Loading rate effects on the R-curve behavior of cortical bone

Rising resistance curve (R-curve) behavior in bone during quasi-static experiments has demonstrated the importance of microstructural toughening mechanisms in resisting fracture. However, despite clinical bone fracture primarily occurring under dynamic loading and the significant changes in material behavior observed with increasing strain rates, there have been no previous investigations into whether crack growth resistance is maintained during dynamic fracture. Using a novel modified split-Hopkinson pressure bar coupled with a high-speed camera to measure crack propagation, we present the first evidence of rising R-curve behavior in bone under dynamic loading (～2 × 10(5)MPam(1/2)s(-1)). Results indicate that rising R-curve behavior is maintained, although with lower crack initiation toughness and propagation resistance than observed in quasi-static experiments. Observations of crack initiation and propagation in double-notched specimens using confocal fluorescence microscopy and electron microscopy suggest that this is due to subtle differences in toughening mechanisms between quasi-static and dynamic fracture.     

Mechanistic aspects of the fracture toughness of elk antler bone

Bone is an adaptive material that is designed for different functional requirements; indeed, bones have a variety of properties depending on their role in the body. To understand the mechanical response of bone requires the elucidation of its structure–function relationships. Here, we examine the fracture toughness of compact bone of elk antler, which is an extremely fast-growing primary bone designed for a totally different function than human (secondary) bone. We find that antler in the transverse (breaking) orientation is one of the toughest biological materials known. Its resistance to fracture is achieved during crack growth (extrinsically) by a combination of gross crack deflection/twisting and crack bridging via uncracked “ligaments” in the crack wake, both mechanisms activated by microcracking primarily at lamellar boundaries. We present an assessment of the toughening mechanisms acting in antler as compared to human cortical bone, and identify an enhanced role of inelastic deformation in antler which further contributes to its (intrinsic) toughness.     

Mixed-mode fracture of human cortical bone

Although the mode I (tensile opening) fracture toughness has been the focus of most fracture mechanics studies of human cortical bone, bones in vivo are invariably loaded multiaxially. Consequently, an understanding of mixed-mode fracture is necessary to determine whether a mode I fracture toughness test provides the appropriate information to accurately quantify fracture risk. In this study, we examine the mixed-mode fracture of human cortical bone by characterizing the crack-initiation fracture toughness in the transverse (breaking) orientation under combined mode I (tensile opening) plus mode II (shear) loading using samples loaded in symmetric and asymmetric four-point bending. Whereas in most structural materials, the fracture toughness is increased with increasing mode-mixity (i.e., where the shear loading component gets larger), in the transverse orientation of bone the situation is quite different. Indeed, the competition between the maximum applied mechanical mixed-mode driving force and the weakest microstructural paths in bone results in a behavior that is distinctly different to most homogeneous brittle materials. Specifically, in this orientation, the fracture toughness of bone is markedly decreased with increasing mode-mixity.     

On the R-curve behavior of human tooth enamel

In this study the crack growth resistance behavior and fracture toughness of human tooth enamel were quantified using incremental crack growth measures and conventional fracture mechanics. Results showed that enamel undergoes an increase in crack growth resistance (i.e. rising R-curve) with crack extension from the outer to the inner enamel, and that the rise in toughness is a function of distance from the dentin enamel junction (DEJ). The outer enamel exhibited the lowest apparent toughness (0.67 ± 0.12 MPa m^0.5), and the inner enamel exhibited a rise in the growth toughness from 1.13 MPa m^0.5/mm to 3.93 MPa m^0.5/mm. The maximum crack growth resistance at fracture (i.e. fracture toughness (K_c)) ranged from 1.79 to 2.37 MPa m^0.5. Crack growth in the inner enamel was accompanied by a host of mechanisms operating from the micro- to the nano-scale. Decussation in the inner enamel promoted crack deflection and twist, resulting in a reduction of the local stress intensity at the crack tip. In addition, extrinsic mechanisms such as bridging by unbroken ligaments of the tissue and the organic matrix promoted crack closure. Microcracking due to loosening of prisms was also identified as an active source of energy dissipation. In summary, the unique microstructure of enamel in the decussated region promotes crack growth toughness that is approximately three times that of dentin and over ten times that of bone.     

