Impact of the porous microstructure on the overall elastic properties of the osteonal cortical bone

Mechanical properties of bones are largely determined by their microstructure. The latter comprises a large number of diverse pores. The present paper analyzes a connection between structure of the porous space of the osteonal cortical bone and bone's overall anisotropic elastic moduli. The analysis is based on recent developments in the theory of porous materials that predict the anisotropic effective moduli of porous solids in terms of pores' shapes, orientations and densities. Bone's microstructure is modeled using available micrographs. The calculated anisotropic elastic constants for porous cortical bone are, mostly, in agreement with available experimental data. The influence of each of the pore types on the overall moduli is examined. The results of the analysis can also be used to estimate the extent of mineralization (hydroxyapatite content) if the overall porosity and the effective moduli are known and, vice versa, to estimate porosity from the measured moduli and the extent of mineralization.     

Age-related properties at the microscale affect crack propagation in cortical bone

The increased risk for fracture with age is associated not only with reduced bone mass but also with impaired bone quality. At the microscale, bone quality is related to porosity, microstructural organization, accumulated microdamage and intrinsic material properties. However, the link between these characteristics and fracture behavior is still missing. Bone tissue has a complex structure and as age-related compositional and structural changes occur at all hierarchical length scales it is difficult to experimentally identify and discriminate the effect of each mechanism. The aim of this study was therefore to use computational models to analyze how microscale characteristics in terms of porosity, intrinsic toughness properties and microstructural organization affect the mechanical behavior of cortical bone. Tensile tests were simulated using realistic microstructural geometries based on microscopy images of human cortical bone. Crack propagation was modelled using the extended finite element method where cement lines surrounding osteons were modelled with an interface damage law to capture crack deflections along osteon boundaries. Both increased porosity and impaired material integrity resulted in straighter crack paths with cracks penetrating osteons, similar to what is seen experimentally for old cortical bone. However, only the latter predicted a more brittle failure behavior. Furthermore, the local porosity influenced the crack path more than the macroscopic porosity. In conclusion, age-related changes in cortical bone affect the crack path and the mechanical response. However, increased porosity alone was not driving damage in old bone, but instead impaired tissue integrity was required to capture brittle failure in aging bone.     

Material heterogeneity,microstructure, and microcracks demonstrate differential influence on crack initiation and propagation in cortical bone

The recent studies have shown that long-term bisphosphonate use may result in a number of mechanical alterations in the bone tissue including a reduction in compositional heterogeneity and an increase in microcrack density. There are limited number of experimental and computational studies in the literature that evaluated how these modifications affect crack initiation and propagation in cortical bone. Therefore, in this study, the entire crack growth process including initiation and propagation was simulated at the microscale by using the cohesive extended finite element method. Models with homogeneous and heterogeneous material properties (represented at the microscale capturing the variability in material property values and their distribution) as well as different microcrack density and microstructure were compared. The results showed that initiation fracture resistance was higher in models with homogeneous material properties compared to heterogeneous ones, whereas an opposite trend was observed in propagation fracture resistance. The increase in material heterogeneity level up to 10 different material property sets increased the propagation fracture resistance beyond which a decrease was observed while still remaining higher than the homogeneous material distribution. The simulation results also showed that the total osteonal area influenced crack propagation and the local osteonal area near the initial crack affected the crack initiation behavior. In addition, the initiation fracture resistance was higher in models representing bisphosphonate treated bone (low material heterogeneity, high microcrack density) compared to untreated bone models (high material heterogeneity, low microcrack density), whereas an opposite trend was observed at later stages of crack growth. In summary, the results demonstrated that tissue material heterogeneity, microstructure, and microcrack density influenced crack initiation and propagation differently. The findings also elucidate how possible modifications in material heterogeneity and microcrack density due to bisphosphonate treatment may influence the initiation and propagation fracture resistance of cortical bone.     

Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.     

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.     

