Strain rate dependence of the mechanical properties of reindeer antler and the cumulative damage model of bone fracture

Carter and Caler have produced a 'cumulative damage' model for the fracture of bone, based on creep experiments on human bone, which has been corroborated by monotonic tensile tests on bone, loaded at various strain rates. Monotonic tensile tests on reindeer's antler, which has a lower modulus of elasticity than human bone, produce very similar results. Unlike human bone, reindeer antler always shows a large post-yield strain, and it is possible to distinguish pre-yield and post-yield behaviour. The 'final stiffness' (ultimate stress/ultimate strain) is invariant with strain rate. This is confirmation that bone fractures when a certain amount of damage has accumulated. However, reindeer antler shows a considerable post-yield increase in stress. This is difficult to accommodate in a cumulative damage model.     

Physical characteristics affecting the tensile failure properties of compact bone

Compact bone specimens from a wide variety of reptiles, birds, and mammals were tested in tension, and their failure properties related to mineral volume fraction, porosity and histological orientation. The principal findings were that the ultimate strain and the work under the stress-strain curve declined sharply with mineralisation, as did the stress and strain appearing after the specimen had yielded. Ultimate tensile strength was not simply related to any combination of the possible explanatory variables, but some relatively poorly mineralised bones, notably antlers, had high stresses at failure. These high strengths were allowed by a great increase in stress after the bones had yielded at quite low stresses.     

Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements

Fracture mechanics studies have characterized bone's resistance to fracture in terms of critical stress intensity factor and critical strain energy release rate measured at the onset of a fracture crack. This approach, although useful, provide a limited insight into fracture behavior of bone because, unlike classical brittle materials, bone is a microcracking solid that derives its resistance to fracture during the process of crack propagation from microfracture mechanisms occurring behind the advancing crack front. To address this shortfall, a crack propagation-based approach to measure bone toughness is described here and compared with crack initiation approach. Post hoc analyses of data from previously tested bovine and antler cortical bone compact specimens demonstrates that, in contrast to crack initiation approach, the crack propagation approach successfully identifies the superior toughness properties of red deer's antler cortical bone. Propagation-based slope of crack growth resistance curve is, therefore, a more useful parameter to evaluate cortical bone fracture toughness.     

Antler stiffness in moose (Alces alces): Correlated evolution of bone function and material properties?

The material properties of bone can vary considerably among skeletal elements from different parts of the body that serve different functions. However, functional demands placed on a specific type of skeletal element also can vary at a variety of scales, such as between different parts of the element, among individuals of a species, and across species. Variation in bone material properties might be correlated with differing functional demands at any of these scales. In this study we performed three-point bending tests on bone specimens extracted from antlers of moose (Alces alces) to test for three types of variation in bone material stiffness (Young's modulus): within the antler structure, between populations of moose, and between moose and other deer species. Because superficial portions of the antler are exposed to greater bending stress and strain than deeper portions, and because the antler beam (the basal shaft that attaches to the skull) is subjected to greater bending moments than more distal parts of the antler, we predicted that superficial bone and bone from the beam would be stiffer than bone from other parts of the antler. Instead, we identified no significant differences in these comparisons. There were also no significant differences in antler stiffness between moose from Michigan and the Yukon, even though the rapid growth required of antlers from northern latitudes like the Yukon has the potential to compromise bone material properties. However, moose have significantly stiffer antlers (11.6 +/- 0.45 GPa, mean +/- SE) than any other deer in the odocoileine lineage. Moreover, phylogenetic reconstructions of the evolution of antler stiffness in deer indicate a strong potential that high antler stiffness is a derived feature of moose. The unusual palmate shape of moose antlers likely subjects their antler beams to higher bending moments than found in other odocoileines, a factor that may have contributed to the evolutionary divergence of moose antler stiffness from that of other members of this clade. Although similarities in the mineral composition of bone across species likely limit the overall range of phylogenetic variation in bone material properties, our results demonstrate that evolutionary diversity in bone material properties can show correspondence with phylogenetic differences in mechanical or ecological demands on skeletal elements.     

