Orientation effect and locational variation in elastic-plastic compressive properties of bovine cortical bone

Bone is a highly heterogeneous and anisotropic material with a hierarchical structure. The effect of diaphysis locations and directions of loading on elastic-plastic compressive properties of bovine femoral cortical bone was examined in this study. The impact of location and loading directions on elastic-plastic compressive properties of cortical bone was found to be statistically insignificant in this study. The variances of most of the compressive properties were also observed to be location and directionality independent except for the locational differences in modulus of resilience (distal to central for longitudinal loading) and plastic work (central to distal for transverse loading) as well as differences in variances of the modulus of resilience and elastic modulus values for two directions of loading. The micro-mechanisms of cortical bone failure for longitudinal and transverse directions of loading were considered to be responsible for the difference in variances in the later properties values as well as for the maximum and minimum coefficient of variation (CV) obtained for compressive properties in two directions of loading. The representative cubical volume at the tested hierarchical level contained all unique microstructural features of the plexiform bone and therefore produced the homogeneous and isotropic elastic-plastic compressive properties of cortical bone. It is expected that the outcome of this study may be helpful in the area of bone tissue engineering and finite element simulation of cortical bone.

Relationship between the microstructural energy release rate of cortical bone and age under compression condition

Most studies evaluated the energy release rate of cortical bone macrostructure under Mode I, Mode II, and mixed Mode I-II loading conditions. However, testing the macrostructural energy release rate requires an initial crack and recording the applied load and the corresponding crack length in real-time, which may introduce measurement errors and differences with the actual fracture scenarios. To further understand how the energy release rate contributed to the cortical bone fracture characteristics, this study predicted the microstructural energy release rate of cortical bone and then investigated its age-related varitions. The microstructural energy release rate of femoral cortical bone in rats from different ages was back-calculated by fitting the experimental and simulated load-displacement curves under compression load. The trends in the microstructural energy release rate were revealed, and the underlying reasons for the age-related changes were investigated by integrating the discussion on the cortical bone mechanical parameters at various levels obtained from the previous experiment. The predicted microstructural energy release rate of femoral cortical bone in the rats from 1, 3, 5, 7, 9, 11, and 15 months of age were in the range of 0.08-0.12, 0.12-0.14, 0.15-0.19, 0.25-0.28, 0.23-0.25, 0.19-0.22, and 0.13-0.16 N/mm, respectively. The statistical analyses showed the significant differences in the microstructural energy release rate at different ages. The results indicated an increasing trend followed by a decrease from 1 to 15 months of age, and the correlations between microstructural energy release rate and age were significant. The age-related variations in the microstructural energy release rate may be linked to the changes in the microarchitecture, and the fracture load is influenced by the micro-level mechanical parameters. Notably, the age-related trends in microarchitecture and energy release rate were similar. These findings were valuable for understanding the mechanism underlying the weakening mechanical properties of cortical bone microstructure with age from an energy perspective.

Prediction of the critical energy release rate for rat femoral cortical bone structure under different failure conditions

BACKGROUND AND OBJECTIVE

Critical energy release rate is a global fracture parameter that could be measured during the failing process, and its value may change under different failure conditions even in the same bone structure. The aim of this study was to propose an approach that combined the experimental test and finite element analysis to predict the critical energy release rates in the femoral cortical bone structures under compression and three-point bending loads.

METHODS

Three-point bending and compression experiments and the corresponding fracture simulations were performed on the rat femoral cortical bone structures. Different values of energy release rate were repeatedly assigned to the finite element models to perform fracture simulations, and then the load-displacement curves predicted in each simulation were compared with the experimental data to back-calculate the critical energy release rate.

RESULTS

The predicted data were similar to the experimental results when the calibrated energy release rate was suitable. The results showed that the cortical bone structure occurred shear open failure under compression load, and the predicted critical energy release rate was 0.12 N/mm. The same cortical bone structure occurred tensile open failure under three-point bending load, and the predicted critical energy release rate was 0.16 N/mm.

