Volume effects on fatigue life of equine cortical bone

Materials, including bone, often fail due to loading in the presence of critical flaws. The relative amount, location, and interaction of these flaws within a stressed volume of material play a role in determining the failure properties of the structure. As materials are generally imperfect, larger volumes of material have higher probabilities of containing a flaw of critical size than do smaller volumes. Thus, larger volumes tend to fail at fewer cycles compared with smaller volumes when fatigue loaded to similar stress levels. A material is said to exhibit a volume effect if its failure properties are dependent on the specimen volume. Volume effects are well documented in brittle ceramics and composites and have been proposed for bone. We hypothesized that (1) smaller volumes of cortical bone have longer fatigue lives than similarly loaded larger volumes and (2) that compared with microstructural features, specimen volume was able to explain comparable amounts of variability in fatigue life. In this investigation, waisted rectangular specimens (n=18) with nominal cross-sections of 3×4 mm and gage lengths of 10.5, 21, or 42 mm, were isolated from the mid-diaphysis of the dorsal region of equine third metacarpal bones. These specimens were subjected to uniaxial load controlled fatigue tests, with an initial strain range of 4000 microstrain. The group having the smallest volume exhibited a trend of greater log fatigue life than the larger volume groups. Each volume group exhibited a significant positive correlation between the logarithm of fatigue life and the cumulative failure probability, indicating that the data follow the two-parameter Weibull distribution. Additionally, log fatigue life was negatively correlated with log volume, supporting the hypothesis that smaller stressed volumes of cortical bone possess longer fatigue lives than similarly tested larger stressed volumes.     

Osteon interfacial strength and histomorphometry of equine cortical bone

The interfacial strength of secondary osteons from the diaphysis of the Thoroughbred equine third metacarpal was evaluated using the fiber pushout test. The pushout was performed on 300-500 microm sections of 4x4x15 mm bone blocks machined from four anatomic regions of the cortex. Pushout strength was evaluated from proximal to distal location within the diaphysis on four osteon types classified under polarized light on adjacent histologic sections from each block. The shear strength of the interfaces were estimated from shear lag theory. Differences were found in the interfacial strength of osteons based on appearance under polarized light with bright field having the highest interfacial strength (40.3 MPa). The lowest strength was found in the dark field osteons (22.8 MPa). The dorsal region had the highest shear strength and toughness compared to all other regions. The cement line and interlamellar interfaces are similar in strength, but exhibit regional dependence--specifically, the palmar region strength is less (17.5 MPa) than the osteon interlamellar interfaces (30.4 MPa) and osteon type dependent (alternating significantly weaker than other types). Histomorphometry revealed significant regional differences (p<0.0001) in osteon area fraction among the four osteon types as well as differences in the osteon diameter (p=0.01), with dorsal regions having larger osteons (170 microm) than the palmar region (151 microm). Fatigue life and fracture toughness of Haversian bone are reported in the literature to be regionally dependent and are known to be associated with osteon pullout--an osteon interfacial phenomenon. Therefore, the results presented in this study are important to further the understanding of the mechanisms of fragility and damage accumulation in cortical bone.     

Advances in the fracture mechanics of cortical bone

As cortical bone is a semi-brittle solid, its fracture is dependent not only on the magnitude of the applied stress, but also on the nature of any intrinsic or introduced cracks. Consequently a variety of fracture mechanics techniques have been utilised to evaluate the fracture toughness of cortical bone, including the single edge notched, centre notched cylindrical and compact tension methods, and values have been established for the critical stress intensity factor (Kc) and the critical strain energy release rate (Gc). The Kc and Gc values obtained depend on the orientation of the cortical bone, as well as on bone density, the velocity of crack propagation and specimen geometry. The significance of these fracture mechanics parameters for cortical bone is critically reviewed.     

Measurement of the microstructural fracture toughness of cortical bone using indentation fracture

The purpose of this work is to investigate the use of indentation fracture as a method of measuring toughness at the microscale in cortical bone. Indentation fracture employs sharp indenters to initiate cracks, whose length can be used to calculate the toughness of the material. Only a cube corner indenter tip is found to initiate cracks at a suitable size scale for microstructural measurement. Cracks from 7 to 56 microm in length are produced using loads from 0.05 to 3N. Preliminary data predicts rising toughness with increasing crack length (rising R-curve behaviour) at the microscale. This technique provides a new insight into fracture in cortical bone since it allows the investigator to observe mechanisms and measure toughness at a size scale at which in vivo damage is known to exist.     

