The micromechanics versus the macromechanics of cortical bone--a comprehensive presentation

Secondary cortical bone is a complicated patchwork of structures which can be viewed as a hierarchy of four different orders. As far as the biomechanical properties of cortical bone are concerned, the lamellae is the most important of the four. The relative distribution of longitudinal lamellae (whose fiber bundles and crystallites have a longitudinal course and withstand loading by tension) with respect to transverse lamellae (whose fiber bundles and crystallites have a transverse course and withstand loading by compression) governs the mechanical properties of bone at macroscopic level both in normal and pathological conditions.     

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.     

Mechanical properties of porcine femoral cortical bone measured by nanoindentation

This study uses a nanoindentation technique to examine variations in the local mechanical properties of porcine femoral cortical bone under hydrated conditions. Bone specimens from three age groups (6, 12 and 42 months), representing developing bone, ranging from young to mature animals, were tested on the longitudinal and transverse cross-sectional surfaces. Elastic modulus and hardness of individual lamellae within bone's microstructure: laminar bone, interstitial bone, and osteons, were measured. Both the elastic modulus and hardness increased with age. However, the magnitudes of these increases were different for each microstructural component. The longitudinal moduli were higher than the transverse moduli. Dehydrated samples were also tested to allow a comparison with hydrated samples and these resulted in higher moduli and hardness than the hydrated samples. Again, the degree of variation was different for each microstructural component. These results indicate that the developmental changes in bone have different rates of mechanical change within each microstructural component.     

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.     

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.     

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.     

The problem of bone lamellation: An attempt to explain different proposed models

Collagen texture and osteocyte distribution were analyzed in human woven‐ and lamellar‐bone using scanning and transmission electron microscopy. We provide data substantiating the concept that lamellar bone is made up of an alternation of dense‐acellular lamellae and loose‐cellular lamellae, all exhibiting an interwoven texture of collagen fibers. An attempt is also made to explain how the present findings might conform to those of authors whose models propose orderly, geometric arrangements of collagen fibers inside bony lamellae. Such a comparison is possible because the present investigation analyzes split loose lamellae and tangentially‐sectioned dense lamellae. It emerged that only loose lamellae can be dissected, revealing a loose interwoven collagen texture and halved osteocyte lacunae. Dense lamellae cannot be split because of their compactness. The analysis of tangentially sectioned dense lamellae demonstrates that they consist of a network of interwoven collagen fiber bundles. Inside each bundle, collagen fibers run parallel to each other but change direction where they enter adjacent bundles, at angles as described by other authors whose TEM investigations were performed at a much higher magnification than those of the present study. Consequently, what these authors consider to be a lamella are, instead, bundles of collagen fibers inside a lamella. There is discussion of the role played by the manner of osteocyte‐recruitment in the deposition of lamellar‐ and woven‐bone and how the presence of these cells is crucial for collagen spatial arrangement in bone tissues. J. Morphol., 2013. © 2013 Wiley Periodicals, Inc.     

Orientation of collagen fibers at the boundary between two successive osteonic lamellae and its mechanical interpretation

By applying an original technique, an investigation has been carried out to determine the orientation of collagen fibrils at the boundary between two successive lamellae in alternate osteons. Evidence is reported that the predominant fiber direction does not change abruptly from one lamella to the next; there is an intermediate system of criss-crossed fibers whose main orientation makes an angle of nearly 45 degrees with the direction of the fibers in the two adjacent lamellae. Taking a composite orthogonally reinforced laminate as a model, a mechanical interpretation of this intermediate system of collagen fibers is given.     

Structural differences between "dark" and "bright" isolated human osteonic lamellae

This investigation presents new insights into the structure of human secondary lamellae. Lamellar specimens that appear dark and bright on alternate osteon transverse sections under circularly polarizing light were isolated using a new technique, and examined by polarizing light microscopy, synchrotron X-ray diffraction, and confocal microscopy. A distribution of unidirectional collagen bundles and of two overlapping oblique bundles appears on circularly polarizing light microscopy images in relation to the angle between the specimen and the crossed Nicols' planes. The unidirectional collagen bundles observed at 45 degrees run parallel to the osteon axis in the dark lamellar specimens and perpendicular to it in the bright ones. Small and wide-angle micro-focus X-ray diffraction indicates that the dark lamellae are structurally quite homogeneous, with collagen fibers and apatite crystals preferentially oriented parallel to the osteon axis. Bright lamellar specimens exhibit different orientation patterns with the dominant ones bidirectional at +/-45 degrees with respect to the osteon axis. Accordingly, confocal microscopy evidences the presence of longitudinal bundles in dark lamellar specimens and oblique bundles in the bright ones. Radial bundles are evidenced in both lamellar types. The alternate osteon structure is described by a rather continuous multidirectional pattern, in which dark and bright lamellae display different mechanical and possibly biological functions.     

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.     

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.     