CONCLUSIONS

The critical energy release rates were different under various failure conditions in one cortical bone structure. A comprehensive analysis from the perspectives of material mechanical properties, failure mode, and damage fracture mechanism was conducted to reveal the reasons for the differences in the critical energy release rate in the cortical bone structure, which provided a theoretical basis for the measurement of the critical energy release rate and the accurate fracture simulation.

Effects of different running intensities on the micro-level failure strain of rat femoral cortical bone structures: a finite element investigation

BACKGROUND

Running with the appropriate intensity may produce a positive influence on the mechanical properties of cortical bone structure. However, few studies have discussed the effects of different running intensities on the mechanical properties at different levels, especially at the micro-level, because the micromechanical parameters are difficult to measure experimentally.

METHODS

An approach that combines finite element analysis and experimental data was proposed to predict a micromechanical parameter in the rat femoral cortical bone structure, namely, the micro-level failure strain. Based on the previous three-point bending experimental information, fracture simulations were performed on the femur finite element models to predict their failure process under the same bending load, and the micro-level failure strains in tension and compression of these models were back-calculated by fitting the experimental load-displacement curves. Then, the effects of different running intensities on the micro-level failure strain of rat femoral cortical bone structure were investigated.

RESULTS

The micro-level failure strains of the cortical bone structures expressed statistical variations under different running intensities, which indicated that different mechanical stimuli of running had significant influences on the micromechanical properties. The greatest failure strain occurred in the cortical bone structure under low-intensity running, and the lowest failure strain occurred in the structure under high-intensity running.

CONCLUSIONS

Moderate and low-intensity running were effective in enhancing the micromechanical properties, whereas high-intensity running led to the weakening of the micromechanical properties of cortical bone. Based on these, the changing trends in the micromechanical properties were exhibited, and the effects of different running intensities on the fracture performance of rat cortical bone structures could be discussed in combination with the known mechanical parameters at the macro- and nano-levels, which provided the theoretical basis for reducing fracture incidence through running exercise.

Biomechanical evaluation of different strain judging criteria on the prediction precision of cortical bone fracture simulation under compression

Introduction: The principal strain or equivalent strain is mainly used in current numerical studies to determine the mechanical state of the element in the cortical bone finite element model and then perform fracture simulation. However, it is unclear which strain is more suitable for judging the element mechanical state under different loading conditions due to the lack of a general strain judging criterion for simulating the cortical bone fracture. Methods: This study aims to explore a suitable strain judging criterion to perform compressive fracture simulation on the rat femoral cortical bone based on continuum damage mechanics. The mechanical state of the element in the cortical bone finite element model was primarily assessed using the principal strain and equivalent strain separately to carry out fracture simulation. The prediction accuracy was then evaluated by comparing the simulated findings with different strain judging criteria to the corresponding experimental data. Results: The results showed that the fracture parameters predicted using the principal strain were closer to the experimental values than those predicted using the equivalent strain. Discussion: Therefore, the fracture simulation under compression was more accurate when the principal strain was applied to control the damage and failure state in the element. This finding has the potential to improve prediction accuracy in the cortical bone fracture simulation.

Investigation on the Differences in the Failure Processes of the Cortical Bone under Different Loading Conditions

Cortical bone is a transversely isotropic material, and the mechanical properties may be related to the loading direction on the osteon. Therefore, analyzing the differences in the failure processes of cortical bone under different loading conditions is necessary to explore the measures for reducing the incidence of fracture. In this study, to investigate the effects of different loading directions on the fracture performance in the cortical bone, a numerical method that could simultaneously simulate the failure processes in the cortical bone structure under compression and bending loads was established based on continuum damage mechanics theory. The prediction accuracy and feasibility of the numerical method were first verified by comparing with the corresponding experimental results. Then, the differences in the failure process and fracture performance of the same cortical bone structure under compression and bending loads were investigated. The simulation results indicated that for the same structure, the slip-open failure mode appeared under compression load, and the crack propagated along a certain angle to the loading direction; the tension-open failure mode appeared under bending load, and the crack propagated along the direction perpendicular to the loading direction. Meanwhile, the fracture load was greater and the fracture time was later in the compression than in the bending condition. These phenomena stated that discrepant failure processes and fracture patterns occurred in the same cortical bone structure under different loading conditions. The main reason may be related to the tension–compression asymmetry and transversely isotropic characteristics in the cortical bone material. The fracture simulations in the cortical bone under different loading conditions could improve the prediction accuracy in bone biomechanics and provide the prevention method for cortical bone damage and fracture.

