DISPARITY OF DRY BONES
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There appears to be less of an effect of species type on the modulus of cortical bone, as the moduli measured in human and animal studies overlap at all strain rates. The compressive response found in this study agreed with other studies on human bones. In general, direct comparisons between embalmed and fresh bone are not recommended because of the significant effects of embalming on bone microstructure and its constituents, leading to altered bone mechanical properties [ 8 ]. In an attempt to quantify these effects, McElhaney et al.
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Like human bone, bovine and equine bone strength measured by Adharapurapu et al. Bovine and equine bones had higher ultimate stresses compared to the human bones used in this study, underscoring the necessity for human tissue studies at high strain rates, as these are the rates that are relevant to extreme dynamic environments when developing material response models to be used for numerical simulations of events where humans are involved. The divergence of animal data from human data at high rate can be seen from this plot.
The overall stress—strain trends of cortical bone measured in this study agree with bovine and equine studies in that the mechanical properties of the bone were anisotropic. Unfortunately, some investigators used dry bones for their studies, making it impractical to draw comparisons of the mechanical response to wet bones because of the significant effect of hydration of collagen on the mechanical behavior [ 14 , 15 ]. The modulus slope of the initial part of the stress—strain curve from this study was lower than moduli reported from other studies Fig.
The modulus of the bone in the longitudinal direction was 9. In the transverse direction, the modulus of the bone was 3. Reilly and Burstein [ 27 ] observed an orientation dependence on the modulus of cortical bone at quasi-static rate; the longitudinal modulus was Ohman et al. The strain rate dependence on modulus in the current study also differed from published dynamic data. Katsimanis and Raftopolus [ 16 ] studied the rate-dependent modulus of human femoral cortical bone in the longitudinal direction and found values of A possible cause for this difference could be that Katsamanis and Raftopolus [ 16 ] used strain gages bonded to the surface of the bone, which included a 2-day drying period of the bones for strain gages to adhere to the surface.
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Differences in the measured modulus could be due to preservation methods and moisture content of the specimens; several other investigators dried bones specimens for an extended period of time, which could have affected the measured stiffness. Choi et al. Essentially, as the specimen size drops and the size of the defects such as pores and channels remain constant, defects have a more profound effect on the measured modulus.
Modulus results from the human studies were consistent showing a linear increase in modulus as a function of increasing log of strain rate. The studies conducted on bovine cortical bone by Adharapurapu et al. At all strain rates, moduli data from Adharapurapu et al.
It is necessary to point out that in most of these experiments, strains are measured using either the Hopkinson bar calculations or from the loading machine, and not directly on the specimen. The mechanical properties of the femur may not represent the mechanical behavior of other cortical bones in the leg or elsewhere.
The compressive results from the present study seem to agree with Ohman et al. However, they mixed femur and tibia specimens and presented them as a single average value. Furthermore, a study comparing tibia bone material properties to those of the femur found a similar range of values for the ultimate strength of both bones at low strain rates [ 40 ]. This finding was consistent with similar comparison studies on the mechanical properties of the femur and tibia [ 36 , 45 , 46 ].
Burstein et al. The mechanical properties of bone differ not only throughout the body, but also within any specific bone [ 47 , 48 ]. Studies of the mechanical properties show that the properties of the subchondral bone of the femoral head [ 49 ] the metaphyseal section , which is located between the diaphysis and the epiphysis in the proximal femur, are different from the properties of the diaphysis [ 50 ]. Regarding the tibia bone, the metaphyseal [ 51 ] and subchondral [ 44 ] bones in the proximal tibia have been shown to have properties of lower magnitude in comparison to the diaphyseal bone.
Because of the differences in the mechanical properties of the femur and tibia, the use of a single value of yield strength, ultimate strength, or modulus for femur and tibia would be inappropriate. Orais et al.
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Therefore, when developing a high-fidelity computational model of a human anatomy, each type of bone must be studied separately to obtain its specific material properties. A uniaxial compressive study of human femoral cortical bone was completed over a range of strain rates from quasi-static 0. Loading was applied in the transverse and longitudinal directions of the bone axis.
