[Frontiers in Bioscience 17, 1551-1581, January 1, 2012]

The osteon: the micromechanical unit of compact bone

Maria-Grazia Ascenzi1, Allison K. Roe1

1UCLA/Orthopaedic Hospital Department of Orthopaedic Surgery, University of California at Los Angeles

TABLE OF CONTENTS

1. Abstract
2. Introduction
3. Osteon composition
4. Techniques to assess basic morphology
4.1. Polarized light
4.2. High-resolution micro-X-ray
5. Mechanical testing of single osteon and of single lamella
5.1. Techniques to isolate single osteons
5.2. Techniques to isolate single lamellae.
5.3. Monotonic tension test.
5.4. Monotonic compression test
5.5. Pin-test
5.6. Bending test
5.7. Monotonic torsion test.
5.8. Shear test
5.9. Cyclic tension-compression
5.10. Cyclic torsion
6. Additional microscopy techniques
6.1. Confocal microscopy
6.2. Electron microscopy
6.3. Micro-computed tomography
7. Assessment of tissue properties: nano-indentation
8. Micro-structural anisotropy
8.1. Collagen orientation patterns in single osteon
8.2. Collagen orientation patterns in macroscopic bone
9. Models and simulations
10. Open problems
11. Acknowledgements
12. References

1. ABSTRACT

The research techniques available for investigation of secondary osteons in human bone enable establishment of their biological composition and quantification of their mechanical properties. Further, the data generated through current research techniques facilitate studies on the significance of osteons in normal and pathological conditions, including via multi-scale modeling conducted with a view of building realistic models of virtual bone, suitable for applications from orthopaedic challenges to endocrine disorders. The understanding of the biomechanical function of the osteon requires clarification of the molecular-cellular processes that form, maintain and remodel the osteon and affect the mechanical function. In turn, the mechanical function affects the biology of the osteon. In retrospective, the investigation of osteons has focused on the unraveling of the complex combination of elementary components to discern the major factors that define the mechanical behavior. The micro-structural environment that leads to macroscopic fracture remains unclear. Arrangement, distribution and quality of the elementary components may participate in fracture risk. The latest results underline the fundamental role of the orientation of collagen type I and of carbonated hydroxyapatite crystallites.

2. INTRODUCTION

Bone presents a series of seemingly contradictory characteristics: rigidity, strength, toughness, flexibility and lightness. It is the concept of multi-scale structure, first introduced by Petersen (1) in the 1930's, that allows for an understanding of the coexistence of such disparate properties. Well prior to Petersen, Galileo first hypothesized in the 1600's that the macro-structure needed reinforcements along the axis of long bones of large animals to avoid that the shaft collapse under its own weight (2). Petersen's further insight as to bone's multi-scale structure synthesizes observations that bone shows structural arrangements that depend on the magnification at which they are observed or measured, a characteristic that became apparent over several centuries of improvement in microscopy resolution. The modern study of bone microstructure began in the 1940's with the studies pursued by the School of Anatomy in Bologna (3).

This chapter discusses the micro-structure of compact adult human bone that forms the Haversian system, and whose basic unit is the secondary osteon (Figure 1). The focus of this chapter is the osteon's mechanical function. During the continuous process of bone remodeling, the secondary osteon forms around a vascular canal, also known as a Haversian canal. The secondary osteon is composed of layers, called lamellae, the structure of which has been an open question since van Leeuwenhoek first observed them in the late 1600's (4). There are two distinct hypotheses on the structural composition of the lamella. Both recognize that there are two types of lamellae that compose the osteons. The first hypothesis is that the two types of lamellae differ in orientation of the main elementary components of bone tissue, namely collagen fibrils and carbonated hydroxyapatite crystallites (5, 6, 7, 8, 9, 10, 11, 12, 13, 14). This hypothesis has evolved in time to become increasingly sophisticated. Gebhardt in the 1900's was the first to theorize a difference in orientation of collagen bundles with a spiral arrangement, either clockwise or counterclockwise, which may vary through an angle from 0 to 90 degrees with the osteon axis. This hypothesis has long been a model for investigating the mechanical behavior of isolated micro-structures (15, 16, 17, 18, 19, 20) and the correlations between micro- and macro-mechanics in compact bone (21). The second hypothesis is that the two lamellar types differ in the relative densities of the elementary components and in particular of collagen (22, 23, 24, 25, 26, 27, 28, 29, 30). The current chapter addresses the experimental results of the research on osteons and their lamellar components, and the related evolution, and ultimate intersection, of the micro-biomechanical hypotheses.

Section 3 summarizes the understanding of osteon composition. Section 4 describes the experimental techniques that are available to investigate the basic morphology of osteons. Section 5 describes the techniques for isolation of a single osteon and a single lamella and the methods to test their mechanical properties. Section 6 describes confocal and electron microscopy techniques and the results of their application to osteons. Section 7 explains the assessment of the mechanical properties of bone tissue within an osteon and its lamellae. Section 8 sets forth insights obtained from findings of collagen and apatite anisotropy within the osteon and throughout the macro-structure. Section 9 offers an overview of techniques from the fields of mathematics and engineering to aid the analysis of experimental results on bone micro-structures. The promise of interdisciplinary collaboration is explained to further the research on bone micro-structure within the multi-scale context. Section 10 addresses the open problems relative to bone micro-structure, the investigation of its elementary components and structures, and the application of such investigations to clinical challenges.

3. OSTEON COMPOSITION

This section describes the biological composition of secondary osteons. Secondary osteons were first observed under regular light microscopy to consist of cylindrical units comprising several layers called lamellae, that are generally coaxial with the axis of the Haversian (or vascular) canal around which they form (Figure 1). So-called interstitial bone fills in the space among the osteons and consists of remnants of osteons left over by the remodeling process. In male young adults free of metabolic bone disease, the osteon diameter ranges between 84 and 300 micron, with a Haversian canal diameter between 11 to 68 micron and a lamellar thickness between 2 and 16 micron (3, 31, 32, 33). These morphological dimensions depend on the skeletal site of the osteon. Because the Haversian system shows morphological heterogeneity that depends on the age of the individual, skeletal site and presence or absence of systemic factors that can alter the bone tissue, well-founded studies of bone composition focus on a specific skeletal site while addressing patients or donors with similar characteristics, separating for instance adolescents, young adults, and the elderly of either sex from each other, as well as distinguishing between pre-menopausal and post-menopausal females, and specific stages of any given pathology.

The calcified tissue of bone consists of three elements: cells, organic matrix and inorganic substance. These components are dependent upon each other, as the cells are known to assemble the organic matrix and generate the organic molecules that participate in the process of calcification. About 90% of the organic matrix of bone consists of collagen. The remaining 10% consists of proteoglycans, Gla-proteins (protein attached to gamma-carboxyglutamic acid), glycoproteins and phospholipids.

Collagens are fibrous proteins with structural properties that control arrangement, assembly, integrity and mechanical properties in many living organisms. Among the large number of collagen types (fibrillar, reticular, fibril surface-associated, periodic beaded filamentous and trans-membrane; 34, 35, 36), type I collagen belongs to the fibrillar type and comprises most of the bone matrix. Three polypeptide chains coiled in a left-handed helix form a collagen molecule, 280-300nm long (37). The collagen molecules align themselves according to a quarter-staggered arrangement with gaps between the front and back of the collagen molecules in sequence (38, 39). The fibrils show diameters of approximately 78nm. Adjacent molecules are connected to each other by intra- and intermolecular cross-links (40, 41, 42). These cross-links stabilize the structure of the collagen bundle, cause low solubility of bone collagen (43), and possibly play a part in the calcification of the collagen fibers. Because collagen is inter-dispersed through the bone matrix and therefore difficult to study independently from other components and without alteration of its structure for extraction, most of the knowledge about the structural characteristics of collagen type I arises from studies based on collagen found in undecalcified tendons and in other soft tissues, for instance skin tissues.

The bundles of type I collagen are mineralized into crystal-like configurations within a three-dimensional (3D) network (34). After the collagen is laid down by the osteoblasts, the process of calcification starts and leads to the formation of a solid, stable, crystalline inorganic phase within the organic phase. Carbonated hydroxyapatite crystals generally parallel collagen bundles (44). The bone turnover rate determines bone age and age-dependent properties of bone (45). The density and composition of the collagen fibrils in the bone matrix vary according to site and types of bone. Collagen fibrils are most dense in the compact bone of the diaphyses because fibrils are condensed together and assembled in an ordered layout called parallel-fibered or lamellar bone. In contrast, fibrils are aligned randomly in woven bone. They intertwine in a sporadic design and give rise to a large interfibrillary space (46), as opposed to the small interfibrillary space in lamellar bone. Therefore, woven bone has a larger portion of non-collagenous material than lamellar bone (47, 48). The orientation of collagen fibrils is important because differences in the amount of space between fibers allows varied amounts of non-collagenous material and because the orientation has implications for bone's mechanical properties (21, 49).