异体皮质人工骨复合物治疗骨折不愈合及骨缺损

背景：异体皮质干燥异体骨为多孔状结构,孔均匀且相互贯通,孔径200 µm 左右,在形态结构上与人类无机骨极为相似。 目的：观察应用骨形态发生蛋白-骨髓间充质干细胞-异体皮质人工骨复合物治疗骨折不愈合及骨缺损的临床效果。 方法：选择33例创伤性骨缺损患者,其中男19例,女14例;年龄26-85岁。首先提取患者自体骨髓间充质干细胞,进一步以异体皮质人工骨为支架材料,同时导入骨形态发生蛋白和骨髓间充质干细胞,通过人工合成方式制成骨形态发生蛋白-骨髓间充质干细胞-异体皮质人工骨复合物,植入骨缺损处,每例植入人工骨复合物20-45 g。 结果与结论：随访6个月-2.5年,根据Mankin及Komender等对同种异体骨移植结果的评分标准,满意32例,不满意1例。复查X射线片示32例达骨性愈合,其中新鲜骨折愈合时间2-7个月,陈旧性骨折愈合时间4-9个月。同种异体松质骨6-9周开始与自体骨融合爬行替代。1例感染性骨缺损移植后迟发性感染,去除内固定及同种异体骨,置管冲洗、局部稳定后再次植骨愈合,随访2年1个月骨感染未复发;1例钢板松动致骨折未愈合,再次行内固定、自体骨移植后骨折愈合。表明应用骨形态发生蛋白-骨髓间充质干细胞-异体皮质人工骨复合物治疗骨折不愈合及骨缺损无明显不良反应,修复效果良好。中国组织工程研究杂志出版内容重点：生物材料;骨生物材料; 口腔生物材料; 纳米材料; 缓释材料; 材料相容性;组织工程全文链接：     

Fracture length scales in human cortical bone: the necessity of nonlinear fracture models

Recently published data for fracture in human humeral cortical bone are analyzed using cohesive-zone models to deal with the nonlinear processes of material failure. Such models represent the nonlinear deformation processes involved in fracture by cohesive tractions exerted by the failing material along a fracture process zone, rather than attributing all damage to a process occurring at a single point, as in conventional linear-elastic fracture mechanics (LEFM). The relationship between the tractions and the net displacement discontinuity across the process zone is hypothesized to be a material property for bone. To test this hypothesis, the cohesive law was evaluated by analyzing published load vs. load-point displacement data from one laboratory; the calibrated law was then used to predict similar data taken for a different source of bone using a different specimen geometry in a different laboratory. Further model calculations are presented to illustrate more general characteristics of the nonlinear fracture of bone and to demonstrate in particular that LEFM is not internally consistent for all cases of interest. For example, the fracture toughness of bone deduced via LEFM from test data is not necessarily a material constant, but will take different values for different crack lengths and test configurations. LEFM is valid when the crack is much longer than a certain length scale, representative of the length of the process zone in the cohesive model, which for human cortical bone ranges from 3 to 10mm. Since naturally occurring bones and the specimens used to test them are not much larger than this dimension for most relevant orientations, it is apparent that only nonlinear fracture models can give an internally consistent account of their fracture. The cohesive law is thus a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality. The analysis of fracture data also requires proper representation of the approximately orthotropic elasticity of the bone specimen; if the specimen is incorrectly assumed to be isotropic, the initial measured compliance cannot be reproduced to within a factor of four and the fracture toughness deduced from the measured work of fracture will be overestimated by approximately 30%.     