Equine cortical bone exhibits rising R-curve fracture mechanics

Previous studies of the fracture properties of cortical bone have suggested that the fracture toughness increases with crack length, which is indicative of rising R-curve behavior. Based on this indirect evidence and the similarity of bone to ceramic matrix composites, we hypothesized that bone would exhibit rising R-curve behavior in the transverse orientation and that the characteristics of the R-curves would be regionally dependent within the cortex due to variations in bone microstructure and toughening mechanisms. To test these hypotheses, we conducted R-curve experiments on specimens from equine third metacarpal bones using standard fracture mechanics testing methods. Compact type specimens from the dorsal and lateral regions in the middle of the diaphysis were oriented for crack propagation transverse to the longitudinal axis of the bone.The test results demonstrate that equine cortical bone exhibits rising R-curve behavior during transverse crack propagation as hypothesized. Statistical analyses of the crack growth initiation toughness, K0, the peak toughness, Kpeak, and the crack extension at peak toughness, deltaa, revealed significant regional differences in these characteristics. Specifically, the lateral cortex displayed higher crack growth initiation and peak toughnesses. The dorsal cortex exhibited greater crack extension at the peak of crack growth resistance. Scanning electron microscopy revealed osteon pullout on fracture surfaces from the dorsal cortex and but not in the lateral cortex. Taken together, the significant differences in R-curves and the SEM fractography indicate that the fracture mechanisms acting in equine cortical bone are regionally dependent.     

Orientation dependence of the fracture mechanics of cortical bone

The fracture mechanics parameter of the critical stress intensity factor (Kc) was determined by a modified compact tension test method, for the fracture of bovine tibia cortical bone at orientations of 0 degrees, 15 degrees, 30 degrees, 45 degrees, 75 degrees and 90 degrees to the bone axis. It was established that, for a given loading rate, a variation in orientation from 0-90 degrees produced average increases in Kc from 3.2 to 6.5 MN m-3/2.     

A mechanostatistical approach to cortical bone remodelling: an equine model

In this study, the development of a mechanostatistical model of three-dimensional cortical bone remodelling informed with in vivo equine data is presented. The equine model was chosen as it is highly translational to the human condition due to similar Haversian systems, availability of in vivo bone strain and biomarker data, and furthermore, equine models are recommended by the US Federal Drugs Administration for comparative joint research. The model was derived from micro-computed tomography imaged specimens taken from the equine third metacarpal bone, and the Frost-based ‘mechanostat’ was informed from both in vivo strain gauges and biomarkers to estimate bone growth rates. The model also described the well-known ‘cutting cone’ phenomena where Haversian canals tunnel and replace bone. In order to make this model useful in practice, a partial least squares regression (PLSR) surrogate model was derived based on training data from finite element simulations with different loads. The PLSR model was able to predict microstructure and homogenised Young’s modulus with errors less than 2.2 % and \(0.6\,\% \), respectively.     

Mineralized collagen fibril network spatial arrangement influences cortical bone fracture behavior

Bone is a hierarchical material exhibiting different fracture mechanisms at each length scale. At the submicroscale, the bone is composed of mineralized collagen fibrils (MCF). At this scale, the fracture processes in cortical bone have not been extensively studied in the literature. In this study, the influence of MCF size and orientation on the fracture behavior of bone under both transverse and longitudinal loading was investigated using novel 3D models of MCF networks with explicit representation of extra-fibrillar matrix. The simulation results showed that separation between MCFs was the main cause of damage and failure under transverse loading whereas under longitudinal loading, the main damage and failure mechanism was MCF rupture. When the MCF network was loaded in the transverse direction the mechanical properties increased as the orientation of fibrils deviated farther from the main fibril orientation whereas the opposite trend was observed under longitudinal loading. The fracture energy was much larger in longitudinal than transverse loading. MCF diameter variation did not affect the mechanical properties under longitudinal loading but led to higher mechanical properties with increasing MCF diameter under transverse loading. The new modeling framework established in this study generate unique information on the effect of MCF network spatial arrangement on the fracture behavior of bone at the submicroscale which is not currently possible to measure via experiments. This unique information may improve the understanding of how structural alterations at the submicroscale due to disease, age-related changes, and treatments affect the fracture processes at larger length scales.     

Fracture in human cortical bone: local fracture criteria and toughening mechanisms

Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in "hard" mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack-microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.     

