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.     

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.     

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.     

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.     

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.     

The role of the lamellar interface during torsional yielding of human cortical bone

Fragility fractures are a result of alterations in bone quantity, tissue properties, applied loads, or a combination of these factors. The current study addresses the contribution of cortical bone tissue properties to skeletal fragility by characterizing the shear damage accumulation processes which occur during torsional yielding in normal bone. Samples of human femoral cortical bone were loaded in torsion and damaged at a post-yield twist level. The number of microcracks within osteons, interstitial tissue, and along cement lines were assessed using basic fuchsin staining. Damage density measures (number of cracks/mm2) were correlated with stiffness degradation and changes in relaxation. Damaged samples exhibited a wide variation in total microcrack density, ranging from 1.1 to 43.3 cracks/mm2 with a mean density of 19.7 +/- 9.8 cracks/mm2. Lamellar interface cracks comprised more than 75% of the total damage, indicating that the lamellar interface is weak in shear and is a principal site of shear damage accumulation. Damage density was positively correlated with secant stiffness degradation, but only explained 22% of the variability in degradation. In contrast, damage density was uncorrelated with the changes in relaxation, indicating that a simple crack counting measure such as microcrack density was not an appropriate measure of relaxation degradation. Finally, a nonuniform microcrack density distribution was observed, suggesting that internal shear stresses were redistributed within the torsion samples during post-yield loading. The results suggested that the lamellar interface in human cortical bone plays an important role in torsional yielding by keeping cracks physically isolated from each other and delaying microcrack coalescence in order to postpone the inevitable formation of the fatal crack.     

Osteonal effects on elastic modulus and fatigue life in equine bone

We hypothesized that recently formed, incompletely mineralized, and thus, relatively deformable osteons in the equine third metacarpus enhance in vitro load-controlled fatigue life in two ways. Macroscopically, there is a compliance effect, because reduced tissue elastic modulus diminishes the stress required to reach a given strain. Microscopically, there is a cement line effect, in which new osteons and their cement lines more effectively serve as barriers to crack propagation. We studied 18 4 x 10 x 100 mm beams from the medial, lateral, and dorsal cortices of metacarpal bones from 6 thoroughbred racehorses. Following load-controlled fatigue testing to fracture in 4 point bending, a transverse, 100 microm thick, basic fuchsin-stained cross-section was taken from the load-bearing region. The number and diameter of all intact (and thus recently formed/compliant) secondary osteons in a 3.8 x 3.8 mm region in the center of the section were determined. The associated area fraction and cement line length of intact osteons were calculated, and the relationships between these variables, elastic modulus (E), and the logarithm of fatigue life (logN(F)) were analyzed. As expected, logN(F) was negatively correlated with E, which was in turn negatively correlated with intact osteon area fraction and density. (LogN(F))/E increased in proportion to intact osteon density and nonlinearly with cement line density (mm/mm(2)). These results support the hypothesis that remodeling extends load-controlled fatigue life both through the creation of osteonal barriers to microdamage propagation and modulus reduction.     

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.     

Prediction of cortical bone elastic constants by a two-level micromechanical model using a generalized self-consistent method

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.     

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.     

An application of nanoindentation technique to measure bone tissue Lamellae properties

Measuring the microscopic mechanical properties of bone tissue is important in support of understanding the etiology and pathogenesis of many bone diseases. Knowledge about these properties provides a context for estimating the local mechanical environment of bone related cells thait coordinate the adaptation to loads experienced at the whole organ level. The objective of this study was to determine the effects of experimental testing parameters on nanoindentation measures of lamellar-level bone mechanical properties. Specifically, we examined the effect of specimen preparation condition, indentation depth, repetitive loading, time delay, and displacement rate. The nanoindentation experiments produced measures of lamellar elastic moduli for human cortical bone (average value of 17.7 +/- 4.0 GPa for osteons and 19.3 +/- 4.7 GPa for interstitial bone tissue). In addition, the hardness measurements produced results consistent with data in the literature (average 0.52 +/- 0.15 GPa for osteons and 0.59 +/- 0.20 GPa for interstitial bone tissue). Consistent modulus values can be obtained from a 500-nm-deep indent. The results also indicated that the moduli and hardnesses of the dry specimens are significantly greater (22.6% and 56.9%, respectively) than those of the wet and wet and embedded specimens. The latter two groups were not different. The moduli obtained at a 5-nm/s loading rate were significantly lower than the values at the 10- and 20-nm/s loading rates while the 10- and 20-nm/s rates were not significantly different. The hardness measurements showed similar rate-dependent results. The preliminary results indicated that interstitial bone tissue has significantly higher modulus and hardness than osteonal bone tissue. In addition, a significant correlation between hardness and elastic modulus was observed.     

