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.

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.

Influence of design features of tibial stems in total knee arthroplasty on tibial bone remodeling behaviors.

In total knee arthroplasty, the optimal length and material of tibial stem remain controversial. This study aimed to evaluate influences of lengths and materials of cementless stems on tibial remodeling behaviors. Three groups of lengths were investigated (i.e., 110, 60, and 30 mm), and four materials (i.e., titanium, flexible 'iso-elastic' material, and two functionally graded materials [FGMs]) were selected for each group. FGM is a kind of material whose composition gradually varies in space. In this study, the compositions of two FGMs were Ti and hydroxyapatite (FGM I), and Ti and bioglass (FGM II), respectively. Tibial models were incorporated with finite element analysis to simulate bone remodeling. Distributions of bone mineral density, von Mises stress, and interface shear stress were obtained. For the length, the long stem produced more serious stress shielding and stress concentration than the short stem, but it could provide better mechanical stability. For the material, FGM I could reduce stress shielding and stress concentration and reduce the risk of loosening. Compared with the length, the material had a pronounced effect on remodeling. This study provided theoretical basis for optimal design of stem to improve service life of tibial components and to reduce pain of patients.

Modeling the Mechanical Consequences of Age-Related Trabecular Bone Loss by XFEM Simulation.

The elderly are more likely to suffer from fracture because of age-related trabecular bone loss. Different bone loss locations and patterns have different effects on bone mechanical properties. Extended finite element method (XFEM) can simulate fracture process and was suited to investigate the effects of bone loss on trabecular bone. Age-related bone loss is indicated by trabecular thinning and loss and may occur at low-strain locations or other random sites. Accordingly, several ideal normal and aged trabecular bone models were created based on different bone loss locations and patterns; then, fracture processes from crack initiation to complete failure of these models were observed by XFEM; finally, the effects of different locations and patterns on trabecular bone were compared. Results indicated that bone loss occurring at low-strain locations was more detrimental to trabecular bone than that occurring at other random sites; meanwhile, the decrease in bone strength caused by trabecular loss was higher than that caused by trabecular thinning, and the effects of vertical trabecular loss on mechanical properties were more severe than horizontal trabecular loss. This study provided a numerical method to simulate trabecular bone fracture and distinguished different effects of the possible occurrence of bone loss locations and patterns on trabecular bone.

Quantification of Age-Related Tissue-Level Failure Strains of Rat Femoral Cortical Bones Using an Approach Combining Macrocompressive Test and Microfinite Element Analysis.

Bone mechanical properties vary with age; meanwhile, a close relationship exists among bone mechanical properties at different levels. Therefore, conducting multilevel analyses for bone structures with different ages are necessary to elucidate the effects of aging on bone mechanical properties at different levels. In this study, an approach that combined microfinite element (micro-FE) analysis and macrocompressive test was established to simulate the failure of male rat femoral cortical bone. Micro-FE analyses were primarily performed for rat cortical bones with different ages to simulate their failure processes under compressive load. Tissue-level failure strains in tension and compression of these cortical bones were then back-calculated by fitting the experimental stress-strain curves. Thus, tissue-level failure strains of rat femoral cortical bones with different ages were quantified. The tissue-level failure strain exhibited a biphasic behavior with age: in the period of skeletal maturity (1-7 months of age), the failure strain gradually increased; when the rat exceeded 7 months of age, the failure strain sharply decreased. In the period of skeletal maturity, both the macro- and tissue-levels mechanical properties showed a large promotion. In the period of skeletal aging (9-15 months of age), the tissue-level mechanical properties sharply deteriorated; however, the macromechanical properties only slightly deteriorated. The age-related changes in tissue-level failure strain were revealed through the analysis of male rat femoral cortical bones with different ages, which provided a theoretical basis to understand the relationship between rat cortical bone mechanical properties at macro- and tissue-levels and decrease of bone strength with age.