Non-collagenous components of the bone matrix are important because they affect bone formation rate and collagen bundle spacing, even though they make up a smaller fraction of compact bone (50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61). Different types of bone show varying amounts of these components, which are more abundant in bone tissues with loose collagen fibrils (62, 63). Proteoglycans are the most abundant non-collagenous components of bone and generally entrapped in the calcified matrix. Decorin is a specific type of proteoglycan which regulates collagen fibrillogenesis (64), inhibits calcification and is associated with type I collagen (65). Biglycan, aggrecan, versican, perlecan and fibromodulin are additional types of proteoglycan less abundant in the bone matrix than decorin.

Osteoblasts, osteocytes and osteoclasts are the cells present in the bone tissue. Osteoblasts synthesize collagen and are therefore considered bone forming cells. Osteocytes make up over 90% of all bone cells and are osteoblasts that become entrapped in the matrix that they produce (66). They are hypothesized to have a sensory role (67, 68, 69) for mechanical loading. Osteoclasts are primarily responsible for bone resorption. The functional interplay of this type of cells is complex, with the three-cell types affecting each other's function (70, 71). Osteocalcin (OC) and matrix Gla-protein (MGP) are two important types of Gla-proteins. OC is restricted to the bone matrix and is assembled by osteoblast cells (72, 73, 74). It requires vitamin K for synthesis, and shows calcium-binding characteristics that help its interaction with hydroxyapatite (75). OC's close interaction with hydroxyapatite is hypothesized to inhibit growth of crystalline hydroxyapatite and to guide its shape and size (76). OC is present at higher levels in cortical than trabecular bone (77, 78) and has been regarded as a local calcification regulator. OC is synthesized at the earliest stage of calcification and is the only non-collagenous protein confined to bone cells and calcified matrix (79). Its function is difficult to determine and has never been clearly defined. Circulating OC is nevertheless involved in bone turnover (54, 80). However, it has also been shown that OC does not interact with lipid-induced hydroxyapatite formation and has no impact on lipid-induced calcification (81). MGP is similar to OC in that it depends on vitamin K for synthesis and it contains Gla (82). Further, MGP negatively regulates calcification (83, 84, 85, 86). Evolutionarily, it is possible that MGP and OC arose due to gene duplication and then divergent evolution due to the similarity in protein sequences (87).

Bone matrix also contains glycoproteins. Glycoproteins that are highly phosphorylated are called phosphoproteins. Different types of bone phosphoproteins are osteonectin, osteopontin, bone sialoprotein, dentin matrix protein 1, matrix extracellular phosphoglycoprotein and acidic glycoprotein-75. Glycoproteins containing glutamic, aspartic and sialic acids are called acidic glycoproteins (88). In order for glycoproteins to become soluble, the bone tissue needs to be decalcified (52, 53, 89, 90). In fact, glycoproteins are buried in the inorganic elements of the bone matrix, which founds the belief that they affect bone calcification (55, 56, 89, 91, 92).

While bone tissue of human and other animals shares many characteristics, research shows that differences exist between human bone and the bone of other mammals, such as monkeys, horses, calves, sheep dogs, rabbits, dogs generically, and ferrets, all of which show osteon remodeling (93, 94, 95, 96, 97). Osteonal remodeling is absent in rat and mouse bone (98).

4. TECHNIQUES TO ASSESS BASIC MORPHOLOGY

A principal focus of research in the late 1940's and 1950's was the identification of the parameters that can explain the heterogeneity of the Haversian system. Polarized light microscopy was chosen because it provides information on organization of components of a translucent material. Further, because bone remodeling targets the osteon unit, the need became apparent to develop radiological instrumentation that would afford a resolution high enough to allow detection of the degree of calcification within the single osteon. The morphological investigations that were carried out then and subsequently have been implemented with increasing refinement on bone sections and on isolated specimens of either osteons or lamellae. In combination, the techniques of polarized light microscopy and high resolution micro-X-ray have allowed assessment of two fundamental micro-structural variables: (i) collagen and apatite anisotropy and (ii) degree of osteon calcification.

4.1.Polarized light

Polarization of light has been used in conjunction with transmitted light microscopy to detect anisotropy of bone since the 1950's (99). Circularly polarized light (CPL) is obtained by means of two crossed Nicol's prisms and two quarter lambda retardation plates. Of the Nicol's prisms, the polarizer is situated between the light source and the bone specimen, and the analyzer is situated above the specimen. The first quarter lambda plate oriented at 45 to 225 degrees is situated between the polarizer and the specimen. The second quarter lambda plate, oriented at 135 to 315 degrees, is situated between the specimen and the analyzer (100, 101).

The crossed Nicol's prisms induce propagation of light on perpendicular planes whose common axis is the direction of propagation. The presence/absence of the first quarter lambda plate differentiates between CPL and linear polarized light. The bright signal of CPL corresponds to the bright signal for all rotations of the specimen on the microscope stage under linear polarization and similarly so for the extinct signal. The second quarter lambda plate removes the extinct Maltese cross effect due to the extinct appearance of structural elements aligned parallel to the transmission axis of the Nicol's prisms.

Extinct and bright signals of CPL are due to birefringence of collagen and in a minor way to hydroxyapatite. This can be checked by comparing the distribution of extinct and bright signals before and after calcification of a bone specimen. Extinction of light is indicative of collagen bundles preferentially parallel to the direction of the propagation of light, while brightness is indicative of collagen generally forming large angles, including transverse collagen, with the direction of propagation. Therefore the CPL signal depends on the orientation of the section: regions that appear extinct on sections transverse to the Haversian system general direction appear bright on longitudinal section. Conversely, regions that appear bright on section transverse to the Haversian system general direction appear extinct on longitudinal section.

Osteons can be classified in terms of appearance under CPL. Throughout this chapter we refer to extinct and bright birefringence of osteons in transverse section (Figure 2). A completely extinct osteon has never been observed. The so-called extinct osteon shows 96 to 97% extinction corresponding to 3 to 4% percent brightness). The so-called bright osteon is 100% bright. The so-called alternate osteon shows alternation of bright and extinct lamellae.

4.2. High-resolution micro-X-ray

The degree of calcification is assessed with a micro-focus microradiograph MCR 3000 (Ital-Structures, Riva del Garda-Trento, Italy) and high-resolution film such as Kodak 649 film (now discontinued), or 1A plates from Microchrome Technology, Inc or VRP-N plates from Slavich with 2000 to 3000 lines/mm (26, 102, 103).

To calibrate and allow quantification of calcium, the bone specimen is micro-X-rayed together with an aluminum scale consisting of four segments of increasing thickness, because aluminum, calcium and phosphorous absorb x-rays with a comparable coefficient within the energy range used by the microradiograph (104). The darker grey shades on the micro-X-ray correspond to initial stages of calcification and the lighter grey shades to final stages of calcification (Figure 3). Haversian canals and resorption lacunae appear black on the micro-X-ray. Interstitial bone appears, in general, whiter than osteons, indicating higher calcification, explained by the older tissue age. Because of the 1 micron resolution, the cement lines, whose thickness ranges between 1 and 2 micron, are visible at the interface between osteons and interstitial bone. Their dark appearance suggests low calcification. The degree of calcification in cement lines is nevertheless a matter of divergent views (105, 106, 107).

5. MECHANICAL TESTING OF SINGLE OSTEON AND OF SINGLE LAMELLA

Because the mechanical behavior of a specimen depends on its composition, specimens are chosen of specific types under CPL (section 4.1) and at specific degree of calcification as established by the micro-X-ray method described (section 4.2). Because the mechanical behavior of a specimen depends also on its dimensions and shape, the issue of isolating osteons of same dimension and shape presents itself. The quasi-static mechanical testing described below requires isolation of single osteons, for which preparation techniques were developed in the 1960's and 1970's. Single osteon specimens have been prepared with a cylindrical shape for compression, pin-test, bending, shear (Figure 4a), and with a cylindrical shape connected to two lugs, one per end, for tension, torsion, cyclic tension-compression, cyclic torsion (Figure 4b). In either case, the cylindrical shape was chosen coaxial to the vascular canal. In specific instances hemi-diametral osteon sections have also been tested. Single lamellar specimens have been prepared (Figure 4c) and tested in tension. Mechanical tests have been performed on both dry specimens and on specimens wetted with either saline solution or distilled water, which replicate physiological conditions. Only results obtained on hydrated specimens are reported here.

