Scaling effects in the fatigue strength of bones from different animals

The bones of vertebrates are all made from the same basic material, despite a huge variation in size from one species to another. This introduces a problem: large structures are more prone to fatigue failure (stress fracture) than smaller structures made of the same material. This implies that bones in larger animals cannot withstand as much stress in daily use as bones in smaller animals. In fact, this is not the case, because all bones experience approximately the same stresses and strains in use. This implies a variation in the underlying material: bone material in large animals must have superior fatigue properties to offset the disadvantages of size. This hypothesis is tested here by reference to fatigue data from the literature, taken from a range of animals from cows to mice. Fatigue strength was plotted as a function of stressed volume and modelled mathematically using a Weibull distribution. This shows a general tendency for fatigue strength to reduce as volume increases. But when the volume effect is taken into account, there remains a tendency for bones from smaller animals to have lower fatigue strength. This can be modelled by a simple variation in one of the parameters in the Weibull equation, which defines the intrinsic fatigue strength of the material. When extrapolated to the size of the whole bone for each animal, all bones were found to have the same fatigue strength. This resolves the anomaly and implies a complex system in which the underlying structure of bone varies with animal size in order to cancel out scaling effects.     

Fracture toughness and fatigue crack propagation rate of short fiber reinforced epoxy composites for analogue cortical bone

Third-generation mechanical analogue bone models and synthetic analogue cortical bone materials manufactured by Pacific Research Laboratories, Inc. (PRL) are popular tools for use in mechanical testing of various orthopedic implants and biomaterials. A major issue with these models is that the current third-generation epoxy-short fiberglass based composite used as the cortical bone substitute is prone to crack formation and failure in fatigue or repeated quasistatic loading of the model. The purpose of the present study was to compare the tensile and fracture mechanics properties of the current baseline (established PRL "third-generation" E-glass-fiber-epoxy) composite analogue for cortical bone to a new composite material formulation proposed for use as an enhanced fourth-generation cortical bone analogue material. Standard tensile, plane strain fracture toughness, and fatigue crack propagation rate tests were performed on both the third- and fourth-generation composite material formulations using standard ASTM test techniques. Injection molding techniques were used to create random fiber orientation in all test specimens. Standard dog-bone style tensile specimens were tested to obtain ultimate tensile strength and stiffness. Compact tension fracture toughness specimens were utilized to determine plane strain fracture toughness values. Reduced thickness compact tension specimens were also used to determine fatigue crack propagation rate behavior for the two material groups. Literature values for the same parameters for human cortical bone were compared to results from the third- and fourth-generation cortical analogue bone materials. Tensile properties of the fourth-generation material were closer to that of average human cortical bone than the third-generation material. Fracture toughness was significantly increased by 48% in the fourth-generation composite as compared to the third-generation analogue bone. The threshold stress intensity to propagate the crack was much higher for the fourth-generation material than for the third-generation composite. Even at the higher stress intensity threshold, the fatigue crack propagation rate was significantly decreased in the fourth-generation composite compared to the third-generation composite. These results indicate that the bone analogue models made from the fourth-generation analogue cortical bone material may exhibit better performance in fracture and longer fatigue lives than similar models made of third-generation analogue cortical bone material. Further fatigue testing of the new composite material in clinically relevant use of bone models is still required for verification of these results. Biomechanical test models using the superior fourth-generation cortical analogue material are currently in development.     

Effects of the basic multicellular unit and lamellar thickness on osteonal fatigue life

A remodeling cycle sets the size of the osteon and associated lamellae in the basic multicellular unit. Treatments and aging affect these micro-structural features. We previously demonstrated decreased fatigue life with an unexplained mechanism and decreased osteon size in cortical bone treated with high-dose bisphosphonate. Here, three finite element models were examined: type-1: a single osteon, as a homogeneous unit and with heterogeneous lamellae and interlamellae, type-2: a control, interstitial-only tissue and type-3: the osteon with cement line, set within the interstitial tissue. Models were loaded in simulated, sinusoidal bending fatigue. As osteon size was decreased, lamellar number and lamellar thickness were incrementally adjusted for each model. As hypothesized, lamellae within the larger type-1 models attained greater cycles to failure and the addition of an osteon to type-2 models (generating a type-3 model set) yielded increased fatigue life. However, as the osteon size was decreased, the potential for compressive damage nucleation was increased within the lamellae of the osteons versus the interstitium. Also, osteons with fewer, thicker lamellae displayed increased fatigue life. Osteonal microstructure plays a role in damage initiation location, especially when BMU size is smaller. Previous findings by us and others could partially be explained by this further understanding of increased probability for damage nucleation in smaller osteons.     

