting strain. When the mean stress is 0 MPa and 0.155 MPa, the ratcheting strain increases with the number of cycles. However, when the mean stress is -0.155 MPa, the ratcheting strain decreases as the cycle goes on. The existence of double stress peak holding time causes the creep deformation of trabecular bone, which leads to the increase of ratcheting strain. It is also noted that the ratcheting strain is greatly increased with prolongation of stress peak holding time. The digital image correlation (DIC) technique was applied to analyze the fatigue failure of trabecular bone under cyclic tension-compression. It is found that the increase of stress amplitude accelerates the damage of sample and further reduces its fatigue life. Cracks are observed in trabecular bone sample, and it is noted that the crack propagation is rapid during cyclic loading.

The Multi-Axial Failure Response of Porcine Trabecular Skull Bone Estimated Using Microstructural Simulations.

The development of a multi-axial failure criterion for trabecular skull bone has many clinical and biological implications. This failure criterion would allow for modeling of bone under daily loading scenarios that typically are multi-axial in nature. Some yield criteria have been developed to evaluate the failure of trabecular bone, but there is a little consensus among them. To help gain deeper understanding of multi-axial failure response of trabecular skull bone, we developed 30 microstructural finite element models of porous porcine skull bone and subjected them to multi-axial displacement loading simulations that spanned three-dimensional (3D) stress and strain space. High-resolution microcomputed tomography (microCT) scans of porcine trabecular bone were obtained and used to develop the meshes used for finite element simulations. In total, 376 unique multi-axial loading cases were simulated for each of the 30 microstructure models. Then, results from the total of 11,280 simulations (approximately 135,360 central processing unit-hours) were used to develop a mathematical expression, which describes the average three-dimensional yield surface in strain space. Our results indicate that the yield strain of porcine trabecular bone under multi-axial loading is nearly isotropic and despite a spread of yielding points between the 30 different microstructures, no significant relationship between the yield strain and bone volume fraction is observed. The proposed yield equation has simple format and it can be implemented into a macroscopic model for the prediction of failure of whole bones.

Comparison of the Lag Screw Placements for the Treatment of Stable and Unstable Intertrochanteric Femoral Fractures regarding Trabecular Bone Failure.

Background. In this study, the cut-out risk of Dynamic Hip Screw (DHS) was investigated in nine different positions of the lag screw for two fracture types by using Finite Element Analysis (FEA). Methods. Two types of fractures (31-A1.1 and A2.1 in AO classification) were generated in the femur model obtained from Computerized Tomography images. The DHS model was placed into the fractured femur model in nine different positions. Tip-Apex Distances were measured using SolidWorks. In FEA, the force applied to the femoral head was determined according to the maximum value being observed during walking. Results. The highest volume percentage exceeding the yield strength of trabecular bone was obtained in posterior-inferior region in both fracture types. The best placement region for the lag screw was found in the middle of both fracture types. There are compatible results between Tip-Apex Distances and the cut-out risk except for posterior-superior and superior region of 31-A2.1 fracture type. Conclusion. The position of the lag screw affects the risk of cut-out significantly. Also, Tip-Apex Distance is a good predictor of the cut-out risk. All in all, we can supposedly say that the density distribution of the trabecular bone is a more efficient factor compared to the positions of lag screw in the cut-out risk.

Limitations of Global Morphometry in Predicting Trabecular Bone Failure

Efforts in finding independent measures for accurate and reliable prediction of trabecular bone failure have led to the development of a number of morphometric indices characterizing trabecular bone microstructure. Generally, these indices assume a high homogeneity within the bone specimen. However, in the present study we found that the variance in bone volume fraction (BV/TV) in a single bone specimen can be relatively large (CV = 9.07% to 28.23%). To assess the limitations of morphometric indices in the prediction of bone failure for specimens in which the assumption of homogeneity is not met, we harvested 13 cadaveric samples from a single human spine. We tested these cylindrical samples using image-guided failure assessment (IGFA), a technique combining stepwise microcompression and time-lapsed micro-computed tomography (µCT). Additionally, we computed morphometric indices for the entire sample as well as for 10 equal subregions along the anatomical axis. We found that ultimate strength was equally well predicted by BV/TV of the entire sample (R(2) = 0.55) and BV/TV of the weakest subregion (R(2) = 0.57). Investigating three-dimensional animations of structural bone failure, we showed that two main failure mechanisms determine the competence of trabecular bone samples; in homogeneous, isotropic trabecular bone samples, competence is determined by a whole set of trabecular elements, whereas in inhomogeneous, anisotropic bone samples a single or a missing trabeculae may induce catastrophic failure. The latter failure mechanism cannot be described by conventional morphometry, indicating the need for novel morphometric indices also applicable to the prediction of failure in inhomogeneous bone samples.