5.1. Techniques to isolate single osteons

Protocols to prepare a single osteon specimen around the vascular canal were developed in the late 1960's. The site for specimen isolation needs to be chosen around a straight Haversian canal and away from Volkman's canals. Consequently, the longitudinal axis of the specimen needs to coincide with the axis of the Haversian canal and the Haversian canal length of the specimen cannot exceed 520-530 micron. To obtain specimens with lugs (Figure 4a), longitudinal sections were cut from the long bone shaft, with a thickness that was slightly larger than the osteon diameter. Such sections were micro-X-rayed to choose osteons with specific degree of calcification (section 4.2). The sections were then observed by CPL to select specific osteon anisotropy. Because the overlapping of lamellae beyond 100 micron thickness may affect the CPL signal, the appearance of the specimen under CPL needs to be confirmed after testing by isolating thinner transverse sections and observing them by CPL. Micro-instrumentation was developed to cut the specimens. To isolate a box shaped specimen from the longitudinal sections, a micro-mill was used where the body of a dental drill replaces the tube in the body of a microscope. The isolation of the specimen was observed with a stereo-microscope. A micro-grinding lathe was then used with the axis of the Haversian canal aligned with the rotating axis of the lathe, to obtain a cylindrical middle portion of the specimen.

To obtain cylindrical specimens (Figure 4b), sections were cut transversely to the Haversian canal's general direction. After conducting micro-x-rays to select osteons of specific degree of calcification and after observation by CPL to select specific structural anisotropy, a circular cut within the chosen osteon was made around the Haversian canal with the micro-lathe. This process produced a cylindrical specimen.

5.2. Techniques to isolate single lamellae

The lamellae that appear bright on sections transverse to the Haversian axes can be isolated by hemi-diametral compression (Figure 4c; 15); and both extinct and bright lamellae can be isolated by excision (Figure 4d; 44). Hemi-diametral light compression of a cylindrical osteon specimen causes fracture of extinct lamellae, while bright lamellae remain intact. Whole bright lamellae exit the osteon specimen in an opening telescopic fashion. The lamella is then cut along its height and carefully laid down flat under microscope observation. The second method consists in excision of lamellae. This technique is carried out on a trapezoid cut from a 70 micron thick transverse section. The bottom portion of the trapezoid is glued to a glass slide in order to hold the specimen while cutting. Approximately two-thirds of the lamellar circumferential length is isolated while the specimen is kept wet.

5.3. Monotonic tension test

Historically, hemi-diametral specimens were first tested in tension (16). Because hemi-diametral sections from alternate osteons showed abrupt changes in slope at low stresses, hemi-diametral specimens were found unsuitable to measure adequately the mechanical properties of the osteons because the specimen preparation removed the longitudinal initial stress that normally protects alternate osteons at low stresses (15). Therefore, cylindrical specimens needed to be employed.

Extinct and alternate osteons at initial and final stages of calcification were chosen to prepare cylindrical specimens endowed with lugs for this experiment. The CPL osteon type needs to be confirmed after the experiment because of the presence of the lugs. In fact, two thin sections need to be cut at each end of the cylindrical shape and viewed by CPL. The osteon specimen diameters ranged between 20 and 50 micron and the height ranged between 400 and 600 micron (33).

The transverse area of the specimen's cylindrical part was used to determine the ultimate tensile stress. A loading apparatus was used to load the osteon specimens and measure the elongations of the specimens (108). The elongation of the specimen under loading was measured by the change in resonance frequency of the apparatus' cavity. The accuracy in osteon specimen elongation measurements fell within 1%. The data determined that extinct specimens resisted tension better than alternate cylindrical specimens at both initial and final stages of calcification. The elastic modulus increased by at least 22% between initial and final degree of calcification. At final degree of calcification, the elastic modulus was found to be 114% larger for the extinct osteon than for the alternate osteon.

Tensional loading of single lamellae (Figure 5) was carried out in an experiment using material from femoral shafts. Investigators used alternate osteons at initial and final stages of calcification for the experiment. The specimens were cut into cylindrical shapes. The lamellae with collagen bundles that had a transverse spiral direction were then isolated using a procedure in which the specimen was compressed perpendicularly to its axis and then pressured at changing diametral points. The isolated lamellae were cut longitudinally, then carefully straightened into ribbon-shaped specimens under microscope observation. The lamellae showed collagen following the direction parallel to the length of the ribbon-shape. The microwave extensometer used for monotonic tensional loading of osteons was adapted to measure the changes in length of lamellae under tensional loading along their ribbon-shape length. Since there was great variation in thickness within and among single lamellae, differences in ultimate tensile strength and modulus of elasticity between different degrees of calcification could not be computed. Ultimate load did not depend on the degree of calcification of the lamellar specimen (109).

5.4. Monotonic compression test

Extinct, alternate and bright osteons were investigated (17). Cylindrical specimens at both initial and final degrees of calcification were used for this experiment. The specimens had a height of 500 micron and the ratio of height to diameter varied between 2.5 and 3. There are two methods that can be used to load and determine the changes in specimen length due to compression. Both are accurate and, unlike tension methods, one of the compression methods permits the investigators to determine the osteon CPL type before isolating the specimen. A special device composed of a thin steel needle inserted into a dental drill was used to isolate the specimens. As the drill and the needle turned, the needle tip cut an osteon specimen with a cylindrical shape that had walls of uniform thickness.

The specimens were loaded by means of a micro-compressor with a microwave micrometer based on the cavity and pulse technique used to measure the tension resistance. The length change measurements were accurate up to 1%. Unlike tensional behavior, the elastic modulus and compressive strength values were maximum for bright osteons, intermediate for alternate osteons and minimum for extinct osteons at the same degree of calcification. These values increased as the osteons became more calcified. The elastic modulus increased by at least 29% between initial and final degree of calcification. At final degree of calcification, the elastic modulus was found to be 47% larger for the bright osteon than for the extinct osteon.

In the second compression test, the same osteon specimen shape as used for tension loading is used. The drawback in this method is that determining the osteon type can only occur after loading the specimens.

5.5. Pin-test

The pin-test measures the osteon wall resistance to internal pressure. Extinct, alternate and bright osteons were tested at both initial and final degrees of calcification (110). Cylindrical specimens were used for this experiment. The specimens had heights of 100 micron and diameters that ranged between 150 and 230 micron. Investigators measured osteonal cell wall resistance by gradually pushing a steel cone through the vascular canals until they fractured. The cone that gave the most precise results of osteonal cell wall resistance had an angular width of 35 degrees. In order to fracture the vascular canals, the investigators loaded the cone onto the specimen and gradually added weights onto the cone. The increasing weight on the cone caused it to progressively press down on the upper end of the vascular canal. The osteons deformed at first, and then the lamellae began to fracture. The lamellae that fractured first were the ones closest to the vascular canal.

The same microwave micrometer from previous techniques was used to measure the increasing drop of the cone until fracture. Bright osteon specimens were found to have the maximum final expanding strength, with alternate and extinct specimens having intermediate, and minimum strengths, respectively. This result gives further evidence that osteon wall resistance is increased by the presence of bright lamellae.

5.6. Bending test

Extinct and alternate osteons at the final degree of calcification were used for this experiment (111). Cylindrical specimens were prepared. The specimen height measured 500 micron. The specimen diameters measured 195 micron and the Haversian canal diameters ranged between 40 and 50 micron. The specimen was placed between two steel strips that were on the same horizontal plane so that its middle portion was not supported (Figure 6). Each end of the specimen had approximately 50 micron resting on the steel strip surface. Investigators loaded a steel point onto the unsupported center of each specimen. The steel point pushed down linearly on the specimen, causing it to bend at its center. The investigators used the same microwave micrometer used in early experiments. This gave an accuracy of the measurement of changes in bending within 1%.

Beam theory was used to calculate the ultimate bending load, ultimate bending deformation, elastic modulus and rupture modulus from experimental data, or these values were determined experimentally. The results concluded that extinct osteon specimens are not as resistant to bending as alternate osteon specimens. The alternate osteon specimens are more resistant due to their larger number of transverse bundles. Extinct osteons have few transverse collagen bundles, causing them to be less structurally compact than alternate osteons. At final degree of calcification, the elastic modulus was found to be at least 16% larger for the extinct osteon than for the alternate osteon.