A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone

Targeted remodeling is activated by fatigue microcracks and plays an important role in maintaining bone integrity. It is widely believed that fluid flow-induced shear stress plays a major role in modulating the mechanotransduction process. Therefore, it is likely that fluid flow-induced shear stress plays a major role in the initiation of the repair of fatigue damage. Since no in vivo measurements of fluid flow within bone exist, computational and mathematical models must be employed to investigate the fluid flow field and the shear stress occurring within cortical bone. We developed a computational fluid dynamic model of cortical bone to examine the effect of a fatigue microcrack on the fluid flow field. Our results indicate that there are alterations in the fluid flow field as far as 150 microm away from the crack, and that at distances farther than this, the fluid flow field is similar to the fluid flow field of intact bone. Through the crack and immediately above and below it, the fluid velocity is higher, while at the lateral edges it is lower than that calculated for the intact model, with a maximum change of 29%. Our results suggest that the presence of a fatigue microcrack can alter the shear stress in regions near the crack. These alterations in shear stress have the potential to significantly alter mechanotransduction and may play a role in the initiation of the repair of fatigue microcracks.     

Quantitative associations between osteocyte density and biomechanics, microcrack and microstructure in OVX rats vertebral trabeculae

Osteocytes actively regulate bone modeling and remodeling, direct skeletal mineralization, and regulate calcium/phosphate homeostasis and extracellular matrix metabolism; yet the specific role of osteocytes in maintaining bone structural integrity and strength is unknown. Studies have shown that the density of osteocytes decreases with age and estrogen deficiency, as seen in postmenopausal women. Here, we examined the relationships between osteocyte density and the related variables, including biomechanics, bone mineral density, microcrack and microstructure of vertebral trabeculae, in ovariectomized rats. We found that osteocyte density correlated with some of the parameters that determine the biomechanical quality of bone. Our findings suggest that osteocytes could play a crucial role in maintaining the mechanical quality of bone, and osteocyte density could be considered as an alternative index in assessing bone quality.     

Ash content modulation of torsionally derived effective material properties in cortical mouse bone

The purpose of this study was to evaluate the effects of isolated alterations in mineral content on mouse bone torsional properties. The femora and tibiae from 25 eight-week-old male A/J strain mice were divided into five groups and selectively decalcified from 5% to 20%. The right femora were then tested to failure in torsion while the tibiae were ashed to determine final mineral content of the decalcified bones. Contralateral femora were serially cross-sectioned to determine geometric properties, and effective material properties were then calculated from the geometric and structural properties of each femoral pair. We found that the relationship between ash content and effective shear modulus or maximum effective shear stress could best be characterized through a power law, with an exponential factor of 6.79 (R2 = 0.85) and 4.04 (R2 = 0.67), respectively. This indicates that in a murine model, as with other species, small changes in ash content significantly influence effective material properties. Furthermore, it appears that (in adolescent A/J strain mice) effective shear modulus is more heavily affected by changes in mineralization than is maximum effective shear stress when these properties are derived from whole bone torsional tests to failure.     

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.     

Dependence of ultrasonic attenuation on bone mass and microstructure in bovine cortical bone

The development of the axial transmission technique now enables in vivo evaluation of cortical bone quality, which plays an important role in bone fragility. Cortical bone is a complex multiscale material, which may be made of different types of microstructure. The interaction between ultrasound and cortical bone remains unclear and most studies have been confined to wave speed analysis. The first aim of this study is to investigate the dependence of the frequency-dependent attenuation on the type of bone microstructure. The second goal is to determine whether broadband ultrasonic attenuation (BUA) is related to volumetric bone mineral density (vBMD) and mass density. Parallelepipedic samples of bovine cortical bone were cut from three specimens and tested in the axial, radial and tangential directions using an ultrasonic transmission device. BUA was evaluated over a 1-MHz wide bandwidth around 4MHz. In addition, the microstructure of each sample was determined using an optical microscope. BUA values measured in porotic microstructure are significantly higher than in Haversian microstructure. The lowest BUA values are obtained for plexiform microstructure. For all structures, BUA in the axial direction is significantly smaller than in the radial and tangential directions. Moreover, BUA is correlated with both vBMD and density (determination coefficient (R2) equal to 0.44 and 0.65, respectively, in the axial direction). BUA variations can be explained by scattering and viscoelastic mechanisms. This study suggests that BUA measurements have the potential to discriminate among different cortical bone microstructures in addition to providing material properties.     

