Micromechanics fracture in osteonal cortical bone: a study of the interactions between microcrack propagation, microstructure and the material properties

A two-dimensional micromechanical fibre reinforced composite materials model for osteonal cortical bone is presented. The interstitial bone is modelled as a matrix, the osteons are modelled as fibres, and the cement line is presented as interface tissue. The interaction between osteons and microcracks is evaluated by linear elastic fracture mechanics theory, followed by a determination of the stress intensity factor at the vicinity of the microcrack tips. The results indicate that bone microstructural heterogeneity greatly influences fracture parameters. Furthermore, microstructural morphology and loading conditions affect growth trajectories, the microcrack propagation trajectory deviates from the osteon under tensile loading, and osteon penetration is observed under compressive loads.     

Orientation of collagen at the osteocyte lacunae in human secondary osteons

This work characterizes an aspect of human bone micro-structure, pertinent to fracture initiation and arrest. It addresses how the orientation of elementary components proximate to osteocyte lacunae influences secondary osteon micro-biomechanics. New data at the perilacunar region concerning orientation of collagen-apatite, and prior data on collagen orientation outside the perilacunar region, are incorporated in a novel simulation of osteons to investigate how orientation relates to strains and stresses during mechanical testing. The perilacunar region was observed by confocal microscopy within single lamellar specimens, isolated from osteons. The specimens were separated by extinct or bright appearance in transverse section under circularly polarizing light. This is because synchrotron diffraction and confocal microscopy had established that each type, away from the perilacunar region, corresponds to specific dominant collagen orientation (extinct lamellae's dominant collagen forming small angles with the original osteon axis, while the bright lamellae's forms larger angles). Morphometry of serial confocal images of each perilacunar region showed collagen orientation generally following the orientation of canaliculi, circumambiently-perpendicular to the lacuna. The lacunae tilted relative to the lamellar walls were more numerous in extinct than in bright lamella. Their apices were less likely in extinct than bright lamella to show collagen following the canalicular orientation. The simulation of osteocyte lacunae in osteons, under tension or compression loading, supports the hypothesis that collagen orientation affects strains and stresses at the equatorial perilacunar region in conjunction with the presence of the lacuna. We further conjecture that collagen orientation diverts propagation of micro-cracks initiating from apices.     

Collagen fiber orientation and geometry effects on the mechanical properties of secondary osteons.

The effects of collagen fiber orientation and osteon geometry on the mechanical properties of secondary osteons under axial compression/tension and combined loadings (compression, bending and torsion) were investigated using a composite-beam finite-element model. Three cross-sectional shapes of secondary osteons were studied to show the effect of geometry. The results of stiffness are presented using the tension and compression properties for each lamella. The model shows that the mechanical properties of osteons are enhanced in bending and torsion when collagen fibers are oriented within 30 degrees of the loading axis. Osteons with alternating lamellar orientation are not well adapted to resist torsional moments, but alternate collagen fiber orientation has virtually no effect on the bending stiffness of osteons. Fiber orientation affects the mechanical properties less significantly when osteons are non-circular. Collagen fiber orientation and osteon geometry interact to determine the mechanical behavior of the osteon, and may act in a compensatory manner in the adaptive process.     

Scaling of Haversian canal surface area to secondary osteon bone volume in ribs and limb bones

Studies of secondary osteons in ribs have provided a great deal of what is known about remodeling dynamics. Compared with limb bones, ribs are metabolically more active and sensitive to hormonal changes, and receive frequent low‐strain loading. Optimization for calcium exchange in rib osteons might be achieved without incurring a significant reduction in safety factor by disproportionally increasing central canal size with increased osteon size (positive allometry). By contrast, greater mechanical loads on limb bones might favor reducing deleterious consequences of intracortical porosity by decreasing osteon canal size with increased osteon size (negative allometry). Evidence of this metabolic/mechanical dichotomy between ribs and limb bones was sought by examining relationships between Haversian canal surface area (BS, osteon Haversian canal perimeter, HC.Pm) and bone volume (BV, osteonal wall area, B.Ar) in a broad size range of mature (quiescent) osteons from adult human limb bones and ribs (modern and medieval) and various adult and subadult non‐human limb bones and ribs. Reduced major axis (RMA) and least‐squares (LS) regressions of HC.Pm/B.Ar data show that rib and limb osteons cannot be distinguished by dimensional allometry of these parameters. Although four of the five rib groups showed positive allometry in terms of the RMA slopes, nearly 50% of the adult limb bone groups also showed positive allometry when negative allometry was expected. Consequently, our results fail to provide clear evidence that BS/BV scaling reflects a rib versus limb bone dichotomy whereby calcium exchange might be preferentially enhanced in rib osteons. Am J Phys Anthropol 151:230–244, 2013. © 2013 Wiley Periodicals, Inc.     

