Читать книгу Fractures in the Horse - Группа авторов - Страница 34

When a load is applied to a material, it will deform. The load can be standardized per unit area, termed stress, and deformation quantified as change in length in relation to its original length, termed strain. The relationship between stress and strain reflects the stiffness, or Young's modulus, of the material (Figure 2.11). A material that deforms little as the stress is increased has a relatively high Young's modulus and is termed stiff, whereas one that has a low modulus is termed compliant or flexible. Many materials, including bone, behave in an elastic manner, deforming proportionally in relation to stress and recoiling to their original shape when the stress is removed (Figure 2.11). However, as the magnitudes of stress, and hence strain, rise, the distracting forces acting within the material increase. If the stress is so great as to strain the material to a point where the internal forces exceed a critical limit, it causes damage. This is referred to as the yield point, and if this is exceeded the structure will undergo plastic deformation and remain permanently deformed when the load is removed (Figure 2.12). If the stress is increased beyond the yield point, then the material will continue to strain to a point where it fails completely, termed its ultimate strain (Figure 2.13). The stress applied to reach this point defines the ultimate strength of the material. The degree of strain that a material can undergo between starting to yield and failure largely determines its energy absorbing capacity. A material that fails quickly after reaching its yield point absorbs little energy and is termed brittle. Conversely, one that undergoes significant plastic deformation absorbs relatively more energy and is termed tough (Figure 2.14).

Bone is a complex material, and there are many factors that affect its mechanical properties. It is a composite made of two different phases: collagen fibres and mineral crystals. The organic phase is relatively compliant, while the mineral endows rigidity. Variation in mineral content has a profound effect on the modulus and stiffness of bone but is less associated with strength [27]. Conversely, the organic component of bone is more related to its strength. The impact of this is apparent from studies that used radiation to disrupt collagen in bone samples. Bone density measurements remained the same with varying levels of collagen damage, but bone strength varied significantly in proportion to the level of collagen damage (Figure 2.15) [28].

Figure 2.12 Graphical and schematic illustrations of the relationship between stress imposed on an object by a tensile load and deformation of the object beyond its yield point.

Figure 2.13 Graphical and schematic illustrations of the relationship between stress imposed on an object by a tensile load and deformation of the object beyond its ultimate strength.

Recently, there has been increasing focus of attention on subtle variation in the organic phase of bone and its impact on the tissue's material properties. The Raman spectral signature of bone provides information on the chemistry of both the mineral and organic phases of bone matrix, which in turn are related to its material properties. Bonds within molecules of a material vibrate, just like a stretching spring: this form of molecular motion is manifest as heat. The frequency of these vibrations depends on the mass of the atoms at either end of the bond. For example, an H−H bond vibrates at a higher frequency than an O−O bond. The frequency of vibration is characteristic of specific chemical bonds and can be used to analyze the chemistry of samples.

Laser light of a specific wavelength, in bone 830 nm, can be used to ‘excite’ molecules, i.e. heat them up. The laser light travelling through the matrix and hitting a molecule is scattered. Most of it is unchanged, but some loses energy when exciting chemical bonds and changes colour – this is called Raman scattering. One million photons of light are required to obtain one Raman photon. Plotting the intensity of the scattered light (or energy absorbed by the sample) against the colour of scattered light gives a Raman spectrum, which shows which bonds are vibrating within the molecules of the matrix.

The spectral signatures of bones with matrices of different composition in both healthy individuals and subjects with or suspected of having disease/degenerative conditions can be identified from the magnitude and width of the spectral peaks. For instance, differences in chemical composition of the matrix from bones with widely differing functional roles can be identified and related to their mechanical needs, e.g. (i) the tympanic bulla has a high mineral to collagen ratio, which makes it suitable for transmission of sound but brittle, (ii) bone in the antler of deer has a low level of mineralization, making it tough and suitable for fighting, and (iii) locomotor long bones have mid‐range mineralization [29].

Figure 2.14 Schematic to illustrate the effects of the mechanical properties of a material on its ability to absorb energy before failing. The dotted line represents a material that behaves in a brittle manner whereas the red line represents a tough material, which undergoes much greater plastic deformation before failing. The shaded areas under the graphs represent the energy absorbed to failure.

