Mechanical properties and the hierarchical structure of bone

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Abstract

Detailed descriptions of the structural features of bone abound in the literature; however, the mechanical properties of bone, in particular those at the micro- and nano-structural level, remain poorly understood. This paper surveys the mechanical data that are available, with an emphasis on the relationship between the complex hierarchical structure of bone and its mechanical properties. Attempts to predict the mechanical properties of bone by applying composite rule of mixtures formulae have been only moderately successful, making it clear that an accurate model should include the molecular interactions or physical mechanisms involved in transfer of load across the bone material subunits. Models of this sort cannot be constructed before more information is available about the interactions between the various organic and inorganic components. Therefore, further investigations of mechanical properties at the `materials level', in addition to the studies at the `structural level' are needed to fill the gap in our present knowledge and to achieve a complete understanding of the mechanical properties of bone.

Introduction

Bone has a varied arrangement of material structures at many length scales which work in concert to perform diverse mechanical, biological and chemical functions; such as structural support, protection and storage of healing cells, and mineral ion homeostasis. Scale is of importance in discussing bone architecture as the structure is hierarchical and complex. Every technique of assessing bone architecture or the properties of a given structure has its own resolution, and therefore a combination of techniques is required to reveal the material structures and properties at the many different length scales. For example, electron microscopy examines bone ultrastructure at the nanometer level, Fourier transform infrared spectroscopy (FT-IR) and x-rays measure components at the Ångstrom level, light microscopy details features at the level of a few microns, and conventional mechanical testing of small specimens measures the mechanical properties of bone at the hundreds of microns or more level (at best).

In order to understand the mechanical properties of bone material, it is important to understand the mechanical properties of its component phases, and the structural relationship between them at the various levels of hierarchical structural organization 1, 2, 3. These levels and structures are: (1) the macrostructure: cancellous and cortical bone; (2) the microstructure (from 10 to 500 μm): Haversian systems, osteons, single trabeculae; (3) the sub-microstructure (1–10 μm): lamellae; (4) the nanostructure (from a few hundred nanometers to 1 μm): fibrillar collagen and embedded mineral; and (5) the sub-nanostructure (below a few hundred nanometers): molecular structure of constituent elements, such as mineral, collagen, and non-collagenous organic proteins. This hierarchically organized structure has an irregular, yet optimized, arrangement and orientation of the components, making the material of bone heterogeneous and anisotropic (Fig. 1).

It has been shown that the mechanical properties of bone vary at different structural levels. For example, the Young's modulus of large tensile cortical specimens has been shown to be in the 14–20 GPa range [4](wet specimen, macrostructural property), while that of micro-bending cortical specimens was 5.4 GPa (wet specimen, microstructural property [5]). However, it is unclear whether this discrepancy is due to the testing method or the influence of microstructure. Recently, the Young's modulus of osteon lamellar bone measured by nanoindentation was approximately 22 GPa (dry specimen, sub-microstructure property [6]) close to that for the macrostructure. There are, at present, no data in terms of Young's modulus for the nanostructure. The basic building blocks (apatite crystals and collagen fibrils) are extremely small, making mechanical testing nearly impossible. The plate-shaped crystals of carbonate apatite are just tens of nanometers long and wide and some 2–3 nm thick [2], the various collagen forms are only a few nanometers wide (fibrils, 1.5–3.5 nm; fibers, 50–70 nm; bundles, 150–250 nm). Unsuccessful attempts have been made to extrapolate the properties of the primary constituents (collagen and mineral) from the macrostructural mechanical properties by working backwards from a mixed composite model 7, 8. Therefore, it seems of primary importance to break down the mechanical testing of bone according to the various levels or architecture within bone material.

Section snippets

Cortical and cancellous bone

At the macrostructure level, bone is distinguished into the cortical (or compact) and cancellous (or trabecular) types. In cross-section, the end of a long bone such as the femur has a dense cortical shell with a porous, cancellous interior. Flat bones such as the calvaria have a sandwich structure: dense cortical layers on the outer surfaces and a thin, reinforcing cancellous structure within. Although both types of bone (cortical and cancellous) are most easily distinguished by their degree

Microstructure

Mineralized collagen fibers form into planar arrangements called lamellae (3–7 μm wide). In some cases these sheets (lamellae) of mineralized collagen fibers wrap in concentric layers (3–8 lamellae) around a central canal to form what is known as an osteon or a Haversian system. The osteon looks like a cylinder about 200–250 μm in diameter running roughly parallel [29]to the long axis of the bone. Other forms of cortical bone where the mineralized collagen fibers are less well registered and no

Collagen fibers from hundreds of nanometers to 1 μm

The most prominent structures seen at this scale are the collagen fibers, surrounded and infiltrated by mineral. The attachment sites of macromolecules onto the collagen framework are not distinctly known, although several immunohistological studies have shown preferential labeling of some macromolecules in a periodic fashion along the collagen molecules and fibers [54].

Crystals and collagen fibrils down to tens of nanometers

The sub-nanostructures of the three main materials are crystals, collagens, and non-collagenous organic proteins. The mature

Composite modeling of bone material

The composition of bone tissue is more complex than most engineering composites. A more fundamental understanding may be achieved by models employing a collagenous matrix and mineral crystals. These organic and inorganic constituents act together to give bone its unique properties. The viscoelastic properties and resistance to fracture cannot yet be explained by explicit molecular mechanisms or commonly measured physical characteristics 58, 59, but models of the elastic properties and their

Mineral, collagen and their interface

The previous theories of macroscopic modeling are different from the material-level models which explore the relationship between the mineral crystals and the collagen matrix [8], although they did originate from the fiber-composite models of mineral and organic matrix [35]. There are still no reliable data regarding the elastic properties of the mineral crystals and the collagen matrix of bone. Isolated crystals retaining all of the native features of bone mineral can be obtained using

Research challenges

This review of the mechanical properties of bone has indicated a number of areas in which additional research would advance our understanding of bone as a structure and a material. The following questions remain unanswered:

  • 1.

    Is there a size effect in bone? If yes, does the critical size depend on the particular property under consideration? What is the hierarchical level at which homogenized material properties can be obtained that are similar to those observed macroscopically in whole bone

Acknowledgements

The work of Jae-Young Rho was supported in part by the Whitaker Foundation and a Faculty Research Grant from The University of Memphis. Liisa Kuhn-Spearing has been supported by an Institutional NIH Training Grant to the Children's Hospital, Boston. Peter Zioupos has been supported in part by AFOSR, the Wellcome Trust and the NATO scientific exchange program.

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