Time-lapsed imaging of implant fixation failure in human femoral heads

The failure mechanisms of bone–implant constructs are still incompletely understood, because the role of the peri-implant bone in implant stability is unclear. We hypothesized that implant fixation failure is preceded by substantial peri-implant bone failure. A new device was developed that combines mechanical testing of large bone–implant constructs with high-resolution peripheral quantitative computed tomography, following the principles of image-guided failure assessment (IGFA). In this study, we investigated the push-in failure behavior of dynamic hip screws (DHS) implanted in human cadaveric femoral heads. For the first time the fixation failure of a clinically used implant in human trabecular bone could be experimentally visualized at the microstructural level. The ultimate force was highly correlated with the peri-implant bone volume fraction (R2=0.85). We demonstrated that primary fixation failure of DHS implants was accompanied by trabecular bone failure in the immediate peri-implant bone region only. Such experimental data are crucial to enhance the understanding on the quality of the bone–implant interface and of the trabecular bone in the process of implant fixation failure. We believe that this newly developed device will be beneficial for the development of new implant designs, especially for use in osteoporotic bone.

Experimental poromechanics of trabecular bone strength: Role of Terzaghi's effective stress and of tissue level stress fluctuations

In the 1920s and 1930s, Terzaghi and coworkers realized that the failure of various porous geomaterials under internal pore pressure is given through evaluating the failure function for the same materials at zero pressure, with ‘total stress plus pore pressure’ instead of ‘total stress alone’ as argument. As to check, probably for the first time, the relevance of this (‘Terzaghi's’) failure criterion for trabecular bone, a series of poromechanical and ultrasonic tests was conducted on bovine and human trabecular bone samples. Evaluation of respective experimental results within the theoretical framework of microporomechanics showed that (i) Terzaghi's effective stress indeed governs trabecular bone failure, (ii) deviatoric stress states at the level of the solid bone matrix (also called tissue level) are primary candidates for initiating bone failure, and (iii) the high heterogeneity of these deviatoric tissue stresses, which increases with increasing intertrabecular porosity, governs the overall failure of trabecular bone. Result (i) lets us use the widely documented experimental results for strength values of bone samples without pore pressure, as to predict failure of the same bone samples under internal pore pressure. Result (ii) suggests a favorable mode for strength modeling of solid bone matrix. Finally, result (iii) underlines the suitability of microfinite element simulations for trabecular bone microstructures.

Insights into the effects of tensile and compressive loadings on microstructure dependent fracture of trabecular bone

The micro-scale finite element models used in the past to understand yielding failure of trabecular bone have not addressed the microcrack formation and its effect on microstructure dependent fracture. An understanding of microcrack based failure mechanisms can be important to develop insights into response of trabecular bone to external loading before final failure. With this goal, we analyze tensile and compressive fracture failure at two different ages in two trabecular bone micrographs obtained from an ovine femur using a recently developed cohesive finite element method (CFEM) framework. The results and analyses indicate that examined trabecular microstructures are optimally designed for resisting compressive loading. Under tensile loading, initial damage in a microstructure is localized in a single random trabecula. Final microstructure failure occurs immediately after the failure of the trabecula. However, under compressive loading, failure of the first trabecula does not precede immediate complete failure of microstructure. Under compression the propagation fracture toughness (characterized by change in energy release rate as a function of crack density) increases with increase in crack density. However, under tension the propagation fracture toughness decreases with increasing crack density. The fracture mechanism remains unaffected by age variation. Effect of tissue property random variation on the variation in fracture strength diminishes under tension and increases under compression with increase in the age. Overall, results indicate that structural arrangement of the trabecular bone (besides the hierarchical chemical composition) can be an important contributor to its unique fracture resistance properties.