Microstructural mechanical study of a transverse osteon under compressive loading: The role of fiber reinforcement and explanation of some geometrical and mechanical microscopic properties

This Finite Element study aims at understanding the transverse osteon as a composite microstructure, and at differentiating the actions of each of its main components and their interactions. Three components of the osteon have been distinguished: the lamellae mineral-collagen matrix, the lamellae mineral-collagen reinforcement fibers and the Haversian canal content made of intracortical fluid and soft tissues. Numerical compression experiments have been performed, varying the microstructure properties. Our results show that fiber reinforcement of transverse osteons is only efficient at resisting dynamic compressive loadings, but that the improvement of the static compressive properties is very poor. Furthermore, the modeled stress distribution within the matrix and reinforcement fibers may explain why transverse osteons are often limited to a small number of lamellae (<8) and why internal lamellae could be stiffer than external ones.     

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.     

Understanding site-specific residual strain and architecture in bovine cortical bone

Living bone is considered as adaptive material to the mechanical functions, which continually undergoes change in its histological arrangement with respect to external prolonged loading. Such remodeling phenomena within bone depend on the degree of stimuli caused by the mechanical loading being experienced, and therefore, are specific to the sites. In the attempts of understanding strain adaptive phenomena within bones, different theoretical models have been proposed. Also, the existing literatures mostly follow the measurement of surface strains using strain gauges to experimentally quantify the strains experienced in the functional environment. In this work, we propose a novel idea of understanding site-specific functional adaptation to the prolonged load in bone on the basis of inherited residual strains and structural organization. We quantified the residual strains and amount of apatite crystals distribution, i.e., the degree of orientation, using X-ray diffraction procedures. The sites of naturally existing hole in bone, called foramen, are considered from bovine femur and metacarpal samples. Significant values of residual strains are found to exist in the specimens. Trends of residual strains noted in the specimens are mostly consistent with the degree of orientation of the crystallites. These features explain the response behavior of bone to the mechanical loading history near the foramen sites. Preferential orientation of crystals mapped around a femoral foramen specimen showed furnished tailored arrangement of the crystals around the hole. Effect of external loading at the femoral foramen site is also explained by the tensile loading experiment.     

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.     

Changes in the Microvasculature and Interstitium of Aged Human Mandibles and Maxillae1

The present study describes the age changes to the microvasculature and connective tissue interstitium of the osteons and periosteums of aged human mandibles and maxillae. The mandibles and maxillae obtained from 14 and 19 year old males, respectively, were also studied. In the nutrient canals of the aged osteons, the walls of the arterioles and venules stained intensely PAS positive, and alcian blue negative. The walls of the blood capillaries were thick and strongly PAS positive. There was a deposition of PAS positive material in the connective tissue stroma of the nutrient canals which progressed to the obliteration of the canal space. Many of the nutrient canals exhibited diffuse calcification within the connective tissue interstitium localized around the blood vessels. The lacunae and canaliculi of those osteons in which the nutrient canals were partially or completely obliterated were filled with PAS material. None of these histochemical changes were seen in the osteons of young individuals. The microvasculature of the aged periosteum showed similar changes. The periosteal tissue consisted of thick collagenous bundles and few osteogenic cells. There was a thin darkly stained amorphous calcified layer forming the bone surface.     

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.     

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.     

Influence of interstitial bone microcracks on strain-induced fluid flow

It is well known that microcracks act as a stimulus for bone remodelling, initiating resorption by osteoclasts and new bone formation by osteoblasts. Moreover, microcracks are likely to alter the fluid flow and convective transport through the bone tissue. This paper proposes a quantitative evaluation of the strain-induced interstitial fluid velocities developing in osteons in presence of a microcrack in the interstitial bone tissue. Based on Biot theory in the low-frequency range, a poroelastic model is carried out to study the hydro-mechanical behaviour of cracked osteonal tissue. The finite element results show that the presence of a microcrack in the interstitial osteonal tissue may drastically reduce the fluid velocity inside the neighbouring osteons. This fluid inactive zone inside osteons can cover up to 10% of their surface. Consequently, the fluid environment of bone mechano-sensitive cells is locally modified.     

Ex-vivo observation of calcification process in chick tibia slice: Augmented calcification along collagen fiber orientation in specimens subjected to static stretch

Bone formation through matrix synthesis and calcification in response to mechanical loading is an essential process of the maturation in immature animals, although how mechanical loading applied to the tissue increases the calcification and improves mechanical properties, and which directions the calcification progresses within the tissue are largely unknown. To address these issues, we investigated the calcification of immature chick bone under static tensile stretch using a newly developed real-time observation bioreactor system. Bone slices perpendicular to the longitudinal axis obtained from the tibia in 2- to 4-day-old chick legs were cultured in the system mounted on a microscope, and their calcification was observed up to 24 h while they were stretched in the direction parallel to the slice. Increase in the calcified area, traveling distance and the direction of the calcification and collagen fiber orientation in the newly calcified region were analyzed. There was a significant increase in calcified area in the bone explant subjected to tensile strain over ∼3%, which corresponds to the threshold strain for collagen fibers showing alignment in the direction of stretch, indicating that the fiber alignment may enhance tissue calcification. The calcification progressed to a greater distance to the stretching direction in the presence of the loading. Moreover, collagen fiber orientation in the calcified area in the loaded samples was coincided with the progression angle of the calcification. These results clearly show that the application of static tensile strain enhanced tissue calcification, which progresses along collagen fibers aligned to the loading direction.