Interfacial fracture toughness between bovine cortical bone and cements

To evaluate the bonding strength of the interfaces within the cemented arthroplasty system, various mechanical tests have been used. Conventional push-out and pull-out tests cannot reveal the actual bonding property of the interface because of the significant influence of surface roughness on the measured adhesion and the failure to account for the mismatch of elastic modulus across the interface. An alternative fracture mechanics approach, which considers the mix of opening and shear modes of the crack tip loading associated with the testing system and the elastic mismatch of materials across the interface, was used to evaluate the bonding ability of various cements. The four-point bend interfacial delamination test by Charalambides et al. (J. Appl. Mech. 56 (1989) 77; Mech. Mater. 8 (1990) 269) was used to quantify the bonding ability of cements. This method is arguably more suitable since the applied loading mode is comparable to the nature of loading within the prosthetic system, which is primarily bending. The bovine bone specimens were polished to mirror finish to eliminate bonding by mechanical interlocking. The results revealed minimal bonding for the conventional bone cement (PMMA) whereas substantial bonding was evident for the glass-ionomer cements tested. However, only the conventional glass-ionomer cements showed evidence of bonding on testing, while the resin-modified glass-ionomer cement (poly-HEMA) did not. The latter appeared to debond before testing because of excessive expansion stresses associated with swelling in water.     

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.     

Quantitative microradiography of cortical bone in disuse osteoporosis following fracture fixation

Stainless steel (elastic modulus 210 GN/m²) and carton fibre reinforced epoxy resin (elastic modulus 65 GN/m²) plates have been attached to intact femora in cats and the development of disuse osteoporosis assessed by microdensitometric methods after 8 months. The bone adjacent to the stainless steel plate showed evidence of considerable demoralization, both uniformly throughout a section and especially at certain focal points. A noticeable, but much smaller amount of osteoporosis developed adjacent to the composite plate. Various methods of presenting quantitative micro-densitometric data are used.     

The fatigue properties of human cortical bone

Rotating cantileverfatigue tests were performed on specimens extracted longitudinally from the cortices of human femora. The usual inverse relationship between stress amplitude and fatigue life was found; the median life was 1·3×10⁴ cycles at a stress amplitude of 12,200 1bf/in² (84·1 MN/m²) and 4·6×10⁶ cycles at 6750 1bf/in² (46·6 MN/m²). Arguments are advanced which suggest that these results are compatible with what is known of the stresses applied in life and the clinical occurrence of fatigue fractures.     

Sub-lamellar microcracking and roles of canaliculi in human cortical bone

Bone is a tough biological material. It is generally accepted that bone's toughness arises from its unique hierarchical structure, which in turn facilitates distributed microcracking prior to fracture. Yet, there has been limited progress on the detailed roles of the structural elements in the microcracking process. The present study examines the structure-microcracking relations at the lamellar and sub-lamellar levels of human cortical bone subjected to compressive loading. Laser scanning confocal microscopy revealed a clear influence of the local structure and porosity of the Haversian systems' lamellae on microcrack development. In particular, crack initiation and growth under transverse compression were associated with stress concentration at canaliculi. Later stages of microcracking showed extensive sub-lamellar cracks forming cross-hatched patterns and regularly spaced 0.5-1.7 μm apart. The density, size and regularity of the crack patterns suggest enhanced inelastic deformation capacity through cracking control at the level of mineralized collagen fibril bundles. The present study thus improves the current understanding of the nature of inelastic deformation and microcracking in bone and further suggests that bone's resistance to fracture is achieved through microcrack control at multiple length scales.     

The effect of strain rate on fracture toughness of human cortical bone: a finite element study

Evaluating the mechanical response of bone under high loading rates is crucial to understanding fractures in traumatic accidents or falls. In the current study, a computational approach based on cohesive finite element modeling was employed to evaluate the effect of strain rate on fracture toughness of human cortical bone. Two-dimensional compact tension specimen models were simulated to evaluate the change in initiation and propagation fracture toughness with increasing strain rate (range: 0.08–18 s⁻¹). In addition, the effect of porosity in combination with strain rate was assessed using three-dimensional models of micro-computed tomography-based compact tension specimens. The simulation results showed that bone’s resistance against the propagation of a crack decreased sharply with increase in strain rates up to 1 s⁻¹ and attained an almost constant value for strain rates larger than 1 s⁻¹. On the other hand, initiation fracture toughness exhibited a more gradual decrease throughout the strain rates. There was a significant positive correlation between the experimentally measured number of microcracks and the fracture toughness found in the simulations. Furthermore, the simulation results showed that the amount of porosity did not affect the way initiation fracture toughness decreased with increasing strain rates, whereas it exacerbated the same strain rate effect when propagation fracture toughness was considered. These results suggest that strain rates associated with falls lead to a dramatic reduction in bone’s resistance against crack propagation. The compromised fracture resistance of bone at loads exceeding normal activities indicates a sharp reduction and/or absence of toughening mechanisms in bone during high strain conditions associated with traumatic fracture.     