Effects of Loading Orientation on the Morphology of the Predicted Yielded Regions in Trabecular Bone

While the effects of bone mineral density and architecture in osteoporotic bone have been studied extensively, the micromechanics of yielding and failure have received less attention. However, understanding architectural features associated with failure should provide insight into assessing bone quality. In this study, microstructural finite element models were used to compute regions of tissue level yielding in ten bovine tibial trabecular bone samples. The morphology, number, and mean volume of the yielded regions were quantified for four apparent strains under two loading conditions. For on-axis loading, the mean aspect ratio of the tissue that yielded due to compressive strain increased with increasing apparent strain, expanding along the principal trabecular orientation. This suggests that tissue level yielding progresses along vertical trabeculae when a specimen is loaded on-axis. The number, but not the volume, of the regions yielded due to tensile strain increased with increasing applied load, consistent with relaxation and redistribution of stresses around the yielded regions. When the specimens were compressed perpendicular to the principal axis, the aspect ratio of the yielded regions was close to one, while the number, mean volume, and mean thickness of the yielded regions increased. This indicates that localized high strains consistent with bending rather than axial deformation of struts occur at the tissue level. Overall, the results provide new insight into trabecular bone failure, which is relevant to assessing diagnostic tests for fracture risk or evaluating osteoporosis treatments.

Comparison of different plasticity criteria for trabecular bone failure modelling

AbstractDifferent plasticity criteria applied to failure analysis of trabecular bone are compared. A cylindrical sample of bovine trabecular bone is mechanically tested in uniaxial compression/tension with 2% applied strain. Obtained response in compared to responses obtained using finite element model of trabecular bone inner structure subjected to the same loading conditions. FE model is reconstructed from micro–CT images. Elastic material properties at the level of trabecula are determined using nanoindentation. Compared plasticity criteria are based on these elastic material properties, i.e. on Young's modulus of elasticity from nanoindentation. The objective of the paper is to demonstrate the importance to reflect the anisotropic plasticity and to evaluate variation in obtained response when the anisotropy is neglected. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Micro-finite element simulation of trabecular-bone post-yield behaviour – effects of material model, element size and type

Micro-finite element (micro-FE) analysis became a standard tool for the evaluation of trabecular bone mechanical properties. The accuracy of micro-FE models for linear analyses is well established. However, the accuracy of recently developed nonlinear micro-FE models for simulations of trabecular bone failure is not known. In this study, a trabecular bone specimen was compressed beyond the apparent yield point. The experiment was simulated using different micro-FE meshes with different element sizes and types, and material models based on cortical bone. The results from the simulations were compared with experimental results to study the effects of the different element and material models. It was found that a decrease in element size from 80 to 40 μm had little effect on predicted post-yield behaviour. Element type and material model had significant effects. Nevertheless, none of the established material models for cortical bone were able to predict the typical descent in the load-displacement curve seen during compression of trabecular bone.

Towards understanding of trabecular bone failure by deformation localisation

Towards understanding of trabecular bone failure by deformation localisation

Modeling the onset and propagation of trabecular bone microdamage during low-cycle fatigue