Secondary osteon size and collagen/lamellar organization (“osteon morphotypes”) are not coupled,but potentially adapt independently for local strain mode or magnitude

In bone, matrix slippage that occurs at cement lines of secondary osteons during loading is an important toughening mechanism. Toughness can also be enhanced by modifications in osteon cross-sectional size (diameter) for specific load environments; for example, smaller osteons in more highly strained “compression” regions vs. larger osteons in less strained “tension” regions. Additional osteon characteristics that enhance toughness are distinctive variations in collagen/lamellar organization (i.e., “osteon morphotypes”). Interactions might exist between osteon diameter and morphotype that represent adaptations for resisting deleterious shear stresses that occur at the cement line. This may be why osteons often have a peripheral ring (or “hoop”) of highly oblique/transverse collagen. We hypothesized that well developed/distinct “hoops” are compensatory adaptations in cases where increased osteon diameter is mechanically advantageous (e.g., larger osteons in “tension” regions would have well developed/distinct “hoops” in order to resist deleterious consequences of co-existing localized shear stresses). We tested this hypothesis by determining if there are correlations between osteon diameters and strongly hooped morphotypes in “tension”, “compression”, and “neutral axis” regions of femora (chimpanzees, humans), radii (horse, sheep) and calcanei (horse, deer). The results reject the hypothesis—larger osteons are not associated with well developed/distinct “hoops”, even in “tension regions” where the effect was expected to be obvious. Although osteon diameter and morphotype are not coupled, osteon diameters seem to be associated with increased strain magnitudes in some cases, but this is inconsistent. By contrast, osteon morphotypes are more strongly correlated with the distribution of tension and compression.     

Mechanical hysteresis loops from single osteons: technical devices and preliminary results

The purpose of this paper is to describe an original apparatus for recording hysteresis loops from single osteons and a special microgrinding lathe for preparing osteonic samples for testing. The results obtained by testing isolated osteons, and composite bone samples ground to the same size as an osteon sample justify one to draw the following main conclusions: at an equal degree of calcification, longitudinal osteons show larger hysteresis loops under compression and alternate osteons show larger hysteresis loops under tension; there seems to be little chance of acquiring detailed information on the mechanical effects of osteon calcification recording hysteresis loops; collagen orientation in lamellae is the main factor determining the kind of hysteresis loops displayed by a composite bone sample.     

Distribution of osteonic and interstitial components in the human femoral shaft with reference to structure, calcification and mechanical properties

This paper analyzes the distribution of osteons and interstitial bone in the femoral compacta according to their structure, degree of calcification and mechanical properties. Three cross sections, 100 microns thick, each located 1 cm from the next, were prepared by grinding from the middle third of a human femoral shaft. Starting from the premise that, in lamellar bone, lamellae whose fiber bundles and crystallites have a longitudinal course withstand loading by tension, whereas those whose fiber bundles and crystallites have a transversal course withstand loading by compression, each osteon and fragment of interstitial bone has been given a number recording the percentage of its surface consisting of lamellae with transversally oriented fiber bundles and crystallites (bright under the polarizing microscope). The degree of calcification of the same structures was determined micro-radiographically. The distribution of both osteons and interstitial bone was assessed using a tungsten grid for reference. The total surface of each bone microstructure, and the percentage of that surface consisting of bright lamellae, were all calculated using a Zeiss Video-plan. Our results confirm the view that the distribution of both osteons and interstitial bone is mainly related to their structure--and hence to their mechanical properties. In addition, bone remodeling seems to be most active in areas capable of supporting tensile stress.     

Interfacial Strength of Cement Lines in Human Cortical Bone

In human cortical bone, cement lines (or reversal lines) separate osteons from the interstitial bone tissue, which consists of remnants of primary lamellar bone or fragments of remodeled osteons. There have been experimental evidences of the cement line involvement in the failure process of bone such as fatigue and damage. However, there are almost no experimental data on interfacial properties of cement lines in human cortical bone. The objective of this study is to design and assemble a precision and computer controlled osteon pushout microtesting system, and to experimentally determine the interfacial strength of cement lines in human cortical bone by performing osteon pushout tests. Thirty specimens were prepared from humeral diaphyses of four human subjects. Twenty specimens were tested under the condition of a small hole in the supporting plate, in which the cement line debonding occurred. The cement line interfacial strength ranged from 5.38 MPa to 10.85 MPa with an average of 7.31±1.73 MPa. On the other hand, ten specimens were tested under the condition of a large hole in the supporting plate, in which the shear failure inside osteons was observed. The specimens tested under the condition of the large hole resulted in an average shear strength of 73.71±15.06 MPa, ranging from 45.97 MPa to 93.74 MPa. Therefore, our results suggest that the cement line interface between osteon and interstitial bone tissue is weaker than that between bone tissue lamellae.     