Do microcracks decrease or increase fatigue resistance in cortical bone?

Fatigue of cortical bone produces microcracks; it has been hypothesized that these cracks are analogous to those occurring in engineered composite materials and constitute a similar mechanism for fatigue resistance. However, the numbers of these linear microcracks increase substantially with age, suggesting that they contribute to increased fracture incidence among the elderly. To test these opposing hypotheses, we fatigued 20 beams of femoral cortical bone from elderly men and women in load-controlled four point bending having initial strain ranges of 3000 or 5000 microstrain. Loading was stopped at fracture or 10(6) cycles, whichever occurred first, and microcrack density and length were measured in the loaded region and in a control region that was not loaded. We studied the dependence of fatigue life and induced microdamage on initial microdamage, cortical region, subject gender and age, and several other variables. When the effect of modulus variability was controlled, longer fatigue life was associated with higher rather than lower initial crack density, particularly in the medial cortex. The increase in crack density following fatigue loading was greater in specimens from older individuals and those initially having longer microcracks. Crack density increased as much in specimens fatigued short of the failure point as in those that fractured, and microcracks were, on average, shorter in specimens with greater numbers of resorption spaces, a measure of remodeling rate.     

Damage rate is a predictor of fatigue life and creep strain rate in tensile fatigue of human cortical bone samples

We present results on the growth of damage in 29 fatigue tests of human femoral cortical bone from four individuals, aged 53-79. In these tests we examine the interdependency of stress, cycles to failure, rate of creep strain, and rate of modulus loss. The behavior of creep rates has been reported recently for the same donors as an effect of stress and cycles. In the present paper we first examine how the evolution of damage (drop in modulus per cycle) is associated with the stress level or the "normalized stress" level (stress divided by specimen modulus), and results show the rate of modulus loss fits better as a function of normalized stress. However, we find here that even better correlations can be established between either the cycles to failure or creep rates versus rates of damage than any of these three measures versus normalized stress. The data indicate that damage rates can be excellent predictors of fatigue life and creep strain rates in tensile fatigue of human cortical bone for use in practical problems and computer simulations.     

Influence of phase angle between axial and torsional loadings on fatigue fractures of bone

Fatigue fractures of cortical bone involve combined axial-torsional loading yet it is unknown how the relationship between axial and torsional loadings affects the fatigue behavior of bone. In this study the effect of superimposing in-phase and out-of-phase torsional on axial loading on the fatigue behavior of bone was investigated by conducting in vitro tests involving 0 degrees and 90 degrees phase shift between cyclic torsional and axial loadings. Results obtained indicate that fatigue life, patterns of moduli loss, microcracking and modes of fractures are dependent on the phase angle between axial and torsional loadings. Specimens subjected to in-phase torsional on axial loading demonstrated greater mixed mode interaction, underwent proportionate stiffness losses in tension, compression, and torsion, and consequently had a shorter fatigue life. In contrast, specimens subjected to out-of-phase loading regime displayed a smaller contribution of mixed mode failure, underwent a disproportionately large stiffness loss in torsion, and had a longer fatigue life. Furthermore, increase in phase angle provided additional planes on which damage was diffused delaying the final failure. Change in phase angle, seen in vivo during a number of physiological activities including walking, running and sprinting, will therefore affect fatigue behavior and contribute to pathogenesis of fatigue fractures.     

Near-terminal creep damage does not substantially influence fatigue life under physiological loading

Cortical bone specimens were damaged using repeated blocks of tensile creep loading until a near-terminal amount of creep damage was generated (corresponding to a reduction in elastic modulus of 15%). One group of cortical bone specimens was submitted to the near-terminal damage protocol and subsequently underwent fatigue loading in tension with a maximum strain of 2000 με (Damage Fatigue, n=5). A second group was submitted to cyclic fatigue loading but was not pre-damaged (Control Fatigue, n=5). All but one specimen (a damaged specimen) reached run-out (10 million cycles, 7.7 days). No significant differences in microscopic cracks or other tissue damage were observed between the two groups or between either group and additional, completely unloaded specimens. Our results suggest that damage in cortical bone allograft that is not obvious or associated with a stress riser may not substantially affect its fatigue life under physiologic loading.     