Relatively small amounts of microdamage have been suggested to have a major effect on the mechanical properties of bone. A significant reduction in mechanical properties (e.g. modulus) can occur even before the appearance of microcracks. This study uses a novel non-linear microdamaging finite-element (FE) algorithm to simulate the low-cycle fatigue behavior of high-density trabecular bone. We aimed to investigate if diffuse microdamage accumulation and concomitant modulus reduction, without the need for complete trabecular strut fracture, may be an underlining mechanism for low-cycle fatigue failure (defined as a 30% reduction in apparent modulus). A μCT constructed FE model was subjected to a single cycle monotonic compression test, and constant and variable amplitude loading scenarios to study the initiation and accumulation of low-cycle fatigue microdamage. Microcrack initiation was simulated using four damage criteria: 30%, 40%, 50% and 60% reduction in bone element modulus (el-MR). Evaluation of structural (apparent) damage using the four different tissue level damage criteria resulted in specimen fatigue failure at 72, 316, 969 and 1518 cycles for the 30%, 40%, 50% and 60% el-MR models, respectively. Simulations based on the 50% el-MR model were consistent with previously published experimental findings. A strong, significant non-linear, power law relationship was found between cycles to failure ( N) and effective strain (Δ σ/ E 0): N=1.394×10 −25(Δ σ/ E 0) −12.17, r 2=0.97, p<0.0001. The results suggest that microdamage and microcrack propagation, without the need for complete trabecular strut fracture, are mechanisms for high-density trabecular bone failure. Furthermore, the model is consistent with previous numerical fatigue simulations indicating that microdamage to a small number of trabeculae results in relatively large specimen modulus reductions and rapid failure.

Damage and failure of trabecular bone with non-linear geometry and inhomogeneous material properties

Damage and failure of trabecular bone with non-linear geometry and inhomogeneous material properties

Interbody Device Shape and Size Are Important to Strengthen the Vertebra–Implant Interface

An in vitro cadaveric study to compare compressive failure load, strength, and stiffness of the implant-vertebra interface. To determine the effect of cage shape (kidney, cloverleaf, or oval) and cage surface area on endplate failure strength and secondly to determine the extent and pattern of trabecular failure adjacent to an interbody device. Recent studies indicate that the posterolateral and peripheral regions of the endplate are stronger than the central. Current implants are not designed to take advantage of these stronger regions of the endplate. The zone of trabecular failure that results from interbody device subsidence has not been reported extensively in the literature. Uniaxial compression testing with unrestricted rotation was carried out on the superior endplates of 48 thoracolumbar (T9-L2) vertebrae with 1 of 3 shaped indentors covering 20% or 40% of the endplate area. Failure load, failure strength, and stiffness were compared. Quantitative computed tomography scans were carried out before and following indentation tests to identify areas of trabecular densification that indicate localized failure. The cloverleaf-shaped indentors resulted in significantly higher (P < 0.001) failure loads (by >45%), strength (>49%), and construct stiffness (>35%) for both the 20% and 40% cross-sectional area sizes. Trabecular bone failure occurred in a semielliptical zone underlying the interbody devices, leaving the endplate and underlying cancellous bone intact. The cloverleaf-shaped indentor displayed an improved strength and stiffness profile when compared to oval or kidney-shaped indentors of similar surface areas.

The Modified Super-Ellipsoid Yield Criterion for Human Trabecular Bone

Despite the importance of multiaxial failure of trabecular bone in many biomechanical applications, to date no complete multiaxial failure criterion for human trabecular bone has been developed. By using experimentally validated nonlinear high-resolution, micromechanical finite-element models as a surrogate for multiaxial loading experiments, we determined the three-dimensional normal strain yield surface and all combinations of the two-dimensional normal-shear strain yield envelope. High-resolution finite-element models of three human femoral neck trabecular bone specimens obtained through microcomputed tomography were used. In total, 889 multiaxial-loading cases were analyzed, requiring over 41,000 CPU hours on parallel supercomputers. Our results indicated that the multiaxial yield behavior of trabecular bone in strain space was homogeneous across the specimens and nearly isotropic. Analysis of stress-strain curves along each axis in the 3-D normal strain space indicated uncoupled yield behavior whereas substantial coupling was seen for normal-shear loading. A modified super-ellipsoid surface with only four parameters fit the normal strain yield data very well with an arithmetic error +/-SD less than -0.04 +/- 5.1%. Furthermore, the principal strains associated with normal-shear loading showed excellent agreement with the yield surface obtained for normal strain loading (arithmetic error +/- SD < 2.5 +/- 6.5%). We conclude that the four-parameter "Modified Super-Ellipsoid" yield surface presented here describes the multiaxial failure behavior of human femoral neck trabecular bone very well.

