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.
Intrinsic flexibility of protein molecules enables them to change their 3D structure and perform their specific task. Therefore, identifying rigid regions and consequently flexible regions of proteins has a significant role in studying protein molecules' function. In this study, we developed a kinematic model of protein molecules considering all covalent and hydrogen bonds in protein structure. Then, we used this model and developed two independent rigidity analysis methods to calculate degrees of freedom (DOF) and identify flexible and rigid regions of the proteins. The first method searches for closed loops inside the protein structure and uses Grübler–Kutzbach (GK) criterion. The second method is based on a modified 3D pebble game. Both methods are implemented in a matlab program and the step by step algorithms for both are discussed. We applied both methods on simple 3D structures to verify the methods. Also, we applied them on several protein molecules. The results show that both methods are calculating the same DOF and rigid and flexible regions. The main difference between two methods is the run time. It's shown that the first method (GK approach) is slower than the second method. The second method takes 0.29 s per amino acid versus 0.83 s for the first method to perform this rigidity analysis.
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.
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