WNT16 influences bone mineral density, cortical bone thickness, bone strength, and osteoporotic fracture risk

We aimed to identify genetic variants associated with cortical bone thickness (CBT) and bone mineral density (BMD) by performing two separate genome-wide association study (GWAS) meta-analyses for CBT in 3 cohorts comprising 5,878 European subjects and for BMD in 5 cohorts comprising 5,672 individuals. We then assessed selected single-nucleotide polymorphisms (SNPs) for osteoporotic fracture in 2,023 cases and 3,740 controls. Association with CBT and forearm BMD was tested for ～2.5 million SNPs in each cohort separately, and results were meta-analyzed using fixed effect meta-analysis. We identified a missense SNP (Thr>Ile; rs2707466) located in the WNT16 gene (7q31), associated with CBT (effect size of -0.11 standard deviations [SD] per C allele, P = 6.2 × 10(-9)). This SNP, as well as another nonsynonymous SNP rs2908004 (Gly>Arg), also had genome-wide significant association with forearm BMD (-0.14 SD per C allele, P = 2.3 × 10(-12), and -0.16 SD per G allele, P = 1.2 × 10(-15), respectively). Four genome-wide significant SNPs arising from BMD meta-analysis were tested for association with forearm fracture. SNP rs7776725 in FAM3C, a gene adjacent to WNT16, was associated with a genome-wide significant increased risk of forearm fracture (OR = 1.33, P = 7.3 × 10(-9)), with genome-wide suggestive signals from the two missense variants in WNT16 (rs2908004: OR = 1.22, P = 4.9 × 10(-6) and rs2707466: OR = 1.22, P = 7.2 × 10(-6)). We next generated a homozygous mouse with targeted disruption of Wnt16. Female Wnt16(-/-) mice had 27% (P<0.001) thinner cortical bones at the femur midshaft, and bone strength measures were reduced between 43%-61% (6.5 × 10(-13)相似文献   

Ultrasound speed in equine cortical bone: effects of orientation, density, porosity and temperature

Ultrasound speed, as measured by a transmission technique in equine cortical bone, was found to vary markedly with the direction of the ultrasound path through the bone. Using bone samples from the mid-site of the third metacarpus of 20 horses, the ultrasound speed was measured as 4125 m s-1 in the longitudinal direction, 3442 m s-1 in the circumferential or transverse direction, and 3428 m s-1 in the radial direction. These results confirm the anisotropic properties of compact bone. Ultrasound speed had a positive linear relationship when compared with bone specific gravity of cortical bone (r = 0.773, n = 35, p less than 0.0001), and an inverse linear relationship with porosity. Specific gravity has an inverse correlation with porosity (r = 0.857, n = 35, p less than 0.0001). Over the temperature range of 4-42 degrees C, ultrasound speed varied inversely according to temperature with a logarithmic function giving the best fit. These results have important implications for the clinical applications of ultrasound speed in assessing bone quality in racehorses and provide important basic information for the understanding of the passage of ultrasound through cortical bone, which has possible clinical applications in humans.     

Deformation behaviour and damage accumulation of cortical bone specimens from the equine tibia under cyclic loading

Despite its clinical importance, the fatigue behaviour of cortical bone has not been examined as widely as its static behaviour. In the present study, specimens from the tibiae of horses have been subjected to load-controlled single step tests. The cyclic deformation behaviour was described by the development of stress-strain hysteresis parameters over the lifetime. The fatigue behaviour of bone is characterised by cyclic softening which is most distinctive towards the end of the lifetime. The microstructural damage accumulated during cyclic loading results in a loss of stiffness, asymmetrical deformation of the bone in tension and compression in cyclic creep. As shown by light and scanning electron microscopy, microcrack formation and growth is the main damage mechanism. The crack growth behaviour is strongly influenced by the microstructure, the stress components and the absolute value of the local stresses. Lower local stresses and/or compressive mean stresses lead to a dominant influence of the shear stress components with shear failure at inner interfaces. With increasing crack length, that is, higher local stress amplitudes, or tensile mean stresses, the microstructure is more and more ignored and failure occurs primarily under the influence of the normal stress components. This can be clearly seen on the fracture and specimen surfaces.     

The effects of testing methods on the flexural fatigue life of human cortical bone

A flexural model of four-point bending fatigue that has been experimentally validated for human cortical bone under load control was used to determine how load and displacement control testing affects the fatigue behavior of human cortical bone in three-point and symmetric four-point bending. Under load control, it was predicted that three-point bending produced no significant differences in fatigue life when compared to four-point bending. However, three-point bending produced less stiffness loss with increasing cycles than four-point bending. In four-point bending, displacement control was predicted to produce about one and a half orders of magnitude greater fatigue life when compared to load control. This prediction agrees with experimental observations of equine cannon bone tested in load and displacement control (Gibson et al., 1998). Displacement controlled three-point bending was found to produce approximately a 25% greater fatigue life when compared to load control. The prediction of longer fatigue life under displacement control may have clinical relevance for the repair of damaged bone. The model can also be adapted to other geometric configurations, including modeling of whole long bones, and with appropriate fatigue data, other cortical bone types.     