Fatigue of bovine trabecular bone

Fatigue loading of bone, from the activities of daily living in the elderly, or from prolonged exercise in the young, can lead to increased risk of fracture. Elderly patients with osteoporosis are particularly prone to fragility fractures of the vertebrae, where load is carried primarily by trabecular bone. In this study, specimens of bovine trabecular bone were loaded in compressive fatigue at four different normalized stresses to one of six maximum strains. The resulting change in modulus and residual strain accumulation were measured over the life of the fatigue test. The number of cycles to reach a given maximum compressive strain increased with decreasing normalized stress. Modulus reduction and specimen residual strain increased with increasing maximum compressive strain, but few differences were observed between specimens loaded to the same maximum strain at different normalized stresses.     

Analysis of crack growth in a 3D Voronoi structure: a model for fatigue in low density trabecular bone

Both creep and crack growth contribute to the reduction in modulus associated with fatigue loading in bone. Here we simulate crack growth and subsequent strut failure in fatigue in an open-cell, three-dimensional Voronoi structure which is similar to that of low density, osteoporotic bone. The model indicates that sequential failure of struts leads to a precipitous drop in modulus: the failure of 1% of the struts leads to about a 10% decrease in modulus. A parametric study is performed to assess the influence of normalized stress range, relative density, initial crack size, crack shape and cell geometry on the fatigue life. The fatigue life is most sensitive to the relative density and the initial crack length. The results lead to a quantitative expression for the fatigue life associated with crack growth. Data for the fatigue life of trabecular bone are compared with the crack growth model described in this paper as well as with a previous model for creep of a three-dimensional Voronoi structure. In our models, creep dominates the fatigue behavior in low cycle fatigue while crack growth dominates in high cycle fatigue, consistent with previous observations on cortical bone. The large scatter in the trabecular bone fatigue data make it impossible to identify a transition between creep dominated fatigue and crack growth dominated fatigue. The parametric study of the crack growth model indicates that variations in relative density among specimens, initial crack size within trabeculae and crack shape could easily produce such variability in the test results.     

A comparison of the fatigue behavior of human trabecular and cortical bone tissue

The fatigue properties of trabecular bone tissue (single trabeculae) and similarly sized cortical bone specimens from human tibia were experimentally determined on a microstructural level using four-point bending cyclic tests, and they were compared based on modulus, mineral density, and microstructural characteristics. The results showed that trabecular specimens had significantly lower moduli and lower fatigue strength than cortical specimens, despite their higher mineral density values. Fracture surface and microdamage analyses illustrated different fracture and damage patterns between trabecular and cortical bone tissue, depending upon their microstructural characteristics. Based on the results from mechanical tests and qualitative observations, a possible mechanical role of the cement lines in trabecular tissue microfracture was suggested.     

Compressive fatigue behavior of human vertebral trabecular bone

Damage accumulation under compressive fatigue loading is believed to contribute significantly to non-traumatic, age-related vertebral fractures in the human spine. Only few studies have explored trabecular bone fatigue behavior under compressive loading and none examined the influence of trabecular architecture on fatigue life. In this study, trabecular bone samples of human lumbar and thoracic vertebrae (4 donors from age 29 to 86, n=29) were scanned with a microCT system prior to compressive fatigue testing to determine morphology-mechanical relationships for this relevant loading mode. Inspired from previous fabric-based relationships for elastic properties and quasi-static strength of trabecular bone, a simple power relationship between volume fraction, fabric eigenvalue, applied stress and the number of cycles to failure is proposed. The experimental results demonstrate a high correlation for this relationship (R2=0.95) and detect a significant contribution of the degree of anisotropy towards prediction of fatigue life. Step-wise regression for total and residual strains at failure suggested a weak, but significant correlation with volume fraction. From the obtained results, we conclude that the applied stress normalized by volume fraction and axial fabric eigenvalue can estimate fatigue life of human vertebral trabecular bone in axial compressive loading.     

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.     

