Sensitivity of multiple damage parameters to compressive overload in cortical bone

Fatigue evaluation of long cortical bone using ultrasonic guided waves

Bone fatigue fracture is a progressive disease due to stress concentration. This study aims to evaluate the long bone fatigue damage using the ultrasonic guided waves. Two-dimensional finite-difference time-domain method was employed to simulate the ultrasonic guided wave propagation in the long bone under different elastic modulus. The experiment was conducted on a 3.8 mm-thick bovine bone plate. The phase velocities of two fundamental guided modes, A1 and S1, were measured by using the axial transmission technique. Simulation shows that the phase velocities of guided modes A1 and S1 decrease with the increasing of the fatigue damage. After 20,000 cycles of fatigue loading on the bone plate, the average phase velocities of A1 and S1 modes were 6.6% and 5.3% respectively, lower than those of the intact bone. The study suggests that ultrasonic guided waves can be potentially used to evaluate the fatigue damage in long bones.

Assessment of compressive failure process of cortical bone materials using damage-based model

The main failure factors of cortical bone are aging or osteoporosis, accident and high energy trauma or physiological activities. However, the mechanism of damage evolution coupled with yield criterion is considered as one of the unclear subjects in failure analysis of cortical bone materials. Therefore, this study attempts to assess the structural response and progressive failure process of cortical bone using a brittle damaged plasticity model. For this reason, several compressive tests are performed on cortical bone specimens made of bovine femur, in order to obtain the structural response and mechanical properties of the material. Complementary finite element (FE) model of the sample and test is prepared to simulate the elastic-to-damage behavior of the cortical bone using the brittle damaged plasticity model. The FE model is validated in a comparative method using the predicted and measured structural response as load-compressive displacement through simulation and experiment. FE results indicated that the compressive damage initiated and propagated at central region where maximum equivalent plastic strain is computed, which coincided with the degradation of structural compressive stiffness followed by a vast amount of strain energy dissipation. The parameter of compressive damage rate, which is a function dependent on damage parameter and the plastic strain is examined for different rates. Results show that considering a similar rate to the initial slope of the damage parameter in the experiment would give a better sense for prediction of compressive failure.

Finite element prediction with experimental validation of damage distribution in single trabeculae during three-point bending tests

There is growing evidence that information on trabecular microarchitecture can improve the assessment of fracture risk. One current strategy is to exploit finite element (FE) analysis applied to experimental data of mechanically loaded single trabecular bone tissue obtained from non-invasive imaging techniques for the investigation of the damage initiation and growth of bone tissue. FE analysis of this type of bone has mainly focused on linear and non-linear analysis to evaluate the bone's failure properties. However, there is a lack of experimentally validated FE damage models at trabecular bone tissue level allowing for the simulation of the progressive damage process (initiation and growth) till complete fracture. Such models are needed to perform enhanced prediction of the apparent failure mechanical properties needed to assess the fracture risk of bone organs. In the current study, we develop a FE model based on a continuum damage mechanics (CDM) approach to simulate the damage initiation and propagation of a single trabecula till complete facture in quasi-static regime. Three-point bending experiments were performed on single bovine trabeculae and compared to FE results. In order to validate the proposed FE mode, (i) the force displacement curve was compared to the experimental one and (ii) the damage distribution was correlated to the measured one obtained by digital image correlation based on stress whitening in bone, reported to be correlated to microdamage. A very good agreement was obtained between the FE and experimental results, indicating that the proposed damage investigation protocol based on FE analysis and testing is reliable to assess the damage behavior of bone tissue and that the current damage model is able to accurately simulate the damaging and fracturing process of single trabeculae under quasi static load.

Mechanical behavior of human cortical bone in cycles of advancing tensile strain for two age groups

The capacity of bone for post-yield energy dissipation decreases with age. To gain information on the causes of such a change, we examined age-related changes in the mechanical behavior of human cadaveric bone as a function of progressive deformation. In this study, tensile specimens from tibiae of nine middle aged and eight elderly donors were loaded till failure in an incremental and cyclic (load-dwell-unload-dwell-reload) scheme. The elastic modulus, maximum stress, permanent strain, stress relaxation, permanent strain energy, elastic release strain energy, and hysteresis energy were determined in each loading cycle at incremental strains. Similar with previous work, the results of the present study also indicated that elderly bone failed at much lower strains compared to middle aged bone. However, no significant differences in the mechanical behavior of bone were observed between the two age groups except for the premature failure of elderly bone. After yielding, the energy dissipation and permanent strain of bone appeared to linearly increase with increasing strain applied, while nonlinear changes occurred in the modulus loss and stress relaxation with increasing strain. Moreover, stress relaxation tended to peak at 1% strain beyond which few elderly bone specimens survived. This study suggests that damaging mechanisms in bone vary with deformation, and aging affects the post-yield mechanisms, thus giving rise to the age-related differences in the mechanical properties of bone, especially the capacity of the tissue for energy dissipation.