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.     

Composition of the cement line and its possible mechanical role as a local interface in human compact bone

Human compact bone may be viewed as a fiber reinforced composite material in which the secondary osteons act as the fiber reinforcements. The cement line, which is the interface between the 'fibers' (osteons) and extraosteonal bone matrix, may impart important mechanical properties to compact bone. The nature of these properties is not known partly because the composition of the cement line is unknown. This analysis examines the constituents of the osteon cement line using scanning electron microscopy and X-ray microprobe analysis to address its biomechanical functions as a local interface. The analysis suggests that the cement line is a region of reduced mineralization which may contain sulfated mucosubstances. This composition is consistent with the hypothesis that the cement line provides a relatively ductile interface with surrounding bone matrix, and that it provides the point specific stiffness differences, poor 'fiber'-matrix bonding and energy transfer qualities required to promote crack initiation but slow crack growth in compact bone.     

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.     

An anatomical model for streaming potentials in osteons

An anatomical model for streaming potentials in osteons is developed to characterize the electromechanical effect in bone. The model accounts for the microstructure of the osteon and is based upon first principles of electrochemistry, electrokinetics, continuum mechanics and fluid dynamics. Intra-osteonal potentials and their relaxation times are numerically evaluated. Many of the previously reported observations of potentials in osteons and across macroscopic specimens are explained for the first time in terms of an electrokinetic model. The cusp-like behavior of intra-osteonal potentials is explained, the dependence of the potentials on solution viscosity and conductivity is demonstrated, and insight is gained relative to the time dependence of stress generated potentials.     

Patterns of femoral bone remodeling dynamics in a medieval Nubian population

The relationship between age, sex and histomorphometry in femoral cortical bone was examined in a skeletal population of late Medieval antiquity (AD 1250–1450) from Kulubnarti, in Sudanese Nubia. These skeletal remains are naturally mummified and in an excellent state of preservation. The study sample consisted of femoral cross sections from 24 females and 19 males ranging in age from 20 to 50+ years. Femoral cross sections were examined using an image analysis system. Numbers of secondary osteons and osteon fragments were counted, osteon area and Haversian canal area were measured, and several variables were calculated to assess differences between sexes and among age groups in bone remodeling variables. The results indicate significant differences between the sexes in osteon number and size. Males had significantly more intact osteons than females, whereas females had significantly larger osteons than males. Haversian canal dimensions were not statistically significant between the sexes. Sex differences in activity patterns in which males were involved in more physically strenuous tasks may have contributed to differences in remodeling variables. Interpopulational comparisons suggest that mechanical strain affects the microstructural features examined in this study. In particular, small Haversian canals in some archaeological skeletal populations are associated with higher bone volume, which may result from high levels of mechanical strain. Am J Phys Anthropol 104:133–146, 1997. © 1997 Wiley-Liss, Inc.     

Three-dimensional reconstruction of Haversian systems in ovine compact bone

Haversian systems or secondary osteons are an integral component of compact bone. However, as their exact shape is debatable, this study describes a technique to view their morphology in three dimensions. Bone remodeling in adult ovine long bones was labelled at intervals using a series of chelating fluorochromes. A series of longitudinal sections were cut at 25 microm intervals through blocks of the distal radius embedded in methylmethacrylate using a sledge macrotome. The chelating agents were used as markers of bone formation in the study of bone growth and osteon morphology. The two-dimensional image of each section was examined using an epifluorescence microscope. Images were transferred to a PC via a CCD low light colour video camera. Surface reference points were noted on each of the sections and, using computer software, a three-dimensional image of a refilling labelled osteon was reconstructed and its dimensions measured. Haversian systems may have a gentle spiral course along the longitudinal axis of the bone. They intertwine with adjacent osteons and give multiple branches along their course producing a complex pattern of organization. The mean labelled length and diameter of the osteons was 1.4 + 1 mm and 145 + 0.42 microm [Mean + S.D], respectively.     