Nanoindentation testing and finite element simulations of cortical bone allowing for anisotropic elastic and inelastic mechanical response

Anisotropy is one of the most peculiar aspects of cortical bone mechanical behaviour, and the numerical approach can be successfully used to investigate aspects of bone tissue mechanics that analytical methods solve in approximate way or do not cover. In this work, nanoindentation experimental tests and finite element simulations were employed to investigate the elastic-inelastic anisotropic mechanical properties of cortical bone. The model allows for anisotropic elastic and post-yield behaviour of the tissue. A tension-compression mismatch and direction-dependent yield stresses are allowed for. Indentation experiments along the axial and transverse directions were simulated with the purpose to predict the indentation moduli and hardnesses along multiple orientations. Results showed that the experimental transverse-to-axial ratio of indentation moduli, equal to 0.74, is predicted with a ～3% discrepancy regardless the post-yield material behaviour; whereas, the transverse-to-axial hardness ratio, equal to 0.86, can be correctly simulated (discrepancy ～6% w.r.t. the experimental results) only employing an anisotropic post-elastic constitutive model. Further, direct comparison between the experimental and simulated indentation tests evidenced a good agreement in the loading branch of the indentation curves and in the peak loads for a transverse-to-axial yield stress ratio comparable to the experimentally obtained transverse-to-axial hardness ratio. In perspective, the present work results strongly support the coupling between indentation experiments and FEM simulations to get a deeper knowledge of bone tissue mechanical behaviour at the microstructural level. The present model could be used to assess the effect of variations of constitutive parameters due to age, injury, and/or disease on bone mechanical performance in the context of indentation testing.     

Assessment of cortical bone fracture resistance curves by fusing artificial neural networks and linear regression

Bone injures (BI) represents one of the major health problems, together with cancer and cardiovascular diseases. Assessment of the risks associated with BI is nontrivial since fragility of human cortical bone is varying with age. Due to restrictions for performing experiments on humans, only a limited number of fracture resistance curves (R-curves) for particular ages have been reported in the literature. This study proposes a novel decision support system for the assessment of bone fracture resistance by fusing various artificial intelligence algorithms. The aim was to estimate the R-curve slope, toughness threshold and stress intensity factor using the two input parameters commonly available during a routine clinical examination: patients age and crack length. Using the data from the literature, the evolutionary assembled Artificial Neural Network was developed and used for the derivation of Linear regression (LR) models of R-curves for arbitrary age. Finally, by using the patient (age)-specific LR models and diagnosed crack size one could estimate the risk of bone fracture under given physiological conditions. Compared to the literature, we demonstrated improved performances for estimating nonlinear changes of R-curve slope (R² = 0.82 vs. R² = 0.76) and Toughness threshold with ageing (R² = 0.73 vs. R² = 0.66).     

Simple constitutive model for a cortical bone

This short study presents a simple, one-dimensional constitutive model for the cortical bone with haversian structure. The model is developed within the general framework of the continuum damage theory. The kinetic equation is derived (rather than assumed a priori) through consideration of the irreversible changes of the mesostructure. As a consequence the analytical results closely approximate experimental measurements even though the theory does not introduce a single experimentally unidentifiable material parameter.     

The relative contributions of non-enzymatic glycation and cortical porosity on the fracture toughness of aging bone

The risk of fracture increases with age due to the decline of bone mass and bone quality. One of the age-related changes in bone quality occurs through the formation and accumulation of advanced glycation end-products (AGEs) due to non-enzymatic glycation (NEG). However as a number of other changes including increased porosity occur with age and affect bone fragility, the relative contribution of AGEs on the fracture resistance of aging bone is unknown. Using a high-resolution nonlinear finite element model that incorporate cohesive elements and micro-computed tomography-based 3d meshes, we investigated the contribution of AGEs and cortical porosity on the fracture toughness of human bone. The results show that NEG caused a 52% reduction in propagation fracture toughness (R-curve slope). The combined effects of porosity and AGEs resulted in an 88% reduction in propagation toughness. These findings are consistent with previous experimental results. The model captured the age-related changes in the R-curve toughening by incorporating bone quantity and bone quality changes, and these simulations demonstrate the ability of the cohesive models to account for the irreversible dynamic crack growth processes affected by the changes in post-yield material behavior. By decoupling the matrix-level effects due to NEG and intracortical porosity, we are able to directly determine the effects of NEG on fracture toughness. The outcome of this study suggests that it may be important to include the age-related changes in the material level properties by using finite element analysis towards the prediction of fracture risk.