5.7. Monotonic torsion test

Torsional loading of osteons has been tested with two different methods. Frasca et al (112, 113) created a method to test whole osteons, In the Frasca method, both single osteons and osteon groups were chosen without determining the type of osteon structural type or the degree of calcification. The specimens were tested wet and dry using a micro-torsional device. A laser light spot was reflected on a rotating mirror in order to evaluate the angular amplitudes. The investigators determined that strain and frequency rely upon shear storage modulus of both single osteons and osteon groups. Single osteons and osteon groups behave differently under torsion when they are wet and when they are dry.

While the previous method tested whole osteons, A. Ascenzi et al (19) developed a method to test osteon specimens. In the A. Ascenzi method, the investigators chose extinct and alternate osteons at final degrees of calcification. Cylindrical specimens connected to two lugs were used for this experiment. The osteon specimens had heights that ranged between 300 and 500 micron. The diameters of the specimens were 210 micron and the diameters of the Haversian canals were 40 micron. A special torsional device that was manufactured by the CECOM Company (Figure 7) was developed. The device consisted of a fixed axis and rotational axis, each axis complete with a set of jaws to secure the ends of the specimen. The specimens were attached to the fixed jaw on one end and the rotational jaw on the other. The rotational jaw turned and twisted the specimen as weights were added to it on the rotational axis. The specific weight that produced unchecked twisting of the specimen was the weight responsible for the failure of the osteons. The twisting angles of the specimen were measured using a laser beam reflection on a small mirror placed in the rotating jaws. They determined the ultimate torque, angular deflection, shear modulus, amount of energy absorbed up to failure and torsional shear stress either experimentally or by using the beam theory to compute it from experimental data. The results concluded that the extinct osteon specimens had higher ultimate torque and shear modulus values than alternate osteon specimens. The shear modulus was found to be 35% larger for the extinct osteon than for the alternate osteon.

5.8. Shear test

Extinct, alternate and bright osteons at both initial and final stages of calcification were tested on their shearing resistance using a double-shearing strength test (114). Cylindrical specimens were used. The specimens had heights of 300 micron and osteonal diameters of 200 to 300 micron. Femoral mid-shafts were cut into transverse sections with osteons oriented perpendicularly to the section plane. Each transverse section was placed on a flat surface with a hole cut from the center. This flat surface acted as a supporting plane for the specimen. The investigators placed a steel cylinder on top of the specimen, orienting it with the osteonal axis. The cylinder had a diameter smaller than the osteonal diameter and was called a "punch". The investigators slowly added weights to the punch, causing it to put pressure on the osteon. This pressure first caused the osteon specimen to deform and then the lamellar connections of lamellae surrounding the punch began to break. The ultimate shearing strength was determined when the connections between lamellae were broken and the osteon specimen began to fall through the hole in the supporting plane.

The same microwave micrometer from previous techniques was used to measure the advancing drop of the punch until reaching the concluding shearing strength. They determined that extinct osteons have the lowest resistance to shearing stress, suggesting that circular collagen bundles strengthen bone compactness of other osteon types. As the specimens' calcification increased, the strength and elastic modulus in shear increased. The elastic modulus increased by 2 to 22% between initial and final degree of calcification. At final degree of calcification, the elastic modulus was found to be 25% larger for the extinct osteon than for the alternate osteon.

5.9. Cyclic tension-compression

Because bone undergoes repetitive, or cyclic loading (e.g. femoral shaft during walking), the degeneration of the mechanical properties of single osteons under cyclic tension-compression was investigated in the 1980's (115). Extinct and alternate osteons at both initial and final stages of calcification were prepared as cylindrical shapes with lugs. The cylindrical part of the specimens had a height of 500 micron and a diameter between 166 and 284 micron. The microwave system previously described (section 5.1) was adapted to measure changes in sample length. One lug of the specimen was attached to the mobile part of the device and one lug was attached to the immobile part. The osteon specimens were subjected to loading-unloading cycles of 40sec. Movement of the device exerted traction or compression on the specimen. Tension caused the specimen to elongate, while compression caused the specimen to shorten. The hysteresis loops of the specimens were recorded. At fixed degree of calcification, extinct osteons displayed a greater increase in strain during compression than during tension, indicating that larger creep is present in extinct osteons under compression (Figure 8). In contrast, alternate osteons showed a greater increase in strain during the tension when compared to compression, implying larger creep is present under tension.

When osteons are cyclically loaded, they display the degrading phenomenon known as pinching. Pinching is caused in osteons by injuries to their structure, such as flexural cracks or bond degradation. In a study in 1997, investigators studied cyclically loaded osteons (20). Similarly to a previous study in 1985, extinct and alternate osteon specimens in the shape of cylinders connected to two lugs were used for this experiment. The experimental osteons were at initial and final stages of calcification. Each specimen was subjected to cyclic tension-compression while the change in length was measured by the micro-wave instrument discussed in section 5.1. Results indicated that loading of the specimens involves mainly the longitudinal fibers of collagen. Lamellae with circular collagen bundles are prestressed and are not loaded along their axes. Therefore, extinct osteons with mainly longitudinal collagen/apatite bundles have more lesions causing pinching because they do not have circular bundles to protect them from collapsing when they are compressed and begin to deform. Alternate osteons have less longitudinal and more circular collagen bundles than extinct osteons; consequently they have fewer lesions that causing pinching. Increasing the number of cycles increased the strain limit and energy absorption and decreased the stiffness in both types of osteons due to the increasing magnitude of lesions and buckling. Extinct osteons had a greater strain limit in compression than tension in both the first and last cycles due to longitudinal collagen/apatite bundles protecting them more effectively when subjected to tension than when subjected to compression (16) Alternate osteons showed opposite results, having a greater strain limit in tension than compression due to circular collagen/apatite fibers preventing buckling and protecting them more effectively against compression than tension (17).

5.10. Cyclic torsion

This mechanical test was suggested by the present of pinching in the tension-compression hysteresis loops (section 5.9). The conjecture was that pinching was indicative of osteons' stability and resistance to micro-crack formation. If were the case, pinching would probably be present under a different cyclic-loading. Therefore, a different cyclic loading experiment was needed. It turned out that all osteon specimens tested under cyclic torsion showed pinching. Further, at the time the investigators determined to investigate osteons in terms of percent birefringent brightness by CPL that describe the range between the extinct and the bright osteons (Figure 1). Therefore, cylindrical specimens with lugs at final stages of calcification and increasing percent brightness by CPL were prepared (Figure 9; 116). The specimens had heights that ranged from 500 to 535 micron. The osteons' diameters ranged between 200 and 228 micron. The Haversian canal diameter measured about 40 micron. The osteon specimens were divided into groups in terms of range of dimensions. The micro-torsimeter previously used for monotonic torsion was adapted to allow both clockwise and counter-clockwise rotation. The lugs of the specimens were secured to the micro-torsimeter with the canal axis of each specimen aligned with the torsional axis. Starting with clockwise torsion orientation, the investigators engaged cyclic torsion by sequentially adding and and removing weights at a constant time of 4sec.

After the first half-cycle, all subsequent cycles on the diagrams share two points at which the cycles are pinched. Investigators examined how the stiffness and pinching of the osteon specimens degraded on the diagrams of torque versus deflection-angle-per-unit-length as they increased the number of cycles. They looked at these cross-sections of specimens under CPL to compare them to the diagrams. In order to describe pinching, investigators adapted material science's Bauschinger effect. The Bauschinger effect was initially classified for metals, but later expanded to involve structures reinforced with metal bars. To explain pinching, investigators used material science's prying effect, the magnification of eccentric tensile load using levers. The mathematical fixed-point theorem was used to analyze the two points through which all full cycles pass. The hypothesis was the presence of a prying effect at the interface between the apatite crystallites and the non-calcified collagen fibril bands. As the percentage of collagen-apatite components forming a greater angle with the osteonal axis increases, the prying effect increases, and the number of micro-cracks increases more than their length as the number of cycles rises.

In conclusion, (1) the experiment helps differentiate characteristics that determine the micro-mechanical behavior in terms of collagen anisotropy by CPL and osteon size (44, 49); and (2) the occurrence of pinching helps explain the bonds between collagen fibrils and carbonated apatite crystallites.

6. ADDITIONAL MICROSCOPY TECHNIQUES

Magnification and resolution higher than those afforded by compound microscopy were needed to observe collagen and apatite patterns and interface between collagen and apatite as well as specifications of elementary components.