Differences in the mechanical behavior of cortical bone between compression and tension when subjected to progressive loading

The hierarchical arrangement of collagen and mineral into bone tissue presumably maximizes fracture resistance with respect to the predominant strain mode in bone. Thus, the ability of cortical bone to dissipate energy may differ between compression and tension for the same anatomical site. To test this notion, we subjected bone specimens from the anterior quadrant of human cadaveric tibiae to a progressive loading scheme in either uniaxial tension or uniaxial compression. One tension (dog-bone shape) and one compression specimen (cylindrical shape) were collected each from tibiae of nine middle aged male donors. At each cycle of loading-dwell-unloading-dwell-reloading, we calculated maximum stress, permanent strain, modulus, stress relaxation, time constant, and three pathways of energy dissipation for both loading modes. In doing so, we found that bone dissipated greater energy through the mechanisms of permanent and viscoelastic deformation in compression than in tension. On the other hand, however, bone dissipated greater energy through the release of surface energy in tension than in compression. Moreover, differences in the plastic and viscoelastic properties after yielding were not reflected in the evolution of modulus loss (an indicator of damage accumulation), which was similar for both loading modes. A possible explanation is that differences in damage morphology between the two loading modes may favor the plastic and viscoelastic energy dissipation in compression, but facilitate the surface energy release in tension. Such detailed information about failure mechanisms of bone at the tissue-level would help explain the underlying causes of bone fractures.

A non-invasive in vitro technique for the three-dimensional quantification of microdamage in trabecular bone

An accurate analysis and quantification of microdamage is critical to understand how microdamage affects the mechanics and biology of bone fragility. In this study we demonstrate the development and validation of a novel in vitro micro-computed tomography (microCT) method that employs lead-uranyl acetate as a radio-opaque contrast agent for automated quantification of microdamage in trabecular bone. Human trabecular bone cores were extracted from the femoral neck, scanned via microCT, loaded in unconfined compression to a range of apparent strains (0.5% to 2.25%), stained in lead-uranyl acetate, and subsequently re-scanned via microCT. An investigation of the regions containing microdamage using the backscatter mode of a scanning electron microscope (BSEM) showed that the lead-uranyl sulfide complex was an effective contrast agent for microdamage in bone. Damaged volume fraction (DV/BV), as determined by microCT, increased exponentially with respect to applied strains and proportionately to mechanically determined modulus reduction (p<0.001). Furthermore, the formation of microdamage was observed to occur before any apparent stiffness loss, suggesting that the localized tissue yielding occurs prior to the structural yielding of trabecular bone. This non-invasive in vitro technique for the detection of microdamage using microCT may serve as a valuable complement to existing morphometric analyses of bone.

Age-related factors affecting the postyield energy dissipation of human cortical bone

The risk of bone fracture depends in part on tissue quality, not just the size and mass. This study assessed the postyield energy dissipation of cortical bone in tension as a function of age and composition. Specimens were prepared from tibiae of human cadavers in which male and female donors were divided into two age groups: middle aged (51 to 56 years, n = 9) and elderly (72 to 90 years, n = 8). By loading, unloading, and reloading a specimen with rest periods inserted in between, tensile properties at incremental strain levels were assessed. In addition, postyield toughness was estimated and partitioned as plastic strain energy related to permanent deformation, released elastic strain energy related to stiffness loss, and hysteresis energy related to viscous behavior. Porosity, mineral and collagen content, and collagen crosslinks of each specimen were also measured to determine the micro- and ultrastructural properties of the tissue. Age affected all the energy terms plus strength but not elastic stiffness. The postyield energy terms were correlated with porosity, pentosidine (a marker of nonenzymatic crosslinks), and collagen content, all of which varied significantly with age. General linear models suggested that pentosidine concentration and collagen content provided the best explanation of the age-related decrease in the postyield energy dissipation. Among them, pentosidine concentration had the greatest contribution to plastic strain energy and was the best explanatory variable of damage accumulation.

A novel approach to assess post-yield energy dissipation of bone in tension

In this study, we proposed a novel approach to assess the energy dissipation during the post-yield deformation of bone. Based on the stress-strain behavior in an incremental and cyclic loading-unloading-reloading scheme in uniaxial tension, we partitioned the post-yield energy dissipation of bone into three distinct pathways: released elastic strain energy (U(er)); irreversible energy (U(i)); and hysteresis energy (U(h)). Among them, U(er) depends on the stiffness loss, U(i) is the energy permanently consumed, and U(h) reflects changes in the viscoelastic behavior of bone in the process of post-yield deformation. As an example, bone specimens from human cadaveric femurs of middle-aged and elderly donors were tested using this approach. The results of this study indicate that there exist age-related differences in post-yield energy dissipation and modulus degradation. These results implicate that this novel approach could detect the age-related differences in energy dissipation of bone and may aid in understanding the underlying mechanisms of such changes.

Sexual dimorphism affects tibia size and shape but not tissue-level mechanical properties

Understanding how growth influences adult bone morphology and tissue quality should provide important insight into why females show a greater incidence of stress fractures early in life and fragility fractures later in life compared to males. The objective of this study was to test whether females acquire similar tissue-level mechanical properties as males by the time peak bone properties are established. Standardized beams of bone were machined from the tibial diaphyses of 14 young, adult females ranging in age from 22 to 46 years. Data for males (n=17, age=17-46 years) were taken from a prior study. Measures of tissue-level mechanical properties, including stiffness, strength, ductility, toughness, and damageability, were compared between sexes using t-tests. The relationship between cross-sectional morphology and tissue-level mechanical properties was also examined. Males and females showed nearly identical tissue-level mechanical properties. Both sexes also showed similar age-related degradation of mechanical properties and a similar relationship between cross-sectional morphology and tissue quality. However, for all body sizes, female tibiae were smaller relative to body size (i.e., less robust) compared to males. The results indicated that sex-specific growth patterns affected transverse bone size, but did not affect tissue-level mechanical properties. This, combined with the observation that young, adult female long bones are undersized relative to body size, suggests that adult females would be expected to accumulate more damage under intense loading compared to males. This may be a contributing factor to the greater incidence of stress fractures observed for female military recruits.