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.     

Contribution, development and morphology of microcracking in cortical bone during crack propagation

A fracture mechanics study of cortical bone is presented to investigate the contribution, development morphology of microcracking in cortical bone during crack propagation. Post-hoc analyses of microcrack orientation, crack propagation velocity and fracture surface roughness were conducted on previously tested human and bovine bone compact tension specimens. It was found that, consistent with its higher toughness, bovine bone formed significantly more longitudinal, transverse and inclined microcracks than human bone. However, in human bone more of the microcracks that formed were longitudinal than transverse or inclined, a feature that would optimise bone's toughness. Crack propagation velocity in human and bovine bone displayed the same characteristic pattern with crack extension, where an increase in velocity is followed by a consequent decrease and vice versa. On the basis of this pattern, a model or crack propagation has been proposed. It provides a detailed account of mocrocrack formation and contribution towards the propagation of a fracture crack. Analyses of fracture surfaces indicated that, consistent with its higher toughness, bovine bone displays a rougher surface than human bone but they both have the same basic fractured element, i.e. a mineralised collagen fibril.     

Fracture mechanics of bone with short cracks

Tensile fracture experiments were performed upon specimens of wet mature bovine Haversian bone, with short, controlled notches. Stress concentration factors were found to be significantly less than values predicted using a maximum stress criterion in the theory of elasticity. Results were also modeled with the aid of linear elastic fracture mechanics. Agreement of experiment with theory was better in this case, however deviations were seen for short notches. Two mechanisms were evaluated for the behavior: plasticity near the crack tip, and effects of the Haversian microstructure, modelled by Cosserat elasticity, a generalized continuum theory. Plastic zone effects were found to be insignificant. Cosserat elasticity, by contrast, predicted stress concentration factors which better approximated observed values. To explore strain redistribution processes, further experiments were conducted upon notched specimens in torsion at small strain. They disclosed a strain redistribution effect consistent with Cosserat elasticity. These microelastic effects were attributed to the Haversian architecture of bone. The implications of the results are that bone resists the effect of stress raisers such as fatigue microcracks and surgical sawcuts to a much greater extent than anticipated on the basis of its elastic or elastoplastic properties.     

In vivo fatigue microcracks in human bone: material properties of the surrounding bone matrix

Human bones sustain fatigue damage in the form of in vivo microcracks as a result of the normal everyday loading activities. These microcracks appear to preferentially accumulate in certain regions of bone and most notably in interstitial bone matrix areas. These are remnants of old bone tissue left unremodelled, which show a higher than average mineral content and consequently the occurrence of microcracks has been attributed to the possible brittleness brought about by such hypermineralisation. There is a need, therefore, for information on the in situ bone matrix properties in the vicinity of such in vivo microcracks to elucidate the possible causes of their appearance. The present study examined the elastic, strain rate (viscous) and plastic properties of bone matrix in selectively targeted areas by nanoindentation and in both quasistatic and dynamic mode. The results showed that in vivo crack areas are not as stiff as some well-known extremely mineralised and brittle bone examples (bulla, rostrum); the strain rate effects of crack regions were identical to those of other regions of human bone and agreed well with values collected for human bone in the past at the macroscale; while the plasticity index of the crack regions was also not statistically different from most bone examples (including human at random, bovine, bulla and rostrum) except antler, which showed lower plasticity and thus a greater fraction of elastic recovery in indentation energy. It is difficult, therefore, to explain the susceptibility of these interstitial regions to crack in terms of the mineral content and its after-effects on elasticity, viscosity and plasticity alone, but one need to attribute the cracks to the cumulative loading history of these areas, or raise the suggestion that these areas of bone matrix are in some measure 'aged' or material/quality defective.     