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.     

Experimental and analytical study of anisotropic strength properties of bovine cortical bone

Biomechanics and Modeling in Mechanobiology - This paper is focused on specification of conditions at failure in bovine cortical bone. Both experimental and analytical studies are conducted. The...     

An investigation of the interactions between lower-limb bone morphology,limb inertial properties and limb dynamics

Bone mass and size clearly affect the safety and survival of wild animals as well as human beings, however, little is known about the interactions between bone size and movement dynamics. A modeling approach was used to investigate the hypothesis that increased bone cortical area causes increased limb moments of inertia, decreased lower-limb movement maximum velocities, and increased energy requirements to sustain submaximum lower-limb locomotion movements. Custom software and digital data of a human leg were used to simulate femur, tibia, and fibula cortical bone area increases of 0%, 22%, 50%, and 80%. Limb segment masses, center of mass locations, and moments of inertia in the sagittal plane were calculated for each bone condition. Movement simulations of unloaded running and cycling motions were performed. Linear regression analyses were used to determine the magnitude of the effect cortical area has on limb moment of inertia, velocity, and the internal work required to move the limbs at a given velocity. The thigh and shank moment of inertia increased linearly up to 1.5% and 6.9%, respectively for an 80% increase in cortical area resulting in 1.3% and 2.0% decreases in maximum unloaded cycling and running velocities, respectively, and in 3.0% and 2.9% increases in internal work for the cycling and running motions, respectively. These results support the hypothesis and though small changes in movement speed and energy demands were observed, such changes may have played an important role in animal survival as bones evolved and became less robust.     

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

     

Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.     

A review of the biomechanical properties of bone as a material

Experimental studies on bone all reveal important difficulties in data interpretation. This paper proposes an analysis of experimental studies performed so far, with particular attention to the anisotropic characteristics of bone, its behaviour in the post-elastic phase, and its dependence on viscoelastic phenomena. Mechanical properties are also correlated with variables such as moisture, deformation rate during testing, density, variations in different regions of the bone, and the most relevant strength criteria are recalled. The investigation performed is also intended to provide an evaluation of the degree of refinement of biomechanical experimental data for use in a numerical approach to bone mechanics.     

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.     

Spatial distribution of tissue level properties in a human femoral cortical bone

The mechanical properties of cortical bone are determined by a combination bone tissue composition, and structure at several hierarchical length scales. In this study the spatial distribution of tissue level properties within a human femoral shaft has been investigated. Cylindrically shaped samples (diameter: 4.4mm, N=56) were prepared from cortical regions along the entire length (20-85% of the total femur length), and around the periphery (anterior, medial, posterior and lateral quadrants). The samples were analyzed using scanning acoustic microscopy (SAM) at 50MHz and synchrotron radiation micro computed tomography (SRμCT). For all samples the average cortical porosity (Ct.Po), tissue elastic coefficients (c(ij)) and the average tissue degree of mineralization (DMB) were determined. The smallest coefficient of variation was observed for DMB (1.8%), followed by BV/TV (5.4%), c(ij) (8.2-45.5%), and Ct.Po (47.5%). Different variations with respect to the anatomical position were found for DMB, Ct.Po and c(ij). These data address the anatomical variations in anisotropic elastic properties and link them to tissue mineralization and porosity, which are important input parameters for numerical multi-scale bone models.