Assessment of the effect of reduced compositional heterogeneity on fracture resistance of human cortical bone using finite element modeling

The recent reports of atypical femoral fracture (AFF) and its possible association with prolonged bisphosphonate (BP) use highlighted the importance of a thorough understanding of mechanical modifications in bone due to bisphosphonate treatment. The reduced compositional heterogeneity is one of the modifications in bone due to extensive suppression of bone turnover. Although experimental evaluations suggested that compositional changes lead to a reduction in the heterogeneity of elastic properties, there is limited information on the extent of influence of reduced heterogeneity on fracture resistance of cortical bone. As a result, the goal of the current study is to evaluate the influence of varying the number of unique elastic and fracture properties for osteons, interstitial bone, and cement lines on fracture resistance across seven different human cortical bone specimens using finite element modeling. Fracture resistance of seven human cortical bone samples under homogeneous and three different heterogeneous material levels was evaluated using a compact tension test setup. The simulation results predicted that the crack volume was the highest for the models with homogeneous material properties. Increasing heterogeneity resulted in a lower amount of crack volume indicating an increase in fracture resistance of cortical bone. This reduction was observed up to a certain level of heterogeneity after which further beneficial effects of heterogeneity diminished suggesting a possible optimum level of heterogeneity for the bone tissue. The homogeneous models demonstrated limited areas of damage with extensive crack formation. On the other hand, the heterogeneity in the material properties led to increased damage volume and a more variable distribution of damage compared to the homogeneous models. This resulted in uncracked regions which tended to have less damage accumulation preventing extensive crack propagation. The results also showed that the percent osteonal area was inversely correlated with crack volume and more evenly distributed osteons led to a lower amount of crack growth for all levels of material heterogeneity. In summary, this study developed a new computational modeling approach that directly evaluated the influence of heterogeneity in elastic and fracture material properties on fracture resistance of cortical bone. The results established new information that showed the adverse effects of reduced heterogeneity on fracture resistance in cortical bone and demonstrated the nonlinear relationship between heterogeneity and fracture resistance. This new computational modeling approach provides a tool that can be used to improve the understanding of the effects of material level changes due to prolonged BP use on the overall bone fracture behavior. It may also bring additional insight into the causes of unusual fractures, such as AFF and their possible association with long term BP use.

Contribution of extrafibrillar matrix to the mechanical behavior of bone using a novel cohesive finite element model

The mechanical behavior of bone is determined at all hierarchical levels, including lamellae (the basic building block of bone) that are comprised of mineralized collagen fibrils and extrafibrillar matrix. The mechanical behavior of mineralized collagen fibrils has been investigated intensively using both experimental and computational approaches. Yet, the contribution of the extrafibrillar matrix to bone mechanical properties is poorly documented. In this study, we intended to address this issue using a novel cohesive finite element (FE) model, in conjunction with the experimental observations reported in the literature. In the FE model, the extrafibrillar matrix was considered as a nanocomposite of hydroxyapatite (HA) crystals bounded through a thin organic interface modeled as a cohesive interfacial zone. The parameters required by the cohesive FE model were defined based on the experimental data reported in the literature. This hybrid nanocomposite model was tested in two loading modes (i.e. tension and compression) and under two hydration conditions (i.e. wet and dry). The simulation results indicated that (1) the failure modes of the extrafibrillar matrix predicted using the cohesive FE model were closely coincided with those experimentally observed in tension and compression tests; (2) the pre-yield deformation (i.e. internal strain) of HA crystals with respect to the applied strain was consistent with that obtained from the synchrotron X-ray scattering measurements irrespective of the loading modes and hydration status; and (3) the mechanical behavior of the extrafibrillar matrix was dictated by the properties of the organic interface between the HA crystals. Taken together, we postulate that the extrafibrillar matrix plays a major role in the pre-yield deformation and the failure mode of bone, thus, giving rise to important insights in the ultrastructural origins of bone fragility.