Fractal dimension and mechanical properties of human cortical bone

Fractal dimension (FD) can be used to characterize microstructure of porous media, particularly bone tissue. The porous microstructure of cortical bone is observable in micro-CT (μCT) images. Estimations of fractal dimensions of μCT images of coupons of human cortical bone are obtained. The same samples were tested on a tensile test machine and Young's modulus (YM) and Failure stress were obtained. When both types of measures were compared, a clear correlation was found (R = ?81%, P < 0.01). Young's modulus of each sample and the FD of its μCT images are correlated. From the assumption that cortical bone is approximately a fractal set, a non-linear constitutive relation involving FD is obtained for YM. Experimental results show good agreement with this constitutive relation. Additional parameters in the non-linear relation between YM and FD have been estimated from experimental results and related to physical parameters.     

Ultrastructure of human cerebral cortical synapses: age-specific aspects

The paper deals with electron microscopic studies of the cerebral cortex in human beings aged 70-80 years. The synapses show a decrease in the number of synaptic vesicles, their impaired distribution in the presynaptic process. There are changes in the mechanisms of interaction of synaptic vesicles and a presynaptic membrane. In the latter, the vesicles loose their discreteness, some of them are replaced by a fine-granular material. The joining of the vesicles and membrane is impaired. A part of active synaptic areas is transformed to desmose-like contacts. The findings are indicative of synaptic dysfunction.     

Respective roles of organic and mineral components of human cortical bone matrix in micromechanical behavior: an instrumented indentation study

Bone is a multiscale composite material made of both a type I collagen matrix and a poorly crystalline apatite mineral phase. Due to remodeling activity, cortical bone is made of Bone Structural Units (BSUs) called osteons. Since osteon represents a fundamental level of structural hierarchy, it is important to investigate the relationship between mechanical behavior and tissue composition at this scale for a better understanding of the mechanisms of bone fragility. The aim of this study is to analyze the links between ultrastructural properties and the mechanical behavior of bone tissue at the scale of osteon.Iliac bone biopsies were taken from untreated postmenopausal osteoporotic women, embedded, sectioned and microradiographed to assess the degree of mineralization of bone (DMB). On each section, BSUs of known DMB were indented with relatively high load (∼500 mN) to determine local elastic modulus (E), contact hardness (H_c) and true hardness (H) of several bone lamellae. Crystallinity and collagen maturity were measured by Fourier Transform InfraRed Microspectroscopy (FTIRM) on the same BSUs. Inter-relationships between mechanical properties and ultrastructural components were analyzed using multiple regression analysis.This study showed that elastic deformation was only explained by DMB whereas plastic deformation was more correlated with collagen maturity. Contact hardness, reflecting both elastic and plastic behaviors, was correlated with both DMB and collagen maturity. No relationship was found between crystallinity and mechanical properties at the osteon level.     

Histovariability in human clavicular cortical bone microstructure and its mechanical implications

The human clavicle (i.e. collarbone) is an unusual long bone due to its signature S‐shaped curve and variability in macrostructure observed between individuals. Because of the complex nature of how the upper limb moves, as well as due to its complex musculoskeletal arrangement, the biomechanics, in particular the mechanical loadings, of the clavicle are not fully understood. Given that bone remodeling can be influenced by bone stress, the histologic organization of Haversian bone offers a hypothesis of responses to force distributions experienced across a bone. Furthermore, circularly polarized light microscopy can be used to determine the orientation of collagen fibers, providing additional information on how bone matrix might organize to adapt to direction of external loads. We examined Haversian density and collagen fiber orientation, along with cross‐sectional geometry, to test whether the clavicle midshaft shows unique adaptation to atypical load‐bearing when compared with the sternal (medial) and acromial (lateral) shaft regions. Because fractures are most common at the midshaft, we predicted that the cortical bone structure would show both disparities in Haversian remodeling and nonrandomly oriented collagen fibers in the midshaft compared with the sternal and acromial regions. Human clavicles (n = 16) were sampled via thin‐sections at the sternal, middle, and acromial ends of the shaft, and paired sample t‐tests were employed to evaluate within‐individual differences in microstructural or geometric properties. We found that Haversian remodeling is slightly but significantly reduced in the middle of the bone. Analysis of collagen fiber orientation indicated nonrandom fiber orientations that are overbuilt for tensile loads or torsion but are poorly optimized for compressive loads throughout the clavicle. Geometric properties of percent bone area, polar second moment of area, and shape (I_max/I_min) confirmed the conclusions drawn by existing research on clavicle macrostructure. Our results highlight that mediolateral shape changes might be accompanied by slight changes in Haversian density, but bone matrix organization is predominantly adapted to resisting tensile strains or torsion throughout and may be a major factor in the risk of fracture when experiencing atypical compression.     