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.     

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.

     

Residual stress distribution in rabbit limb bones

The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).     

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.     

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.     

Hysteretic pinching of human secondary osteons subjected to torsion

The mechanical behavior of bone tissue's ultra- and micro- structure is fundamental to assessment of macroscopic bone mechanics. This paper explores the ultra-structural characteristics of human femoral tissue responsible for energy absorption of secondary osteons under mechanical loading. A novel mathematical interpretation of single osteon mechanics elucidates the behavior of the collagen-apatite interface. Fully calcified single osteon specimens were mechanically tested quasi-statically under cyclic torsional loading about their longitudinal axis. On each hysteretic diagram, all cycles after the initial monotonic cycle appear pinched and share two points. Stiffness degradation and pinching degradation were investigated on the torque versus deflection-angle-per-unit-length diagrams as the number of cycles increases, in relation to the appearance of osteons in cross-section under circularly polarized light microscopy. Material science's Bauschinger effect, originally defined for metals and later extended to structures reinforced with metal bars, is adapted to describe pinching. Material science's prying effect, defined as amplification of eccentric tensile load through lever action, is employed to explain pinching. The presence of the two points shared by all complete cycles is analyzed in terms of the mathematical fixed point theorem. The results allow formulation of the following conjectures: (1) the prying of carbonated apatite crystallites at the interface with the 40 nm long bands of non-calcified collagen fibrils causes pinching; (2) the prying effect increases with the increasing percentage of collagen-apatite elements that form a larger angle with the osteon axis; and (3) micro-cracks increase more in number than in length as the number of cycles increases.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Histologic estimation of age at death using the anterior cortex of the femur

This report describes a new histologic method for determination of age at death, the latest in a series of studies that began with Kerley's pioneer presentation in 1965. The study population was collected from 328 documented individuals from an anatomy dissecting room in the United States, from two modern cemeteries in the Dominican Republic, and from autopsies performed in a Chilean hospital. Undecalcified thin sections 1.0 cm wide were made from specimens taken from the femoral midshaft directly opposite the linea aspera. Five 0.886 mm2 fields were located at the periosteal edge and photographed, mainly for purposes of defining the fields and providing a permanent record. Secondary osteons, type II osteons, osteon fragments, resorption spaces, and non-Haversian canals were recorded as number/mm2, and a 100-space grid was used to measure average percent of unremodeled, osteonal, and fragmental bone. Stepwise regression analysis of the measurements produced a series of regression equations for age estimation for females, males, and sexes combined. Most equations have a standard error of estimate of about 10 years, but the coefficients of determination (r2) range from 0.48 to 0.72. In practice, sex-specific equations gave better results than opposite-sex or nonspecific equations, mainly because males and females differed in the pattern of relations between osteons and osteon fragments with advancing age.     

Micromechanics modeling of Haversian cortical bone properties.

A finite-element micromechanics model for Haversian cortical bone tissue has been developed and studied. The model is an extension of two-dimensional micromechanics techniques for fiber-reinforced composite materials. Haversian systems, or secondary osteons, are considered to be the fiber component, and interstitial lamellar bone the matrix material. The cement line is included as an 'interphase' component along the fiber/matrix interface. The model assumes a regular repeatable spacing of the longitudinally aligned continuous fibers and is, therefore, restricted to approximating Haversian cortical bone in its present form. Haversian porosity is modeled explicitly by incorporating a hollow fiber to represent the Haversian canal. Solutions have been obtained by applying uniform macroscopic stresses to the boundaries of the repeating unit cell model. Macroscopic mechanical property predictions correspond reasonably well with the experimental data for cortical bone, but are necessarily dependent on the input properties for each constituent, which are not well established. The predicted variation in the elastic modulus with porosity is not as sensitive as that observed experimentally. Stresses within the constituents can also be modeled with this method and are demonstrated to deviate from the macroscopic applied stress levels.