Figure 2.15 Effects of progressive radiation damage to the organic phase of bone on its overall mechanical properties.

Source: Based on Currey et al. [28].

Raman spectroscopy is sufficiently sensitive and precise to demonstrate subtle differences in matrix chemical composition within an individual bone. For instance, in a weight‐bearing bone of the appendicular skeleton, such as the third metacarpal of the horse, the material properties are uniquely and site specifically adapted at the molecular level to optimize function. The mid‐diaphysis is most highly mineralized, which results in maximum stiffness to resist bending forces yet allows flexural strains for energy efficient locomotion. Conversely, bone matrix in the metaphyseal and epiphyseal regions, which are loaded more in compression, has lower levels of mineralization, making the material more compliant and so better suited to absorption of peak and shock loads, thereby protecting the articular cartilage and associated structures. The changes in chemistry have been shown to be at the millimetre level of spatial resolution [30].

At a larger scale, in all except woven bone the collagen is deposited in regular arrays in the form of sheets, lamellae, in which the fibres are aligned in parallel. The orientation of fibres relative to the long axis of the bone can vary between lamellae and has a significant effect on the way the bone responds to stress. The lamellae may be laid down in one of several different arrangements (microstructures), which are also associated with different mechanical properties [10]. In young, fast growing, animals, lamellar and woven bone are often deposited in combination to form regularly repeating layers (e.g. plexiform bone), combining the benefits of the rapid formation of woven bone with the superior material properties of lamellar bone.

Bone contains many holes (porosities) at various different scales, from canaliculi (sub‐micrometres), through Haversian canals (tens of micrometres) to resorption canals (hundreds of micrometres). Holes reduce the density (V _f) of the material, weakening it, and potentially act as stress risers. However, they can also stop cracks by blunting the tip of the crack if it enters the hole [31]. Remodelling creates a temporary porosity between the temporal phases of resorption and new bone formation, and the secondary osteon that is created effectively acts as an embedded ‘fibre’ of new bone within the matrix that is only bound to the surrounding structure by a relatively weak cement line. The secondary osteon contains bone that is younger and, therefore, less densely mineralized than the surrounding tissue. Consequently, remodelled bone is generally less strong or stiff than primary bone, but the reduced mineral content and more ‘fibrous’ structure make it more compliant and tougher than the primary tissue [31].

Composite materials, for example fibreglass, often sustain damage in the form of microcracks when deformed beyond their point of yield. Cracks typically form either within the stiffer phase or at the interface between the stiffer and more compliant phases. The formation of increasing numbers of microcracks due to repetitive loading is associated with a progressive decline in the stiffness of the material [32]. There is substantial evidence that in many cases bone behaves in a similar manner. Cyclical loading of bone specimens at relatively high strains in vitro results in a progressive reduction in their elastic modulus, which is associated with increase in the density of microcracks throughout the sample [33]. Similarly, experiments that result in bones being overloaded in vivo result in a rise in the density and size of microcracks, which is demonstrable when the bones are subsequently examined post‐mortem [32]. Bone is remarkably good at absorbing microdamage without significant detriment to its mechanical properties: the two phases and the numerous small holes (e.g. lacunae, Harversian canals and secondary osteons) deflect and/or ‘retain’ cracks at varying scales, preventing their extension to dangerous lengths. Short cracks remain inherently stable, while those exceeding a critical (>100–300 μm) length [31] are able to ‘punch through’ the natural crack arrestors and grow. There is mathematical and experimental evidence to suggest that small microcracks may actually increase the fatigue life of bone by absorbing strain energy and redistributing stress [34]. Indeed, the ability to sustain and absorb damage without a significant increase in risk of failure is a critical feature of bone, and microcracks may not be entirely detrimental to its mechanical function.

The material properties of bone are strain‐rate dependent. Most importantly, as the rate of loading rises above a critical threshold, bone behaves in a more brittle manner [35]. This may be clinically significant in areas of high impact loading, which are more common in the distal limb of the horse.