Similar damage initiation but different failure behavior in trabecular and cortical bone tissue

The mechanical properties of bone tissue are reflected in its micro- and nanostructure as well as in its composition. Numerous studies have compared the elastic mechanical properties of cortical and trabecular bone tissue and concluded that cortical bone tissue is stiffer than trabecular bone tissue. This study compared the progression of microdamage leading to fracture and the related local strains during this process in trabecular and cortical bone tissue. Unmachined single bovine trabeculae and similarly-sized cortical bovine bone samples were mechanically tested in three-point bending and concomitantly imaged to assess local strains using a digital image correlation technique. The bone whitening effect was used to detect microdamage formation and propagation. This study found that cortical bone tissue exhibits significantly lower maximum strains (trabecular 36.6%±14% vs. cortical 22.9%±7.4%) and less accumulated damage (trabecular 16100±8800 pix/mm2 vs. cortical 8000±3400 pix/mm2) at failure. However, no difference was detected for the maximum local strain at whitening onset (trabecular 5.8%±2.6% vs. cortical 7.2%±3.1%). The differences in elastic modulus and mineral distribution in the two tissues were investigated, using nanoindentation and micro-Raman imaging, to explain the different mechanical properties found. While cortical bone was found to be overall stiffer and more highly mineralized, no apparent differences were noted in the distribution of modulus values or mineral density along the specimen diameter. Therefore, differences in the mechanical behavior of trabecular and cortical bone tissue are likely to be in large part due to microstructural (i.e. orientation and distribution of cement lines) and collagen related compositional differences.     

Elastic anisotropy and off-axis ultrasonic velocity distribution in human cortical bone

Elastic structure in cortical bone is usually simplified as orthotropic or transversely isotropic, which allows estimates of three-dimensional technical constants from ultrasonic and density measurements. These elastic property estimates can then be used to study phenotypic changes in cortical bone structure and function, and to create finite element models of skeletal structures for studies of organismal variation and functional adaptation. This study examines assumptions of orthotropic or transversely isotropic material structure in cortical bone through the investigation of off-axis ultrasonic velocities in the cortical plane in 10 samples each from a human femur, mandible and cranium. Longitudinal ultrasonic velocities were measured twice through each bone sample by rotating the perimeter of each sample in 1 ° angular intervals between two ultrasonic transducers. The data were fit to sine curves f(x)=(A × sin(x + B) + C) and the goodness of fit was examined. All the data from the femur fit closely with the ideal sine curve model, and all three coefficients were similar among specimens, indicating similar elastic properties, anisotropies and orientations of the axes of maximum stiffness. Off-axis ultrasonic velocities in the mandible largely fit the sine curve model, although there were regional variations in the coefficients. Off-axis ultrasonic velocities from the cranial vault conformed to the sine curve model in some regions but not in others, which shows an irregular and complex pattern. We hypothesize that these variations in ultrasonic velocities reflect variations in the underlying bulk microstructure of the cortical bone, especially in the three-dimensional patterns of osteonal orientation and structure. Elastic property estimates made with ultrasonic techniques are likely valid in the femur and mandible; errors in estimates from cranial bone need to be evaluated regionally. Approximate orthotropic structure in bulk cortical bone specimens should be assessed if ultrasound is used to estimate three-dimensional elastic properties.