Animal Models of Osteochondral Defect for Testing Biomaterials

The treatment of osteochondral defects (OCD) remains a great challenge in orthopaedics. Tissue engineering holds a good promise for regeneration of OCD. In the light of tissue engineering, it is critical to establish an appropriate animal model to evaluate the degradability, biocompatibility, and interaction of implanted biomaterials with host bone/cartilage tissues for OCD repair in vivo. Currently, model animals that are commonly deployed to create osteochondral lesions range from rats, rabbits, dogs, pigs, goats, and sheep horses to nonhuman primates. It is essential to understand the advantages and disadvantages of each animal model in terms of the accuracy and effectiveness of the experiment. Therefore, this review aims to introduce the common animal models of OCD for testing biomaterials and to discuss their applications in translational research. In addition, we have reviewed surgical protocols for establishing OCD models and biomaterials that promote osteochondral regeneration. For small animals, the non-load-bearing region such as the groove of femoral condyle is commonly chosen for testing degradation, biocompatibility, and interaction of implanted biomaterials with host tissues. For large animals, closer to clinical application, the load-bearing region (medial femoral condyle) is chosen for testing the durability and healing outcome of biomaterials. This review provides an important reference for selecting a suitable animal model for the development of new strategies for osteochondral regeneration.

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

Finite Element Investigation of the Effects of the Low-Frequency Vibration Generated by Vehicle Driving on the Human Lumbar Mechanical Properties

Long-term exposure to low-frequency vibration generated by vehicle driving impairs human lumbar spine health. However, few studies have investigated how low-frequency vibration affects human lumbar mechanical properties. This study established a poroelastic finite element model of human lumbar spinal segments L2–L3 to perform time-dependent vibrational simulation analysis and investigated the effects of different vibrational frequencies generated by normal vehicle driving on the lumbar mechanical properties in one hour. Analysis results showed that vibrational load caused more injury to lumbar health than static load, and vibration at the resonant frequency generated the most serious injury. The axial effective stress and the radial displacement in the intervertebral disc, as well as the fluid loss in the nucleus pulposus, increased, whereas the pore pressure in the nucleus pulposus decreased with increased vibrational frequency under the same vibrational time, which may aggravate the injury degree of human lumbar spine. Therefore, long-term driving on a well-paved road also induces negative effects on human lumbar spine health. When driving on a nonpaved road or operating engineering machinery under poor navigating condition, the auto seat transmits relatively high vibrational frequency, which is highly detrimental to the lumbar spine health of a driver.

Determination of a tissue-level failure evaluation standard for rat femoral cortical bone utilizing a hybrid computational-experimental method

Macro-level failure in bone structure could be diagnosed by pain or physical examination. However, diagnosing tissue-level failure in a timely manner is challenging due to the difficulty in observing the interior mechanical environment of bone tissue. Because most fractures begin with tissue-level failure in bone tissue caused by continually applied loading, people attempt to monitor the tissue-level failure of bone and provide corresponding measures to prevent fracture. Many tissue-level mechanical parameters of bone could be predicted or measured; however, the value of the parameter may vary among different specimens belonging to a kind of bone structure even at the same age and anatomical site. These variations cause difficulty in representing tissue-level bone failure. Therefore, determining an appropriate tissue-level failure evaluation standard is necessary to represent tissue-level bone failure. In this study, the yield and failure processes of rat femoral cortical bones were primarily simulated through a hybrid computational-experimental method. Subsequently, the tissue-level strains and the ratio between tissue-level failure and yield strains in cortical bones were predicted. The results indicated that certain differences existed in tissue-level strains; however, slight variations in the ratio were observed among different cortical bones. Therefore, the ratio between tissue-level failure and yield strains for a kind of bone structure could be determined. This ratio may then be regarded as an appropriate tissue-level failure evaluation standard to represent the mechanical status of bone tissue.