Analysis of creep strain during tensile fatigue of cortical bone

During fatigue tests of cortical bone specimens, at the unload portion of the cycle (zero stress) non-zero strains occur and progressively accumulate as the test progresses. This non-zero strain is hypothesised to be mostly, if not entirely, describable as creep. This work examines the rate of accumulation of this strain and quantifies its stress dependency. A published relationship determined from creep tests of cortical bone (Journal of Biomechanics 21 (1988) 623) is combined with knowledge of the stress history during fatigue testing to derive an expression for the amount of creep strain in fatigue tests. Fatigue tests on 31 bone samples from four individuals showed strong correlations between creep strain rate and both stress and "normalised stress" (sigma/E) during tensile fatigue testing (0-T). Combined results were good (r(2)=0.78) and differences between the various individuals, in particular, vanished when effects were examined against normalised stress values. Constants of the regression showed equivalence to constants derived in creep tests. The universality of the results, with respect to four different individuals of both sexes, shows great promise for use in computational models of fatigue in bone structures.     

Influence of the change in stem length on the load transfer and bone remodelling for a cemented resurfaced femur

The effect of a short-stem femoral resurfacing component on load transfer and potential failure mechanisms has rarely been studied. The stem length has been reduced by approximately 50% as compared to the current long-stem design. Using 3-D FE models of natural and resurfaced femurs, the study is aimed at investigating the influence of a short-stem resurfacing component on load transfer and bone remodelling. Applied loading conditions include normal walking and stair climbing. The mechanical role of the stem along with implant–cement and stem–bone contact conditions was observed to be crucial. Shortening the stem length to half of the current length (long-stem) led to several favourable effects, even though the stress distributions in the implant and the cement were similar in both the cases. The short-stem implant led not only to a more physiological stress distribution but also to bone apposition (increase of 20–70% bone density) in the superior resurfaced head, when the stem–bone contact prevailed. This also led to a reduction in strain concentration in the cancellous bone around the femoral neck–component junction. The normalised peak strain in this region was lower for the short-stem design as compared to that of the long-stem one, thereby reducing the initial risk of neck fracture. The effect of strain shielding (50–75% reduction) was restricted to a small bone volume underlying the cement, which was approximately half of that of the long-stem design. Consequently, bone resorption was considerably less for the short-stem design. The short-stem design offers better prospects than the long-stem resurfacing component.     

Compressive strength of mandibular bone as a function of microstructure and strain rate

An investigation has been made of the compressive strength of the porcine mandible and its depedence upon microstructure and strain rate. The results are compared with the fracture behavior of bovine femoral bone. Regarding microstructural dependence, it was found that fracture behavior depends upon regularity of structure, morphology of subunits, orientation of lamellae with respect to the stress axis, amount of ground substance, density and mineral content. Fracture mode was found to be a strong function of strain rate. For both porcine mandibular and bovine femoral bone, there is a ductile-to-brittle transition which results in a change of strain rate sensitivity coefficient from 0.1 to 0.0 at the transition region. This is corroborated by a large change in work-to-fracture values at this region. Therefore, the existence of a critical velocity for bone is supported by the present data.     

A phenomenological model for predicting fatigue life in bovine trabecular bone

Cyclic loading of bone during daily activities can lead to fatigue degradation and increased risk of fracture in both the young and elderly population. Damage processes under cyclic loading in trabecular bone result in the reduction of the elastic modulus and accumulation of residual strain. These effects increase with increasing stress levels, leading to a progressive reduction in fatigue life. The present work analyzes the effect of stress and strain variation on the above damage processes in bovine trabecular bone, and develops a phenomenological model relating fatigue life to the imposed stress level. The elastic modulus reduction of the bone specimens was observed to depend on the maximum compressive strain, while the rate of residual strain accumulation was a function of the stress level. A model was developed for the upper and lower bounds of bone elastic modulus reduction with increasing number of cycles, at each stress range. The experimental observations were described well by the model. The model predicted the bounds of the fatigue life with change in fatigue stress. The decrease in the fatigue life with increasing stress was related to corresponding increases in the residual strain accumulation rates at the elevated stress levels. The model shows the validity of fatigue predictions from relatively few cyclic experiments, by combining trends observed in the monotonic and the cyclic tests. The model also presents a relatively simple procedure for predicting the endurance limit for bovine trabecular bone specimens.     