Microstructure and nanomechanical properties in osteons relate to tissue and animal age

Material property changes in bone tissue with ageing are a crucial missing component in our ability to understand and predict age-related fracture. Cortical bone osteons contain a natural gradient in tissue age, providing an ideal location to examine these effects. This study utilized osteons from baboons aged 0-32 years (n=12 females), representing the baboon lifespan, to examine effects of tissue and animal age on mechanical properties and composition of the material. Tissue mechanical properties (indentation modulus and hardness), composition (mineral-to-matrix ratio, carbonate substitution, and crystallinity), and aligned collagen content (aligned collagen peak height ratio) were sampled along three radial lines in three osteons per sample by nanoindentation, Raman spectroscopy, and second harmonic generation microscopy, respectively. Indentation modulus, hardness, mineral-to-matrix ratio, carbonate substitution, and aligned collagen peak height ratio followed biphasic relationships with animal age, increasing sharply during rapid growth before leveling off at sexual maturity. Mineral-to-matrix ratio and carbonate substitution increased 12% and 6.7%, respectively, per year across young animals during growth, corresponding with a nearly 7% increase in stiffness and hardness. Carbonate substitution and aligned collagen peak height ratio both increased with tissue age, increasing 6-12% across the osteon radii. Indentation modulus most strongly correlated with mineral-to-matrix ratio, which explained 78% of the variation in indentation modulus. Overall, the measured compositional and mechanical parameters were the lowest in tissue of the youngest animals. These results demonstrate that composition and mechanical function are closely related and influenced by tissue and animal age.     

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.     

The effect of hydration on mechanical anisotropy,topography and fibril organization of the osteonal lamellae

The effect of hydration on the mechanical properties of osteonal bone, in directions parallel and perpendicular to the bone axis, was studied on three length scales: (i) the mineralized fibril level (~100 nm), (ii) the lamellar level (~6 µm); and (iii) the osteon level (up to ~30 µm).We used a number of techniques, namely atomic force microscopy (AFM), nanoindentation and microindentation. The mechanical properties (stiffness, modulus and/or hardness) have been studied under dry and wet conditions. On all three length scales the mechanical properties under dry conditions were found to be higher by 30–50% compared to wet conditions. Also the mechanical anisotropy, represented by the ratio between the properties in directions parallel and perpendicular to the osteon axis (anisotropy ratio, designated here by AnR), surprisingly decreased somewhat upon hydration. AFM imaging of osteonal lamellae revealed a disappearance of the distinctive lamellar structure under wet conditions. Altogether, these results suggest that a change in mineralized fibril orientation takes place upon hydration.     

Geometric determinants to cement line debonding and osteonal lamellae failure in osteon pushout tests

Cement lines are the boundaries between secondary osteons and the surrounding interstitial bone matrix in cortical bone. The interfacial properties of cement lines have been determined by osteon pushout tests. However, distinctively different material properties were obtained when osteon pushout tests were performed under different test geometries. In the present study, an axisymmetric two-dimensional finite element model was used to simulate an osteon pushout test using the test geometry of actual experiments. The results indicated that shear failure within the osteonal lamellae would occur when the osteon pushout test was performed under the condition of a thick specimen and large supporting hole. On the other hand, cement line debonding occurred when the osteon pushout test was performed using a thin specimen and small supporting hole. The finite element results were consistent with previous experiments of osteon pushout tests under different test geometries. Furthermore, the finite-element results suggest that a smoothly curved punch would most likely cause debonding at the cement line instead of osteonal lamellae.     

The bending properties of single osteons

The bending properties of two fully calcified osteon types (longitudinal and alternate) have been investigated in 62 cylindrical samples by applying the technique of three-point bending loading. The bending of each sample was recorded using a microwave micrometer based on the cavity and pulse technique. It has been shown that alternate osteons are better able to withstand bending stress than longitudinal ones. This result offers a definitive explanation for the high concentration of transverse lamellae in pathologically bowed bone shaft.     

Cortical bone failure mechanisms during screw pullout

An experimental and computational study of screw pullout from cortical bone has been conducted. A novel modification of standard pullout tests providing real time image capture of damage mechanisms during screw pullout was developed. Pullout forces, measured using the novel test rig, have been validated against standard pullout tests. Pullout tests were conducted, considering osteon alignment, to investigate the effect of osteons aligned parallel to the axis of the orthopaedic screw (longitudinal pullout) as well as the effect of osteons aligned perpendicular to the axis of the screw (transverse pullout). Distinctive alternate failure mechanisms, for longitudinally and transversely orientated cortical bone during screw pullout, were uncovered. Vertical crack propagation, parallel to the axis of the screw, was observed for a longitudinal pullout. Horizontal crack propagation, perpendicular to the axis of the screw, was observed for a transverse pullout. Finite element simulation of screw pullout, incorporating material damage and crack propagation, was also performed. Simulations revealed that a homogenous material model for cortical bone predicts vertical crack propagation patterns for both longitudinal and transverse screw pullout. A bi-layered composite model representing cortical bone microstructure was developed. A unique set of material and damage properties was used for both transverse and longitudinal pullout simulations, with only layer orientations being changed. Simulations predicted: (i) higher pullout forces for transverse pullout; (ii) horizontal crack paths perpendicular to screw axis for transverse pullout, whereas vertical crack paths were computed for longitudinal pullout. Computed results agreed closely with experimental observations in terms of pullout force and crack propagation.