6.1. Confocal microscopy

Scanning confocal microscopy on isolated lamellar specimens is a method of assessing canalicular and collagen orientation patterns through lamellar thickness, which is the radial direction of the osteon prior to isolation (Figure 10). Confocal microscopes attain a higher magnification and resolution than compound microscopes and employ a pinhole opening in front of the photo-detector that allows observation at specific depth of specimen. In fact, a point-by-point brightening procedure prevents unfocused light coming from above and below the plane of focus from arriving at the photo-detector. This method allows observation of different collagen orientation patterns in successive planes of focus throughout the thickness of the specimen.

Extinct and bright lamellar specimens by CPL were examined by confocal microscopy (44, 117, 118). The arrangement of the collagen was measured using confocal microscopy image stacks. They determined the different collagen orientations using polarized light microscopy and the local collagen arrangement as it moved through the thickness of the specimen using X-ray diffraction. The investigators scanned the lamellar specimens when they were wet. It was not necessary to stain the specimen due to the natural fluorescence of the wet bone, also called endogenous fluorescence (119). Atoms and molecules absorb light at specific wavelengths and then emit that light at longer wavelengths than absorbed (120). The protein content of bone is dominated by collagen type I (119, 121), which has a fluorescent light range between 300 to 700nm (122). Therefore, confocal microscopy uses lasers of wavelengths within this range. Argon-ion lasers with wavelengths of 405, 514 and 594nm supplied equivalent images with the same quality in the fluorescent components. Because the other principal components of bone do not show fibrous patterns throughout lamellar specimens as collagen does, the auto-fluorescent images at 3000-4000x were concluded to be collagen. The extinct and bright outermost lamellae were isolated (Figure 4d). The isolated lamellar specimens measured between 5 and 15 micron in thickness. The specimens were first flattened and then inspected to ensure there were no cracks.

Collagen bundles are observed using confocal microscopy on the background of mucopolysaccharides and glycoproteins. Collagen fibers are dispersed in layers overlying each other through the thickness of the lamellae. The collagen bundles had mostly a unidirectional orientation and areas of these bundles are called domains (123). Domains gradually change throughout consecutive layers by a few degrees and several can be visible along down the length of the same layer in both types of lamellae. The direction of the fibers also changes within each layer. Confocal microscopy allows investigators to control their depth of field and separate the different collagen orientations that overlap as they move through the lamellar thickness, helping them to evaluate the different collagen orientation patterns (118).

In both extinct and bright specimens, collagen bundles that were cut during isolation of the lamellae appear as dots. These bundles are arranged almost perpendicular to the lamellae. The extinct and bright lamellae show different patterns of collagen arrangement in the confocal microscopy images. In the extinct lamellae specimens, the collagen bundles follow the specimen's breadth, illustrating parts that have a polished fibrillar structure. These fibrils for the most part have a 90 degree or smaller angle to the width of the specimen, while the bright lamellae collagen bundles have a roughly 45 degree angle to the width of the specimen. Extinct lamellar collagen bundles are also clearer in the more spread out areas than the bright lamellar bundles. In extinct lamellae, collagen arranged longitudinal to the osteon axis shows a parabolic distribution, while this distribution is seen in collagen oriented transverse to the osteon axis in bright lamellae. Collagen arranged oblique to the osteon axis in both types of lamellae also show a parabolic distribution through the thickness of the specimen. Both transverse collagen in bright lamellae and longitudinal collagen in extinct lamellae have their peaks at middle third of the thickness of the lamellae. In both extinct and bright lamellae, the oblique collagen peaks at the outer thirds. Extinct lamellar specimens display mostly longitudinal collagen arrangement and bright lamellar specimens typically have oblique collagen orientations to the osteon axis.

Collagen components seem to be less tightly packed when observing them under confocal microscopes than when observing them under high-resolution electron microscope. The electron microscopes give images that have a magnification at least five times higher than confocal microscopes. Confocal images are also enlarged two or three times, so the collagen orientation resolution is reduced due to a sharp change between dark and bright pixels. This shows a lack of information that would be provided by higher-resolution microscopes and causes collagen fibrils to seem less tight in confocal images. On one hand, CPL allows for observation of a larger area of focus than confocal microscopy, and therefore of variation of orientation of collagen on a wider region. On the other hand, confocal microscopy allows for observation of changes in collagen orientation within the depth of the specimen (117). Confocal microscopy was also used on bone section transverse to the shaft of the long bone (124). The results are discussed in section 8.

Confocal microscopy is a one-photon microscopy technique. Multi-photon microscopy allows for increased resolution especially in connection with second harmonic generation. Multi-photon microscopy has been applied to cancellous bone but not cortical bone (125).

6.2. Electron microscopy

Various types of electron microscopy have been applied to bone by many research groups around the world since the 1950's. The magnification of transmission electron microscopy (TEM) ranges up to 10,000,000x and up to 1,000,000x for scanning electron microscopy (SEM). In particular, both TEM and SEM have shown the orientation patterns of collagen fibrils within osteons. TEM showed patterns that were found in agreement with patterns established by other techniques. The collagen bundle orientation was observed to form criss-crosses, many at an angle of 45 degrees with respect to the edge of the bright lamella (Figure 11; 126).

For SEM observation, the bone specimens are examined after they are extracted with ethane diamine for two days and then rinsed in absolute ethanol, which removes the organic phase and leaves the mineralized phase. The mineralized phase follows the orientation pattern of collagen bundles no longer present in the specimen. The specimens are then observed by SEM to determine the mineralization and the different collagen bundle patterns (123). Before scanning, SEM specimens must first either be permanently mounted or coated. When mounted, the specimens are attached to a metal support that changes according to the type of SEM used. Sufficiently sturdy specimens can be scanned without metal support in the SEM (127). Bone specimens can only be analyzed without a conductive coating if they are scanned at a low accelerating voltage. For backscattered electron imaging, scientists use carbon coating. Gold, silver or gold-palladium coatings help increase the SEM signals (128). Removal of the coating material is used to remove the cells, matrix or embedding medium of the bone specimen. After properly preparing the specimens, the beam voltage and current, orientation of the specimen, signal mode and detector strategy must be chosen in order properly to scan the specimen (127). The images of collagen bundles in extinct osteons have longitudinal and nearly longitudinal orientations, while the images of bright osteon collagen bundles show mostly coexisting longitudinal and transverse bundles (129). SEM demonstrates that canicular densities remain relatively constant throughout secondary osteons (66). SEM images also show the differences between normal and abnormal bone specimens. Normal bone shows ordered structure, while abnormal bone with overgrown organic tissue appears disordered (130). SEM has shown that collagen bundles run longitudinally in extinct osteons and both longitudinally and transversely in bright osteons (129, 131). SEM also indicates that extinct osteons are composed of thicker lamellae and contain more numerous osteocyte lacunae (131).

The scanning transmission electron microscope (STEM) can be used in either transmission or scanning mode. Recently, STEM in TEM mode was used to observe the sections with the width of the section, oriented parallel to the Haversian canal, as the reference direction for the orientation of collagen bundles. Specimens were prepared following the protocol for TEM as here set forth (126). Longitudinal bone sections were dehydrated and embedded in Araldite® (Huntsman Advanced Materials Americas Inc.). Ultra-thin 70-80nm serial sections were prepared with MT-1 Ultra Microtome (DuPont Instruments- Sorval, Miami, Florida) using a diamond cutter. The specimens were placed in TEM grids. Each grid containing the specimens was placed on a STEM holder and examined using a field emission gun scanning electron microscope (FESEM, Zeiss SUPRA VP-40) equipped with a STEM detector at an accelerating voltage of 20kV and at a working distance of 4mm. The STEM rasters the focused incident probe across the specimen that, as with the regular transmission electron microscope, has been thinned to facilitate detection of electrons scattered through the specimen. The STEM detector enables pure bright field, or extinct field, imaging to achieve optimum contrasts and rich imaging details of unstained thin sections. Further, the transmission mode of the FESEM has the advantages of avoiding chromatic aberration. This allows for a larger aperture to obtain higher transmission, signal to noise ratio, and contrast enhancement due to the lower electron energy within the 10 to 30kV range. Collagen was observed preferentially running longitudinally, that is parallel, to the Haversian canal on lamellae that appear bright in longitudinal sections and therefore corresponding to extinct appearance in transverse section under CPL (Figure 12). Collagen was observed to form larger angles with the longitudinal direction on lamellae that appear extinct in longitudinal sections and therefore corresponding to bright appearance in transverse section under CPL.