A role for retinoic acid in regulating the regeneration of deer antlers

Deer antlers are the only mammalian organs that can be repeatedly regenerated; each year, these complex structures are shed and then regrow to be used for display and fighting. To date, the molecular mechanisms controlling antler regeneration are not well understood. Vitamin A and its derivatives, retinoic acids, play important roles in embryonic skeletal development. Here, we provide several lines of evidence consistent with retinoids playing a functional role in controlling cellular differentiation during bone formation in the regenerating antler. Three receptors (alpha, beta, gamma) for both the retinoic acid receptor (RAR) and retinoid X receptor (RXR) families show distinct patterns of expression in the growing antler tip, the site of endochondral ossification. RAR alpha and RXR beta are expressed in skin ("velvet") and the underlying perichondrium. In cartilage, which is vascularised, RXR beta is specifically expressed in chondrocytes, which express type II collagen, and RAR alpha in perivascular cells, which also express type I collagen, a marker of the osteoblast phenotype. High-performance liquid chromatography analysis shows significant amounts of Vitamin A (retinol) in antler tissues at all stages of differentiation. The metabolites all-trans-RA and 4-oxo-RA are found in skin, perichondrium, cartilage, bone, and periosteum. The RXR ligand, 9-cis-RA, is found in perichondrium, mineralised cartilage, and bone. To further define sites of RA synthesis in antler, we immunolocalised retinaldehyde dehydrogenase type 2 (RALDH-2), a major retinoic acid-generating enzyme. RALDH-2 is expressed in the skin and perichondrium and in perivascular cells in cartilage, although chondroprogenitors and chondrocytes express very low levels. At sites of bone formation, differentiated osteoblasts which express the bone-specific protein osteocalcin express high levels of RALDH2. The effect of RA on antler cell differentiation was studied in vitro; all-trans-RA inhibits expression of the chondrocyte phenotype, an effect that is blocked by addition of the RAR antagonist Ro41-5253. In monolayer cultures of mesenchymal progenitor cells, all-trans-RA increases the expression of alkaline phosphatase, a marker of the osteoblastic phenotype. In summary, this study has shown that antler tissues contain endogenous retinoids, including 9-cis RA, and the enzyme RALDH2 that generates RA. Sites of RA synthesis in antler correspond closely with the localisation of cells which express receptors for these ligands and which respond to the effects of RA.     

Fracture-toughening mechanisms responsible for differences in work to fracture of hydrated and dehydrated dentine

This study investigates the nature of deformation and differences in the mechanisms of fracture and properties of dentine where there has been a loss of moisture, as may occur with removal of the pulp in the endodontic treatment of teeth. Controlled fracture toughness testing was conducted on bovine teeth to determine the influence of hydration on the work of fracture of dentine. Significant differences (p<0.01) were observed between the fracture toughness of hydrated (554+/-27.7J/m2) and dehydrated (113+/-17.8J/m2) dentine. Observations of the crack tip region during crack extension revealed extensive ligament formation occurred behind the crack tip. These ligaments provide considerable stability to the crack by significantly increasing the work of fracture, thereby acting as a fracture-toughening mechanism. Micro-cracking, reported as a fracture-toughening mechanism in bone, is also clearly seen. A zone of in-elastic deformation may occur as hydrated specimens revealed upon crack extension, a region about the tip that appeared to suck water into the structure and to exude water behind the crack tip. In dehydrated dentine, no in-elastic zone was observed. Micro-cracking is present though the cracks are smaller, straighter and with less opening than hydrated dentine. Only limited ligament formation just behind the crack tip was observed. These differences resulted in a significantly lower work of fracture with unstable brittle fracture characteristics. Based on these results, several fracture-toughening mechanisms were identified in dentine, with micro-cracking not considered the most important. These findings may be relevant for bone, a similar mineralised hydrated tissue.     