The fatigue strength of compact bone in torsion

We have conducted a series of fatigue tests on samples of bovine compact bone loaded in cyclic torsion. The fatigue strength (i.e. the range of stress needed to cause failure in a given number of cycles) was found to be lower than the fatigue strength of the same material in compression by more than a factor of two. We also tested intact chicken metatarsals and found a similar reduction in strength compared to compression testing of chicken tibiae. These results were predicted using a theoretical model in which fatigue failure was assumed to be dependent on the growth of microcracks, oriented approximately parallel to the bone's longitudinal axis but having misorientation angles of up to 30 degrees. An effective stress range was derived which is a function of the normal and shear stresses, and thus of the Mode I and Mode II stress intensities experienced by the crack. These results may have important consequences for the understanding of fatigue in bone in vivo; relatively small amounts of longitudinal shear stress, which are often ignored in analysis, may contribute significantly to fatigue failures. This may shed light on the phenomenon of stress fractures and on the need for repair and adaptation in living bone.     

Three‐dimensional characterization of osteocyte volumes at multiple scales,and its relationship with bone biology and genome evolution in ray‐finned fishes

Osteocytes, cells embedded within the bone mineral matrix, inform on key aspects of vertebrate biology. In particular, a relationship between volumes of the osteocytes and bone growth and/or genome size has been proposed for several tetrapod lineages. However, the variation in osteocyte volume across different scales is poorly characterized and mostly relies on incomplete, two‐dimensional information. In this study, we characterize the variation of osteocyte volumes in ray‐finned fishes (Actinopterygii), a clade including more than half of modern vertebrate species in which osteocyte biology is poorly known. We use X‐ray synchrotron micro‐computed tomography (SRµCT) to achieve a three‐dimensional visualization of osteocyte lacunae and direct measurement of their size (volumes). Our specimen sample is designed to characterize variation in osteocyte lacuna morphology at three scales: within a bone, among the bones of one individual and among species. At the intra‐bone scale, we find that osteocyte lacunae vary noticeably in size between zones of organized and woven bone (being up to six times larger in woven bone), and across cyclical bone deposition. This is probably explained by differences in bone deposition rate, with larger osteocyte lacunae contained in bone that deposits faster. Osteocyte lacuna volumes vary 3.5‐fold among the bones of an individual, and this cannot readily be explained by variation in bone growth rate or other currently observable factors. Finally, we find that genome size provides the best explanation of variation in osteocyte lacuna volume among species: actinopterygian taxa with larger genomes (polyploid taxa in particular) have larger osteocyte lacunae (with a ninefold variation in median osteocyte volume being measured). Our findings corroborate previous two‐dimensional studies in tetrapods that also observed similar patterns of intra‐individual variation and found a correlation with genome size. This opens new perspectives for further studies on bone evolution, physiology and palaeogenomics in actinopterygians, and vertebrates as a whole.     

Fatigue of immature baboon cortical bone

Strain-controlled uniaxial fatigue and monotonic tensile tests were conducted on turned femoral cortical bone specimens obtained from baboons at various ages of maturity. Fatigue loading produced a progressive loss in stiffness and an increase in hysteresis prior to failure, indicating that immature primate cortical bone responds to repeated loading in a fashion similar to that previously observed for adult human cortical bone. Bone fatigue resistance under this strain controlled testing decreased during maturation. Maturation was also associated with an increase in bone dry density, ash fraction and elastic modulus. The higher elastic modulus of more mature bone meant that these specimens were subjected to higher stress levels during testing than more immature bone specimens. Anatomical regions along the femoral shaft exhibited differences in strength and fatigue resistance.     

The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus

The elastic moduli of human subchondral, trabecular, and cortical bone tissue from a proximal tibia were experimentally determined using three-point bending tests on a microstructural level. The mean modulus of subchondral specimens was 1.15 GPa, and those of trabecular and cortical specimens was 4.59 GPa and 5.44 GPa respectively. Significant differences were found in the modulus values between bone tissues, which may have mainly resulted from the differences in the microstructures of each bone tissue rather than in the mineral density. Furthermore, the size-dependency of the modulus was examined using eight different sizes of cortical specimens (heights h = 100-1000 microns). While the modulus values for relatively large specimens (h greater than 500 microns) remained fairly constant (approximately 15 GPa), the values decreased as the specimens became smaller. A significant correlation was found between the modulus and specimen size. The surface area to volume ratio proved to be a key variable to explain the size-dependency.     