SEM in backscattered mode (123, 132, 133) measures degree of calcification and provides an alternative to the high-resolution micro-X-ray method. Backscattered electrons are higher energy electrons and backscattered electron imaging is preferentially used to examine mineralized bone matrix (128). Specimens are first scanned by the SEM beam. Then the analog output of the backscattered electron detector is translated using the detector's voltage levels into pixels with gray-level values. The gray-levels correspond to the degree of osteonal calcification (132). Backscattered SEM images have shown that the degree of osteonal calcification decreases from the Haversian canal to the cement line (133).

6.3. Micro-computed tomography

Since the late 1980's, micro computed tomography (microCT) has been extensively used to assess bone mineral density (BMD) on human and animal bone specimens (Figure 13; 135). The microCT provides a 3D evaluation, while the micro-X-ray provides a two-dimensional (2D) evaluation. The specimens that can be microCT'd are usually smaller in size than specimens that can be micro-X-rayed. The resolution of the microCT is not as high as the 1 micron of the micro-X-ray. In particular, the microCT cannot detect cement lines and therefore distinction of single osteons from interstitial bone. The microCT is nevertheless appropriate for studies of cortical porosity. Micro-CT provides the basis for finite element (FE) models of bone that are helpful in the understanding of the role of calcification in biomechanical setting, such as implant-cement-bone interface (section 9). While regular CT scan provides a lower resolution of bone tissue, it provides a basis for FE models of macroscopic bone to which the micro-FE models are now beginning to be linked (section 9).

7. ASSESSMENT OF TISSUE PROPERTIES: NANO-INDENTATION

Nano-indentation allows measurements of structural and mechanical properties of bone at the tissue-level in situ. That is, nano-indentation allows the assessment of the mechanical properties of the tissue that forms either single osteons or single lamellae. This technique addresses the mechanical properties at a level lower in the hierarchy of bone than the single osteon and single lamella level previously addressed in this chapter by mechanical testing as a unit. The elastic properties of bone tissue computed from nano-indentation data vary according to skeletal site, micro-structural specifications and individual characteristics such as age. Bone tissue with high turnover rates has lower mineralization and elastic properties. The results of nano-indentation suggest that heterogeneity affects fracture risk (136).

A small probe presses on a flat surface to indent at a submicron depth. The measured force and displacement of the probe can provide an estimate of the elastic, plastic and viscous properties of the specimen. To measure the indentation properties of bone specimens, Paietta et al. used an indentation tip in the shape of a sphere to press down on specimens of cortical bone (Figure 14; 137). The investigators used a range of indentation depths as well as a range of spherical tip sizes in order to determine different effects on the nano-mechanical properties. A ramp-and-hold method with a constant loading and unloading rate of mN/s was used to test the how the specimens' lamellar bone structures influence their nano-indentation properties. The investigators determined that using a small tip creates a more plastic response while a larger tip creates a more elastic response. In order to give a more accurate estimation of the modulus, it is best to indent the specimens to low depths to prevent stiffening. Measuring smaller volumes also gives better information on the specific structural features (136).

Nano-indentation properties were found to be highly dependent upon the bone's lamellar structure. The difference in elastic properties found between anatomical locations may involve turnover rate and osteon type (136). A higher turnover rate reduces the mean age of the osteons and therefore reduces mineralization. Different distributions of osteon types by CPL can also affect the results of the penetration of the indenting tip because of the relative change in orientation between collagen-apatite orientation and orientation of penetration (137). Interstitial bone was found to be consistently stiffer than osteonal bone (138). This difference was used to estimate, from relative volumes of osteonal and interstitial bone, differences in the elastic modulus of whole bone at different ages.

8. MICRO-STRUCTURAL ANISOTROPY

The study of the orientation and organization of collagen and apatite within single osteons and single lamellae has evolved in time. At first collagen/apatite was hypothesized to form helicoidal, almost longitudinal patterns in extinct osteons, transverse patterns in bright osteons, and alternating orientations forming 90 degree angles in alternate osteons. In time, the understanding of the osteon structure has become more sophisticated so as to include the variation of the pattern with each of extinct and bright lamella and the transition of the pattern between adjacent lamellae. As this line of research progressed, another question relative to organization was investigated. It dealt with the link between the micro- and macro- structure and whether the collagen/apatite orientation had a meaning at the macro-structural level. In particular, the question was whether such orientation is random or site-specific.

8.1. Collagen orientation patterns in single osteon

Collagen orientation plays a major role in the formation, elongation and arrest of micro-cracks (118). Carbonated apatite crystals in osteons generally match the orientation of the adjacent collagen (38), which varies in the bone tissue, and can either facilitate or arrest the elongation of the micro-cracks that form at the collagen-apatite interface (139, 140, 141). Whether the lamellae outside the perilacunar region are extinct or whether they are bright, characterizes the orientation of the collagen in a cross section viewed under CPL (117). The extinct lamellae show a collagen orientation that generally forms small angles with the osteon axis, whereas the bright lamellae show a collagen orientation that forms larger angles (Figure 16). Collagen bundle orientation in the region around the lacunae is not random and follows specific patterns (Figure 17a, 17b). The collagen bundles and the adjacent canaliculi have a 360 degree distribution. For the lacunae in extinct lamellar specimens, 72% of observed collagen in the proximal, 72% of observed collagen in the distal, 81% of the observed collagen on the lateral left, and 79% of collagen at the lateral right, regions followed the adjacent canalicular orientation. For the lacunae in bright lamellar specimens, 72% of collagen in the proximal, 71% of the collagen in the distal region, and 80% of collagen in each of the lateral left and right regions followed the adjacent canalicular orientation. That is, for the mentioned percentages for each of the lamellar types, the collagen follows locally at the perilacunar region the canalicular orientation, which is circumambiently- perpendicular to the lacunar/ECM interface. The percentage of radially tilted lacunae with collagen following the adjacent canalicular orientation at the slender apex is significantly smaller in extinct, than in bright, lamellae.

Confocal microscopy was used to study collagen with its relation to caniculi and lacunae because it has a very high resolution when compared to polarized light microscopy and it allows investigators to directly monitor collagen orientation through consecutive images without gaps between slices. X-ray diffraction and electron microscopy were give collagen virtual slices with gaps between them, making them less preferable. Collagen orientation at the region around the lacunae that was away from the lacunar apices showed collagen orientation that mostly demonstrated circumambiently perpendicular orientation matching canalculi orientation in both extinct and bright lamellae types. Extinct lamellae appear to be thicker than the bright lamellae when looking at cross sections under CPL and confocal microscopy, implying that extinct lamellae would be able to have lacunae with larger radial tilts than bright lamellae would. It is more likely in collagen departing the perilacunar region that the extinct lamellae will show a smaller circumferential tilt than the bright lamellae (117).

The orientation of collagen and apatite affects micro-cracks' initiation and spread under axial loading (Figure 17c, 17d). Micro-cracks begin at the lacunar apices under axial loading, implying that they are associated with the osteocyte lacuna tilts in combination with the collagen and apatite organization. These fractures depend on the angle between the lacuna and osteon axes and on the surrounding tissue grain (140, 142). They will most likely form at the lacunar apex because extinct lamellae are more likely to have radially tilted lacunae than bright lamellae. Since the collagen is not as likely to orient itself with the canalculi at the apex in extinct lamellae, a micro-crack is less likely to radiate longitudinally, which helps reduce the chances of added propagation. However, in bright lamellae, micro-cracks are probably going to begin at the lacunar apex because the collagen does orient itself with the canaliculi and would turn away from the osteon axis. In bright lamellae, collagen bundles are oriented transversely to the axis (141).

8.2. Collagen orientation patterns in macroscopic bone

The distribution of collagen orientation within cortical bone is not random at load-bearing sites. Rather it forms 3D patterns in human bone, whether healthy or affected by metabolic disease, as well in animals (Figure 18; 21, 143, 144, 145, 146, 147, 148, 149). The patterns link collagen orientation to the force distribution during function. The percent of collagen forming small angles with the long bone axis is higher at the sites mostly stimulated in tension (e.g. tension due to bending of the femur) while the percent of collagen forming larger angles with the long bone axis is higher at the sites mostly stimulated in compression (e.g. compression due to bending of the femur). Additional research is needed to investigate how such distribution changes with age and with the presence of bone disease. For instance, when the macro-geometry of the bone is altered by rickets, the distribution of the collagen orientation is altered to compensate for the altered distribution of loading (21).

