Bone Material Properties and Skeletal Fragility

Abstract

Deformations of vertebrae and sudden fractures of long bones caused by essentially normal loading are a characteristic problem in osteoporosis. If the loading is normal, then the explanation for and prediction of unexpected bone failure lies in understanding the mechanical properties of the whole bone—which come from its internal and external geometry, the mechanical properties of the hard tissue, and from how well the tissue repairs damage. Modern QCT and MRI imaging systems can measure the geometry of the mineralized tissue quite well in vivo—leaving the mechanical properties of the hard tissue and the ability of bone to repair damage as important unknown factors in predicting fractures. This review explains which material properties must be measured to understand why some bones fail unexpectedly despite our current ability to determine bone geometry and bone mineral content in vivo. Examples of how to measure the important mechanical properties are presented along with some analysis of potential drawbacks of each method. Particular attention is given to methods useful to characterize the loss of bone toughness caused by mechanical fatigue, drug side effects, and damage to the bone matrix.

Appendices

Appendix 1: Assumptions and Simplifications of a Linear Analysis

To convert the force and displacement of a specific structural test of a bone into material properties that can be compared between different laboratories, three important concepts are needed. The first two are normalizations of the force and displacement. The normalization of force is stress (Fig. 8) defined as the force-per-unit-area. The normalization of the displacement is the strain which is the displacement divided by the appropriate size of the specimen (Fig. 8). There are three normal stresses and three shear stresses at each point in a material. Similarly, there are three normal strains and three shear strains. (See [94]) for outstanding detail on stress and strain.) For a normal stress applied to a linear material, stress is proportional to the strain as: Stress = (Young’s Modulus) × Strain. Similarly for a simple shear stress: Stress = (Shear Modulus) × Strain. The Young’s modulus (E) is related to the shear modulus (G) through the formula, E = 2G(1 + ν), where ν is the Poisson’s ratio. For most materials, when a compressive normal stress is applied to a cube, the compressive strain is accompanied by a lateral expansion of the material. Poisson’s ratio is the ratio of the lateral to the normal strain under a normal stress. Only two of the linear isotropic properties (E, G, ν) are independent of each other. The third thing needed to convert a force–displacement result into a stress–strain result is a mathematical stress analysis of the specific specimen type used in the test. Examples of such an analyses are presented in the main text of the paper.

Fig. 8

These are simple definitions for normal and shear stress or strain based on the size and deformation of a cube. In general, the stress and strain are the values that result as the size of the cube is reduced to zero. In this figure d _n is the normal displacement and d _s is the shear displacement

Appendix 2: Best Practices for Specimen Preparation and Testing

Mechanical properties of bone samples measured ex vivo depend on many factors. Some of these factors are a reflection of the physiological condition of the subject or animal from which they were obtained, including initial bone mineral density, bone quality, and relevant pathologies or treatments. However, postmortem handling of bones and bone samples can have just as profound of an effect on the measured mechanical properties, therefore, care must be taken to ensure the fidelity of samples for mechanical testing in order to obtain accurate and controlled results.

Fixation, hydration, and freezing are known to affect the mechanical properties of bone and bone samples, therefore, care must be taken to maintain the integrity of bone during storage. The freezing process [95, 96] and multiple freeze/thaw cycles [96, 97] have been found to have some effect on the mechanical properties, although bone samples generally maintained their mechanical integrity during freezing. Additionally, the amount of exposure time following thawing can affect measured material properties of fresh-frozen bone specimens [98]. Studies have also compared the properties of embalmed and fresh–frozen bone and found a significant decrease in mechanical integrity after embalming [99]. Hydration of bone samples can also strongly affect the mechanical behavior of bone, with dehydrated samples appearing stiffer and more brittle than wet/rehydrated samples [95]. Rehydration of dry/dehydrated samples has been shown to effectively restore the original mechanical properties of fresh wet/hydrated bone [96]. In general, the most widely accepted storage method for bone mechanical testing samples is freezing fresh, unfixed bone samples in saline-soaked gauze at −20° C. Samples should be completely thawed before mechanical testing, and should be kept hydrated throughout testing.

Demineralization of bone samples can be useful for isolating the mechanical behavior of the organic matrix of bone [100–102]. Demineralized bone samples are typically cut into “dog bone” samples and tested in tension.

Specimen size is also an important consideration for bone mechanical testing samples. Samples must be large enough to be considered a continuum (i.e., the mechanical behavior of the heterogenous material approaches that of a homogeneous material with the same apparent mechanical properties). This is confounded by the fact that bone is a relatively heterogeneous tissue, with cancellous bone being particularly heterogeneous. For a continuum, the minimum sample dimension must be significantly larger than the dimensions of the subunit (greater than five times the subunit dimension is the general rule). For example, human trabeculae are typically 100–300 μm thick, with spacing of 300–1500 μm. It is important to create mechanical testing samples that are large enough that these heterogeneities do not result in stress concentrations that will result in misleading mechanical tests.

It is not uncommon to test whole bones (typically femur, tibia, radius, or vertebral bodies) when using small animal models such as mice or rats. However, when larger animal models or human subjects are used, smaller bone samples are typically created for mechanical testing. These include “dog bone” samples, cancellous bone cores, or bone beams (including notched beams). The process of creating these samples may introduce a certain amount of error into the mechanical tests. Cutting samples from larger whole bones typically involves sawing and/or grinding larger samples to specific dimensions, which can involve high temperatures that may act to dehydrate the bone sample. Therefore, it is recommended to always thoroughly rehydrate bone samples prior to mechanical testing. Additionally, microdamage may be created in bone samples during preparation, therefore, steps should be taken to minimize disruptive loading or damaging conditions during preparation. Finally, if notched samples will be used for mechanical testing, the process of creating the notch must be performed consistently and carefully to ensure the fidelity of mechanical tests.

The different loading modes described above can have a strong effect on the measured mechanical properties. The most commonly used loading methods for bone samples are axial compression, tensile testing, 3-point bending, and 4-point bending (Fig. 9). Bone is stronger in compression than tension, since the bone mineral phase confers resistance to compression and shear, while the organic phase (collagen) provides the tensile strength. Bending will create a combination of compression and tension, with failure occurring at sites of maximum tension. Cancellous bone specimens (cores) are typically testing in compression; demineralized bone samples are typically tested in tension; long bones from small animal models, bone beams, or notched specimens are typically tested in 3- or 4-point bending. The choice of using 3-point bending versus 4-point bending can be important for accurately determining mechanical properties, and is often dependent on the type of specimen being tested. 3-point bending places the load directly above the site of failure, while 4-point bending applies loads away from the site of failure, which is more desirable. However, 4-point bending setups can be difficult to fine tune, and can apply loads unevenly to samples, so that one side is being loaded with more force than the other. Additionally, 4-point bending is more likely to violate the slenderness assumption, since it used four contact points rather than three. The “slenderness ratio” of a sample is the ratio of the length of the sample to its cross-sectional dimension. A sufficiently high slenderness ratio (>10) is necessary when beam theory will be used to determine material properties from measured structural properties. Whole femurs from small animal models are often tested in bending and simple beam theory is used to estimate material properties. However, the femur has a low slenderness ratio (~5) and therefore does not conform to an ideal bending specimen (e.g., shear stresses may not be negligible compared to bending stresses). The radius, on the other hand, has a much higher slenderness ratio (~13), and has therefore been proposed as a better choice for material property estimation, although direct comparisons of femur versus radius were not reported [103].

Fig. 9

Common sites of damage in a four-point bending specimen. The linear solution for this problem does not account for damage. Damage at or outside of the inner load points is particularly problematic