Failure of trabecular bone with simulated lytic defects can be predicted non-invasively by structural analysis

Pathologic fracture is a significant risk for patients afflicted with metastatic or benign skeletal tumors. The quandary for physicians who treat these patients is that after making the diagnosis they must try to predict the load bearing capacity of the involved bone and the fracture risk from images seen in radiological examinations. Since bone fails at a relatively constant strain independent of density we demonstrate that using a mechanics of materials approach that the cross-sectional structural properties of the bone most affected by the lytic defect governs the load bearing capacity of the entire bone. Homogeneous cylindrical cores of trabecular bone were harvested from the vertebral bodies of whale spines, and prepared with circular or slotted through-hole defects of varying sizes to simulate lytic skeletal tumors. Each specimen was imaged using quantitative computed tomography (CT), dual energy X-ray absorptiometry (DXA), and magnetic resonance imaging (MRI) to obtain data for calculating cross-sectional structural properties: axial, flexural, and torsional rigidity. The specimens were then divided into groups uniformly distributed with respect to defect sizes and shapes, and subjected to uniaxial tension, four-point bending or torsion until failure. A strong positive relationship was found between measured tensile yield loads, bending, and torsional yield moments vs. axial, flexural and torsional structural rigidities respectively, calculated from QCT, DXA, and MRI data [QCT: tension r2 = 0.951, bending r2 = 0.909, torsion r2 = 0.914 (p < 0.001); DXA: tension r2 = 0.926, bending r2 = 0.841, torsion r2 = 0.916 (p < 0.001), MRI: tension r2 = 0.916; bending r2 = 0.856, torsion r2 = 0.852 (p < 0.001)]. For cylindrical cores of trabecular bone with simulated lytic defects, the load bearing capacity of the entire core was directly proportional to the axial, bending, or torsional rigidity at the weakest cross-section through the core containing the defect. Therefore structural rigidity analysis of cross-sectional geometric data measured non-invasively by QCT, DXA, and MRI of bones containing lytic defects may be used to predict the load bearing capacity of the involved bone and the relative fracture risk in vivo. © 2003 Orthopaedic Research Society. Published by Elsevier Ltd. All rights reserved.

Failure of trabecular bone with simulated lytic defects can be predicted non-invasively by structural analysis

Pathologic fracture is a significant risk for patients afflicted with metastatic or benign skeletal tumors. The quandary for physicians who treat these patients is that after making the diagnosis they must try to predict the load bearing capacity of the involved bone and the fracture risk from images seen in radiological examinations. Since bone fails at a relatively constant strain independent of density we demonstrate that using a mechanics of materials approach that the cross-sectional structural properties of the bone most affected by the lytic defect governs the load bearing capacity of the entire bone. Homogeneous cylindrical cores of trabecular bone were harvested from the vertebral bodies of whale spines, and prepared with circular or slotted through-hole defects of varying sizes to simulate lytic skeletal tumors. Each specimen was imaged using quantitative computed tomography (CT), dual energy X-ray absorptiometry (DXA), and magnetic resonance imaging (MRI) to obtain data for calculating cross-sectional structural properties: axial, flexural, and torsional rigidity. The specimens were then divided into groups uniformly distributed with respect to defect sizes and shapes, and subjected to uniaxial tension, four-point bending or torsion until failure. A strong positive relationship was found between measured tensile yield loads, bending, and torsional yield moments vs. axial, flexural and torsional structural rigidities respectively, calculated from QCT, DXA, and MRI data [QCT: tension r 2=0.951, bending r 2=0.909, torsion r 2=0.914 ( p<0.001); DXA: tension r 2=0.926, bending r 2=0.841, torsion r 2=0.916 ( p<0.001); MRI: tension r 2=0.916; bending r 2=0.856, torsion r 2=0.852 ( p<0.001)]. For cylindrical cores of trabecular bone with simulated lytic defects, the load bearing capacity of the entire core was directly proportional to the axial, bending, or torsional rigidity at the weakest cross-section through the core containing the defect. Therefore structural rigidity analysis of cross-sectional geometric data measured non-invasively by QCT, DXA, and MRI of bones containing lytic defects may be used to predict the load bearing capacity of the involved bone and the relative fracture risk in vivo.