Detection of fatigue microdamage in whole rat femora using contrast-enhanced micro-computed tomography

Microdamage in bone tissue is typically studied using destructive, two-dimensional histological techniques. Contrast-enhanced micro-computed tomography (micro-CT) was recently demonstrated to enable non-destructive, three-dimensional (3-D) detection of microdamage in machined cortical and trabecular bone specimens in vitro. However, the accumulation of microdamage in whole bones is influenced by variations in the magnitude and mode of loading due to the complex whole bone morphology. Therefore, the objective of this study was to detect the presence, spatial location, and accumulation of fatigue microdamage in whole rat femora in vitro using micro-CT with a BaSO₄ contrast agent. Microdamage was detected and observed to accumulate at specific spatial locations within the cortex of femora loaded in cyclic three-point bending to a 5% or 10% reduction in secant modulus. The ratio of the segmented BaSO₄ stain volume (SV) to the total volume (TV) of cortical bone was adopted as a measure of damage. The amount of microdamage measured by micro-CT (SV/TV) was significantly greater for both loaded groups compared to the control group (p<0.05), but the difference between loaded groups was not statistically significant. At least one distinct region of microdamage, as indicated by the segmented SV, was observed in 85% of loaded specimens. A specimen-specific finite element model confirmed elevated tensile principal strains localized in regions of tissue corresponding to the accumulated microdamage. These regions were not always located where one might expect a priori based upon Euler–Bernoulli beam theory, demonstrating the utility of contrast-enhanced micro-CT for non-destructive, 3-D detection of fatigue microdamage in whole bones in vitro.     

Dependence of mechanical compressive strength on local variations in microarchitecture in cancellous bone of proximal human femur

Human cancellous bone is a heterogeneous material. Despite this, most of the published studies report correlations between mechanical properties and morphometric parameters averaged on the whole specimen. This work investigated whether local variations in morphometric parameters were linked to the localized failure regions of cancellous bone. Additionally, it was examined whether local values of morphometric parameters can predict the ultimate stress better than the average bone volume fraction (BV/TV). Cylindrical cancellous bone specimens extracted along the primary compressive group of human femoral heads were studied. These were microCT-imaged to assess the morphometric parameters, compressed to determine the ultimate stress, and rescanned by microCT to visualize the failure region. Failure involved slightly less than half of the free height of the specimens. Significant differences were found in the morphometric parameters calculated in the failure and in the non-failure regions. The cross-sections containing minimum BV/TV values were those most often located inside the failure region (83%, p<0.001). Regression analysis confirmed that variations in BV/TV best describe variations in ultimate stress (R2=0.84) out of the averaged morphometric parameters. The prediction of ultimate stress increased when minimum or maximum values of the morphometric parameters were taken, with the highest prediction found by considering the minimum BV/TV (R2=0.95). In conclusion, due to the heterogeneity of cancellous bone, there may exist regions characterized by a different microarchitecture, where the bone is weaker and consequently is more likely to fail. These regions mostly contain minimum values in BV/TV, which were found to predict ultimate stress better than average BV/TV.     

Micro-finite element simulation of trabecular-bone post-yield behaviour – effects of material model,element size and type

Micro-finite element (micro-FE) analysis became a standard tool for the evaluation of trabecular bone mechanical properties. The accuracy of micro-FE models for linear analyses is well established. However, the accuracy of recently developed nonlinear micro-FE models for simulations of trabecular bone failure is not known. In this study, a trabecular bone specimen was compressed beyond the apparent yield point. The experiment was simulated using different micro-FE meshes with different element sizes and types, and material models based on cortical bone. The results from the simulations were compared with experimental results to study the effects of the different element and material models. It was found that a decrease in element size from 80 to 40 μm had little effect on predicted post-yield behaviour. Element type and material model had significant effects. Nevertheless, none of the established material models for cortical bone were able to predict the typical descent in the load-displacement curve seen during compression of trabecular bone.     

Micro-finite element simulation of trabecular-bone post-yield behaviour--effects of material model, element size and type

Micro-finite element (micro-FE) analysis became a standard tool for the evaluation of trabecular bone mechanical properties. The accuracy of micro-FE models for linear analyses is well established. However, the accuracy of recently developed nonlinear micro-FE models for simulations of trabecular bone failure is not known. In this study, a trabecular bone specimen was compressed beyond the apparent yield point. The experiment was simulated using different micro-FE meshes with different element sizes and types, and material models based on cortical bone. The results from the simulations were compared with experimental results to study the effects of the different element and material models. It was found that a decrease in element size from 80 to 40 mum had little effect on predicted post-yield behaviour. Element type and material model had significant effects. Nevertheless, none of the established material models for cortical bone were able to predict the typical descent in the load-displacement curve seen during compression of trabecular bone.