Collagen bundles are organized in 3D patterns in macroscopic bone through the specific osteon types classified by CPL (section 4.1). Such organization of osteons, perhaps in conjunction with their degree of calcification, may determine the bone tissue response to loading (145). In a study by Beraudi et al., the three CPL osteon types were found differently distributed through the length of a human fibula. The alternate osteons dominated the mid-shaft, while extinct and bright osteons dominated proximal and distal ends of shaft. This differentiation may be linked to the force distribution at the fibula in terms of the combination of influence of collagen orientation within the lamellae on mechanical properties of osteons (section 5), adequate resistance of alternate osteons under both tension and compression than extinct or bright alone, and rarity of bright osteons (147).

9. MODELS AND SIMULATIONS

Hand-in-hand with the generation of experimental findings, mathematical and engineering techniques have been applied to carry out in depth data analysis. Models of secondary osteons and lamellae have been developed to reflect their multi-directional structures so as to investigate the functions of the elementary components when they are under different loading conditions (7, 110, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167).

Over the years, 2D and 3D models of specific aspects of the Haversian system have contributed to the understanding of the experimental observation. A 2D model of the quarter-staggered configuration of collagen demonstrated the relationship of loci on individual collagen molecules within the fibril. For example, the amino-terminal edge of the "hole zone" is the site where the collagen molecule is cleaved by tadpole collagenase, by a disaccharide unit is covalently bound to the α1-CB5 peptide, and by the carboxyl-terminal intermolecular cross-linking. The carboxyl-terminal edge of the "hole zone" is the site of aminoterminal cross-linking (168). Material properties that depend on collagen bundle orientation and degree of calcification were included in the "lacuna-enhanced osteon" model, which is the first to include the collagen-apatite orientation of bone. This model investigated the influence of the collagen-apatite's orientation with respect to the loading direction in terms of the specimen's strain and stress fields. The model showed the axial deformation in the experiments and the difference in the greatest principal strain of the specimens (Figure 19; 16, 17, 20, 115).

The lacunar major axis parallels the axis of the osteons, and the model simulations of osteon with lacunae show that the lacunar strain concentration role (169, 170). The average concentration factor is the ratio between stress at the perilacunar region and axial strain on the osteon. The extinct osteons had higher average concentration factors than the bright osteons when observing them under elastic compression. Local mechanical response is not affected by larger perilacunar regions (171). The mid-equatorial region is the furthest region from the lacunar axis, so it moves the most as lacunar space decreases under tension and increases under compression. This causes it to have the greatest strains when it is stressed or compressed. Collagen orientation in this region can help the ECM to resist stress from tensional loading. The lacuna-enhanced model parallels the 2D osteon model with lacunae (172) and 3D "boxed" models of a perilacunar region of one lacuna and ten canaliculi (171). These three models show that perilacunar strains are intensified under tension and compression. The lacuna-enhanced osteon model simulation of canalculi with diameters of 1mm showed that canaliculi increase the strain at the equator of the lacunar wall (118).

In recent years, system biologists, mechanical and software engineers and applied mathematicians have increasingly collaborated towards developing 3D multi-scale virtual rendering of bone tissue able to address specific clinical issues (165, 166). On the basis of definition by clinicians of the challenges that they face, expert researchers in disparate fields, from orthopaedics, dentistry, bone biology, biomechanical engineering, and biomaterials, to applied mathematics are pushing the limit of their individual expertise to share techniques specific to each field, that, appropriately marshaled, make possible to prepare and validate cost-effective hierarchical (or multi-scale) models for clinical assessment of bone. The clinical problems that are viewed from a multi-scale perspective are: (i) assessment from bone parameters of bone fracture risk at various skeletal sites, including hip and spine, (ii) evaluation of osteo-integration of implants at hip, knee, spine, mandible and maxilla; (iii) evaluation of stress adaptive bone remodeling and bone repair in the presence of disease at various skeletal sites including hip, knee, spine, mandible and maxilla, and (iv) appraisal of effect of bone metastases on the mechanical properties of the bone tissue. In the US, the Interagency Modeling and Analysis Group aims and the National Institutes of Health Roadmap have encouraged researchers to design a common plan of action to develop state-of-the-art 3D multi-scale models of bone. Experts from different fields will likely continue to need to teach each other the latest developments concerning bone modeling and to design collaborative plans to solve challenging problems.

In the last two decades, clinicians have used imaging to assess bone quality, broadly understood as the ability of the bone tissue to perform its appropriate function. Dual energy X-ray absorptiometry (DXA), quantitative ultrasound, quantitative computed tomography, peripheral quantitative tomography, microCT, magnetic resonance, radiographic texture analysis, and FE models based on such imaging methods, have shown that BMD, trabecular and cortical micro-architecture, mass, and tissue mechanical and compositional properties, play an important, but yet undefined role in bone quality. Such parameters are in turn varied as functions of age, sex, weight, height, previous fracture occurrence, parent hip fracture, smoking, use of glucocorticoids, rheumatoid arthritis, secondary osteoporosis, and alcohol consumption (173). Since 2000, when the scientific community reached the conclusion that BMD alone does not assess the biomechanical health of the bone tissue, the interest in bone micro-structure has mounted. However, the imaging techniques mentioned and the related modeling do not view the bone tissue below a resolution of 0.5mm. At such resolution, the micro-structural elementary components are indiscernible.

From a bio-material point of view, bone can be considered a natural composite-hybrid material (174) in terms of the three-phases of (i) organic collagen fibers, (ii) inorganic carbonated hydroxyapatite crystals and (iii) a matrix of additional proteins and water (section 3). Both the collagen-apatite orientation and the degree of tissue calcification were found to vary through the tissue and play a role in the local material properties of the bone tissue (sections 4 and 5). For instance, collagen-apatite orientation and the degree of tissue calcification affect the osteo-integration at the bone-implant interface (141). By creating discontinuities in the bone tissue, osteocyte lacunae were found to alter the strain and stress distribution at the perilacunar region (118, 170). Both collagen-apatite orientation and presence of osteocyte lacunae are hypothesized to play a role in the elongation, propagation and arrest of micro-cracks (141). The mechanical stimulation of the osteocyte lacuna is of great interest to researchers in reference to the potential role of the osteocyte in mechano-transduction (167). The cited literature shows that laboratories around the world have amassed significant information on the biomechanical implications of micro- and nano-structures. There is accordingly a sufficient knowledge about the lower level structures to undertake the challenge of interfacing the various multi-scale levels in integrated models.

Systemic modeling and simulation approaches for multi-scale structures have greatly developed during the last decade. Currently, extensive research is devoted to the linkage of the material and mechanical properties of cortical bone among the various levels of the hierarchy (175, 176). The study of the mechanical properties of macro-specimens per se has been matter of research by many investigators (e.g. 177, 178, 179, 180, 181, 182, 183). The question of the ultra- and micro-structural specifications that lead to macroscopic fracture remains largely unknown. Micro-structural heterogeneity is hypothesized to have direct bearing upon the fracture behavior of the Haversian cortical bone because the micro-crack behavior varies in dependence of the specifications of the elementary components that form the micro-structure. A mathematical structural model of prestress in the bright lamella allows estimate of the magnitude of the prestress and proposes a role of the oblique collagen bundle of the bright lamella in the prestress mechanism (Figure 20; 15). Other phenomena are present at the micro-structural levels that cannot be observed in macroscopic specimens because they become buried in the complex variation of tissue level parameters within the macro-specimen. For instance, pinching of osteons' hysteresis loops is characteristic of the micro-structure (sections 5.9 and 5.10). Application of the fixed-point-theorem allowed interpretation of pinching in terms of high stability of osteon structure and resistance to micro-cracking (116). Engineering theories, such as Cosserat theory, continue to be applied to reconcile the parametric changes of bone mechanical properties across the hierarchical levels to understand the contribution of each structural scale to the overall behavior of bone (Figure 21; 184).

The loading conditions and the specifications of the Haversian system each guide the direction of micro-crack growth. Short cracks are found more frequently in tissue than long cracks. Under tension, osteons have been observed to act as stoppers of micro-cracks coalescing and propagating through the interstitial bone. However, if a micro-crack elongates to a critical length, the micro-crack can penetrate osteons and then move through the lamellae in the osteon. If the micro-crack is able to break through a Haversian canal, the bone will likely fracture. If osteons are loaded under compression in the same direction as their micro-cracks, it is likely that the micro-crack will enter the osteon (185).