Computational investigation of ultrastructural behavior of bone using a cohesive finite element approach

Bone ultrastructure at sub-lamellar length scale is a key structural unit in bone that bridges nano- and microscale hierarchies of the tissue. Despite its influence on bulk response of bone, the mechanical behavior of bone at ultrastructural level remains poorly understood. To fill this gap, in this study, a two-dimensional cohesive finite element model of bone at sub-lamellar level was proposed and analyzed under tensile and compressive loading conditions. In the model, ultrastructural bone was considered as a composite of mineralized collagen fibrils (MCFs) embedded in an extrafibrillar matrix (EFM) that is comprised of hydroxyapatite (HA) polycrystals bounded via thin organic interfaces of non-collagenous proteins (NCPs). The simulation results indicated that in compression, EFM dictated the pre-yield deformation of the model, then damage was initiated via relative sliding of HA polycrystals along the organic interfaces, and finally shear bands were formed followed by delamination between MCF and EFM and local buckling of MCF. In tension, EFM carried the most of load in pre-yield deformation, and then an array of opening-mode nano-cracks began to form within EFM after yielding, thus gradually transferring the load to MCF until failure, which acted as crack bridging filament. The failure modes, stress-strain curves, and in situ mineral strain of ultrastructural bone predicted by the model were in good agreement with the experimental observations reported in the literature, thus suggesting that this model can provide new insights into sub-microscale mechanical behavior of bone.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics

PURPOSE OF REVIEW

The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale.

RECENT FINDINGS

Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

Material heterogeneity, microstructure, and microcracks demonstrate differential influence on crack initiation and propagation in cortical bone

The recent studies have shown that long-term bisphosphonate use may result in a number of mechanical alterations in the bone tissue including a reduction in compositional heterogeneity and an increase in microcrack density. There are limited number of experimental and computational studies in the literature that evaluated how these modifications affect crack initiation and propagation in cortical bone. Therefore, in this study, the entire crack growth process including initiation and propagation was simulated at the microscale by using the cohesive extended finite element method. Models with homogeneous and heterogeneous material properties (represented at the microscale capturing the variability in material property values and their distribution) as well as different microcrack density and microstructure were compared. The results showed that initiation fracture resistance was higher in models with homogeneous material properties compared to heterogeneous ones, whereas an opposite trend was observed in propagation fracture resistance. The increase in material heterogeneity level up to 10 different material property sets increased the propagation fracture resistance beyond which a decrease was observed while still remaining higher than the homogeneous material distribution. The simulation results also showed that the total osteonal area influenced crack propagation and the local osteonal area near the initial crack affected the crack initiation behavior. In addition, the initiation fracture resistance was higher in models representing bisphosphonate treated bone (low material heterogeneity, high microcrack density) compared to untreated bone models (high material heterogeneity, low microcrack density), whereas an opposite trend was observed at later stages of crack growth. In summary, the results demonstrated that tissue material heterogeneity, microstructure, and microcrack density influenced crack initiation and propagation differently. The findings also elucidate how possible modifications in material heterogeneity and microcrack density due to bisphosphonate treatment may influence the initiation and propagation fracture resistance of cortical bone.

Structural role of osteocyte lacunae on mechanical properties of bone matrix: A cohesive finite element study

Despite the extensive studies on biological function of osteocytes, there are limited studies that evaluated the structural role of osteocyte lacunae on local mechanical properties of the bone matrix. As a result, the goal of this study was to elucidate the independent contribution of osteocyte lacunae structure on mechanical properties and fracture behavior of the bone matrix uncoupled from its biological effects and bone tissue composition variation. This study combined cohesive finite element modeling with experimental data from a lactation rat model to evaluate the influence of osteocyte lacunar area porosity, density, size, axis ratio, and orientation on the elastic modulus, ultimate strength, and ultimate strain of the bone matrix as well as on local crack formation and propagation. It also performed a parametric study to isolate the influence of a single osteocyte lacunae structural property on the mechanical properties of the bone matrix. The experimental measurements demonstrated statistically significant differences in lacunar size between ovariectomized rats with lactation history and virgin groups (both ovariectomized and intact) and in axis ratio between rats with lactation history and virgins. There were no differences in mechanical properties between virgin and lactation groups as determined by the finite element simulations. However, there were statistically significant linear relationships between the physiological range of osteocyte lacunar area porosity, density, size, and orientation and the elastic modulus and ultimate strength of the bone matrix in virgin and lactation rats. The parametric study also revealed similar but stronger relationships between elastic modulus and ultimate strength and lacunar density, size, and orientation. The simulations also demonstrated that the osteocyte lacunae guided the crack propagation through local stress concentrations. In summary, this study enhanced the limited knowledge on the structural role of osteocyte lacunae on local mechanical properties of the bone matrix. These data are important in gaining a better understanding of the mechanical implications of the local modifications due to osteocytes in the bone matrix.