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.
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.
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.
Macro-level failure in bone structure could be diagnosed by pain or physical examination. However, diagnosing tissuelevel 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 tissuelevel 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.
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