Traditional mono-scale approaches have been found inadequate to model multi-scale materials because of the range of scales and the prohibitively large number of variables involved (186). Because the multi-scale environment often shows that different scales are governed by characteristically different physical laws (e.g. quantum mechanics at one scale and classical mechanics at another), fields such as mathematical physics and stochastic processes are developing rapidly (187, 188). Approaches such as the Car-Parrinello method, quasi-continuum method, super-parametrization, heterogeneous multi-scale method, Vanden-Eijinden's method, coarse-grained Monte-Carlo models, adaptive model refinement and patch dynamics, have become available for possible bone applications.

Homogenization theory allows computation of the material properties of one scale from the components of the sub-scale. It has been applied to FE models of groups of secondary osteons (e.g. 157). Various homogenization approaches are now being adapted to evaluate properties effecting bone tissues: (1) numerical up-scaling to compute effective mechanical properties; (2) asymptotic expansions based on multiple scales to derive effective parameters as functions of solution on the lowest scale; (3) analytical relations based on spectral representation, which give the effective property of bone tissues as an analytic function in the complex plane; and (4) coupled bounds to evaluate bone tissue properties from other known parameters (e.g. estimation of permeability or elastic moduli from electric properties). Mathematically challenging problems are related to the computation of viscoelastic properties: e.g. nonlinear dispersive models of bone marrow and nonlinear homogenization methods. Homogenization can also be adapted to assess bone structural properties from acoustic and electro-magnetic waves in bone tissue (e.g. 169).

Often defined as the "science of patterns" (189), mathematics can be applied to identify statistical patterns within the variation of specifications of components (190). Also, the appraisal of the key micro-structural elements that vary statistically was investigated a decade ago by two distinct approaches. Yeong and Torquato (191) thoughts were in terms of pixel-by-pixel representations (conceivable by materials scientists), while Portilla and Simoncelli (192) use a wavelet basis (conceivable by image processors). This advancement in imaging analysis could be used to complement the current microCT studies that usually refer to relatively smaller regions. Indeed, the description of micro-structural variation in 3D throughout specific extended sites is challenging. Inverse problem approaches have started to be used to study the trabecular network, although not the Haversian network (193). Computational geometry also offers a variety of techniques for optimization of data collections from images (e.g. 194). Percolation theory, recently applied to ice to explain the global warming-induced process of ice melt (195) and to trabecular bone (196), can be applied to compact bone hierarchy and offers the potential to explain the porosity of one scale that can be compatible with the phenomena at the next scale.

Various groups around the world have built models of bone tissue that address portions of the bone hierarchy described by subsets of parameters. Such models are of: (1) a cell network within the mineralized matrix viewed as a combination of collagen and apatite needles; and (2) compact bone micro-structure comprised of single osteons or osteon groups characterized by various arrangements of elementary components. The removal of one of the limiting assumptions of isotropy becomes an engineering challenge with the introduction of the anisotropy. An example is the issue of which failure criterion to choose (197). Various publications of the last three years on bone tissue point to the need to combine the models that address two scales into a full 3D model that maintains the essential characteristics of each level (e.g. 198, 199). In addition to the insights from studies of the 3D multi-scale structure of bone to be gained in respect of the clinical problems here addressed, such studies will offer further insights pertinent to (I) the in vitro development of bioengineered bone and (II) the understanding of bone as an organ in the human body (200, 201, 202, 203, 204).

10. OPEN PROBLEMS

We consider here open problems from an experimental and a computational/modeling point of view. In terms of experimental/structural understanding of the relation between bone micro- and macro- structure, we have seen in the previous sections that the distribution of osteonic lamellae and interstitial bone in cross sections of long bone shafts is not random. In fact, the distribution of osteonic lamellae in cross sections of long bone shafts shows a pattern compatible with the shaft shape and the distribution of forces usually operating on long bone under both normal and pathological condition. In general terms, there is indication of a high incidence of birefringent extinct in bone regions loaded in tension and bright lamellae in bone sectors loaded in compression. Patterns should be defined under healthy and pathological conditions in relation to mechanical loading. Pending questions are (a) the relation between osteonic lamellar distribution and geometry of the bone shaft loaded in bending and torsion, with respect to the mechanical properties of extinct and bright lamellae; (b) the relation between osteonic lamellar distribution and geometry of the bone shape in determining fractures, especially in bending, with respect to the mechanical properties of extinct and bright lamellae; and (c) the structural classification of osteons in diaphysis of vertebrates, whose lamellar structure somewhat differs from that of humans, to increase accuracy of interpretations.

The effect of specific clinical factors on bone architecture that renders it prone to fracture is largely an open question. While age is known to decrease cortical porosity, the occurrence of fracture may be related to the distribution of the increased porosity and to the decreased heterogeneity of the tissue (205, 206). Interestingly, the mechanical properties of single osteon at specific degree of calcification do not change with age (16). Therefore, the weakening of bone may result from higher percent of older bone showing higher percent of osteons at late stages of calcification, higher percent of resorption lacunae, possibly altered collagen orientation and increased percent of micro-cracks. Such weakening may result in a fracture when it occurs at sites more mechanically challenged. Since the early 2000s the clinical community has reported occurrence of fractures not typical before use of bisphosphonates (207). So-called atypical femoral fractures usually occur without a fall in patients with increased femoral cortical thickness, just below the smaller trochanter or at mid-diaphysis, oriented transversely rather than spirally with a medial spike. Some of these patients had been on long-term bisphosphonate therapy.

The effect of anti-resorption bisphosphonates on the micro-structural components of the compact bone is largely unknown. Bisphosphonates have been shown to lower the amount of bone turnover. Therefore, bone treated with bisphosphonates shows reduced bone loss and higher percentage of older tissue, i.e. more mature mineral and matrix bone tissue (208). Specifically, risedronate has been shown to curtail bone remodeling and lessen the area and number of cortical pores. Reduction of bone remodeling and porosity has been associated with reduced fracture risk in epidemiological studies (209).

The effect of bone anabolic agents on bone micro-structure is beginning to be explored. The effect of recombinant human parathyroid hormone PTH(1-34) has been investigated on patients affected by osteoporosis since the 1970's (210, 211, 212, 213, 214, 215, 216, 217). PTH(1-34) helps to build up bone regardless of whether it is given to patients alone or if it is given along with anti-resorptive treatments like estrogen and calcitonin. Short-term PTH(1-34) treatment has been associated with decreased fracture risk in patients (214, 218, 219) and animal models (220, 221). Male and female patients display different anabolic actions of PTH when studying their compact and cancellous elements. In post-menopausal women, cortical volume, cortical thickness, endocortical wall width and porosity increased notably (222). Studies that were focused to uncover the cellular or molecular means that lead to PTH's anabolic effect on bone have shown that PTH increases the mesenchymal stem cell number and activates the vascular endothelial growth factor (223). PTH treatment was also found to reduce osteocytic sclerostin and Dkk1, which negatively affect Wnt binding to Lrp5 (179, 180, 224, 225). Reduction of sclerostin by PTH would stimulate Wnt and Bmp, both of which stimulate osteoblast function (226, 227). In a recent study on the micro-structural component of iliac crest biopsies of post-menopausal patients affected by osteoporosis and treated with PTH(1-34), lamellar thickness was found to be increased in comparison to age- and sex- matched osteoporotic patients to match the thickness values of pre-menopausal women (228). If this result is confirmed at weight-bearing sites, the lamellar thickening by PTH(1-34) treatment may reverse the thinning of bright lamellae observed at the femoral neck of patients who suffered femoral neck fracture, but not present in non-fractured controls (229).

11. ACKNOWLEDGEMENTS

Maria-Grazia Ascenzi provided overall outline, references, writing and editing. Allison Roe searched references and contributed writing and editing.

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Abbreviations: OC: osteocalcin, MGP: matrix Gla-protein, CPL: circularly polarized light, TEM: transmission electron microscopy, SEM: scanning electron microscopy, STEM: scanning transmission electron microscope, microCT: micro computed tomography, BMD: bone mineral density, FE: finite element, DXA: dual energy X-ray absorptiometry.

Key Words: Bone, Finite element, Lacuna, Lamella, Mathematical model, Mechanical properties, micro-structure, Osteocyte, Seconday osteon, Review.

Send correspondence to: Maria-Grazia Ascenzi, UCLA, Orthopaedic Hospital Department of Orthopaedic Surgery, University of California at Los Angeles, Rehabilitation Bldg 22-69, 1000 Veteran Avenue, Los Angeles, CA 90095, Tel: 310-825-6341, Fax: 310-825-5290, E-mail:mgascenzi@mednet.ucla.edu.