Optical strain measurements were performed using DIC with a variety of cameras, depending on the strain rate. The ultimate strength and modulus were found to be anisotropic, where the longitudinal direction was both stronger and stiffer than the transverse direction. Ultimate strength and modulus increased with increasing strain rate while ultimate strain was constant for longitudinal specimens and depended on strain rate for transverse specimens.
The compressive response measured in this study agreed with other studies on human bones. Any correlations based on the specimen harvest location could not be concluded from this study with the limited sampling size, even though differences in strength, moduli, and hardness have been shown to vary with specimen location along the femur shaft diaphysis as well as at the ends epiphysis.
DISPARITY OF DRY BONES
Conclusions about the relationship of age to ultimate compressive strength or stiffness could not be made due to the narrow age range of the donors in this study. Mechanical properties of the femur should not be applied to other bones for numerical modeling purposes, especially in the case of the tibia, which has been found to have different failure strengths and moduli compared to the femur. Further work is needed to quantify rate-dependent regional variations within the same bone. Additional studies are needed to assess the relationship between possible changes of failure strength with donor age or microstructural details such as osteon density and diameter, mineral content and porosity.
Skip to main content Skip to sections. Advertisement Hide. Download PDF. Article First Online: 09 February Introduction Human long bone has a complex hierarchical structure organized at a variety of length scales, as shown in Fig. At the nano-scale, cortical bone is comprised of collagen and hydroxyapatite crystals.
At the micro-scale, these constituents organize into mineralized collagen fibrils. Fiber arrays are further organized into a lamellar. Cylindrical structures Haversian structure of multiple concentric lamellae surrounding central blood vessel Haversian canal are osteons. This orientation of osteons creates an anisotropic mechanical response such that cortical bone demonstrates different properties based on orientation. This anisotropy must be understood and incorporated into material models to properly represent the deformation behavior. Several studies on bone have been conducted to study the fracture behavior at the micro-scale during quasi-static loading [ 2 , 3 ].
The fracture behavior of human bone has also been investigated at high loading rate [ 4 , 5 , 6 ]. In addition to fracture response, understanding the anisotropic compressive response of bone is critical for building accurate material models. Open image in new window. Material Cortical bone samples were extracted from the femur diaphysis shown in Fig.
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Samples were extracted from the anterior, posterior, medial, and lateral regions along the diaphysis. The location of each specimen was carefully recorded. The gage lengths of the longitudinal long and transverse trans specimens were 3. A total of 71 experiments were conducted for samples taken from directions longitudinal and transverse to the osteon direction in the bone.
Roughly the same number of samples from each donor at each rate was used to obtain an average behavior of cortical bone in uniaxial compression. The setup, made of aluminum, consisted of a solid The transmission bar used semiconductor strain gages to improve the signal to noise ratio of the weak transmitted signal. A triangular-shaped incident pulse, such as the one shown in Fig. The incident bar pulse was shaped to increase the rise time to ensure that the bone specimen was in a state of dynamic equilibrium over the course of the experiment.
The typical forces measured or calculated on either side of the specimen, shown in Fig. The force history calculated at the front surface incident bar-specimen interface is much noisier than the back surface specimen—transmission bar interface because of the higher signal-to-noise ratio of the hollow transmission bar and semiconductor gages in it, compared to the solid incident bar with resistive gages. Force at the input bar is calculated by subtracting the reflected signal from the incident signal, which are approximately of the same magnitude.
This further amplifies noise and hence the fluctuation in the calculated force.
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Reduction of noise would improve equilibrium verification and could be achieved with the addition of semi-conductor gages to the incident bar. Even though the calculated force at the input bar interface shows large fluctuations, its average trend follows the output bar interface force. In addition to being in dynamic equilibrium, the cortical bone specimen experienced an approximately constant rate of deformation after an initial ramp loading, as shown in typical strain and strain rate histories in Fig.
The strain data shown in Fig. Measurement of small displacements of the bar ends is inaccurate because of slight variations in strain gage factor and the inability to prepare perfectly flat and parallel loading specimen surfaces. Elastic behavior is not reported for most materials using only bar signals; specimens with directly bonded strain gages or other techniques are necessary to accurately obtain the small strain mechanical response.