Patient specific quantitative analysis of fracture fixation in the proximal femur implementing principal strain ratios. Method and experimental validation

Computational patient-specific modeling has the potential to yield powerful information for selection and planning of fracture treatments if it can be developed to yield results that are rapid, focused and coherent from a clinical perspective. In this study we introduce the utilization of a principal strain fixation ratio measure (SR) defined as the ratio of principal strains that develop in a fixated bone relative to the principal strains that develop in the same bone in an intact state. The SR field output variable is theoretically independent of load amplitude and also has a direct clinical interpretation with SR<1?a representing stress shielding and SR>1+b representing overstressed bone. A combined experimental and numerical study was performed with cadaveric proximal femora (n=6) intact and following fracture fixation to quantify the performance of the SR variable in terms of accuracy and sensitivity to uncertainties in density–elasticity relationships and load amplitude as model input variables. For a given axial compressive force the SR field output variable was found to be less sensitive to changes in density–elasticity relationships and the response function to be more accurate than strain values themselves; errors were reduced by 44% on comparing SR with strain in the fixated model. In addition, the experimental data confirmed the assumption that the SR values behave independent of load amplitude. The load independent behavior of SR and its direct clinical interpretation may ultimately provide an appropriate and easily understood comparative computational measure to choose between patient specific fracture fixation alternatives.     

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.     

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.     

Perforation of cancellous bone trabeculae by damage-stimulated remodelling at resorption pits: a computational analysis

Loss of trabeculae in cancellous bone is often attributed to a general decline in the bone mass leading to fracture of the thin trabeculae. It has never been investigated whether trabecular perforation may have any other biomechanical mechanism. In this paper, an alternative hypothesis is proposed and tested using a computational model. Taking it as given that osteoclastic resorption is targeted to microdamage, it is hypothesised that the creation of a resorption cavity during normal bone remodelling could cause a stress-concentration in the bone tissue. If the resorption cavities were excessively deep, as is seen during osteoporosis, then this stress concentration may be sufficient to generate more microdamage so that osteoclasts "chase" newly formed damage leading to perforation. If this were true then we should find that, for a given trabecular thickness, there is a critical depth of resorption cavity such that smaller cavities refill whereas deeper cavities cause microdamage accumulation, continued osteoclast activity, and eventual trabecular perforation. Computer simulation is used to test this hypothesis. Using a remodelling stimulus calculated from both strain and damage and a simplified finite element model of a trabeculum with cavities of different sizes, it is predicted that such a critical depth of resorption cavity does indeed exist. Therefore we suggest that an increase in resorption depth relative to the thickness of trabeculae may be responsible for trabecular perforation during osteoporosis, rather than simply trabecular fracture due to insufficient strength.     

Heterogeneity of the mechanical properties of demineralized bone

Knowledge of the mechanical properties of the collagenous component of bone is required for composite modeling of bone tissue and for understanding the age- and disease-related reductions in the ductility and strength of bone. The overall goal of this study was to investigate the heterogeneity of the mechanical properties of demineralized bone which remains unexplained and may be due to differences in the collagen structure or organization or in experimental protocols. Uniaxial tension tests were conducted to measure the elastic and failure properties of demineralized human femoral (n = 10) and tibial (n = 13) and bovine humeral (n = 8) and tibial (n = 8) cortical bone. Elastic modulus differed between groups (p = 0.02), varying from 275 +/- 94 MPa (mean +/- SD) to 450 + 50 MPa. Similarly, ultimate stress varied across groups from 15 + 4.2 to 26 + 4.7 MPa (p = 0.03). No significant differences in strain-to-failure were observed between any groups in this study (pooled mean of 8.4 +/- 1.6%; p = 0.42). However, Bowman et al. (1996) reported an average ultimate strain of 12.3 +/- 0.5% for demineralized bovine humeral bone, nearly 40% higher than our value. Taken together, it follows that all the monotonic mechanical properties of demineralized bone can display substantial heterogeneity. Future studies directed at explaining such differences may therefore provide insight into aging and disease of bone tissue.