GEOMETRIC CHARACTERISTICS OF BONES

The mechanical efficiency of bone is not solely dependent on the quality and accumulation of material but also on the optimisation of its spatial distribution and is therefore the product of its material and geometric properties (62). The external and internal architectures of bones are both important factors in the distribution and transmission of loads, and have a significant effect on how fractures initiate and propagate throughout the material (130).

Cortical and trabecular bone both have anisotropic properties.This is manifested by the preferential orientation along the principal loading axis by the osteons of cortical bone and the plate shaped trabeculae in the spongiosa. This best adapts bone to withstand the greatest forces to which it is habitually subjected (135). Figure 1.11 shows the relative differences in ultimate stress that can be tolerated by a typical long bone in various loading directions. Kreider et al (130) discuss a study of trabecular bone samples from osteoporotic hip fracture patients that found a substantially greater orientation of bone tissue in the direction of habitual loading compared to controls with equivalent bone density. They suggest that this increased aniostrophy in these patients could reduce their ability to withstand impacts due to falls in directions orthogonal to the customary loading direction. They also report parallel findings in osteoporotic vertebrae and postulate that remodelling in osteoporotic bone may compensate for low material density by increasing anisotrophy to maximise strength in the direction of the most frequent loading.

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Fig. 1.11. Diagram showing the anisotropic behaviour of bone (111).

As force is applied to a material a fracture may be initiated, by debonding atoms of the material, which will propagate until the energy from that force is dissipated. The elastic and plastic deformation properties of bone are a major determinant in energy dissipation along with various geometric factors (136).Stresses in a material can be concentrated by small ‘defects’ or ‘stress risers’ such as small holes, spaces or cracks that are integral to bone tissue composition e.g. lacunae and resorption cavities (137, 138). Conversely, other structural components may serve to dissipate energy, for example cement lines. These contain minimal collagen and are less well mineralised than surrounding bone tissue thereby providing weak interfaces that may mitigate fatigue damage elsewhere by allowing cracks to occur along these lines (139, 140). The degree of porosity in both cortical and trabecular bone is a well studied area and it has been demonstrated that fracture incidence is strongly related to increased porosity (141).

The specific geometric properties of cortical and trabecular bone will be discussed below:-

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 Trabecular geometry.

Optimised for strength and weight, trabecular bone has a high surface area to volume ratio that is an important factor in its potential to adapt via the remodelling process (63). Its open, porous texture can be described by a range of structural parameters that include; trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), trabecular number (Tb.N), bone surface area (BS), bone volume (BV), total tissue volume (TV), trabecular volume fraction (BV/TV), and trabecular surface density (BS/TV) (142). The connectivity of trabeculae is an important determinant of strength as more numerous, thin but well connected trabeculae are more structurally competent than an equivalent quantity of bone distributed as fewer, thicker, more widely distributed and disconnected trabeculae (138). In clinical terms, heavy reliance has been placed on the density of bone as a surrogate for bone fragility i.e. quantity rather quality. True BMD is a measure of bone mineral content (BMC) divided by volume (34). Studies that use bone density as an indicator of bone quality generally show a reduction in strength and modulus as density decreases. In a computational model, equal values of trabecular bone mass were shown to be associated with different values of biomechanical stiffness explaining how clinical bone integrity can be maintained despite significant reduction in bone mass (143). These results explain the observation that bone mass accounts for 65% of variation in bone strength whilst consideration of the full range of micro-architectural parameters may improve fracture predictability up to 94% (51).

The architectural factors that determine trabecular bone strength are interrelated in a complex fashion but the greatest mechanical competency is afforded by high

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connectivity, high trabecular number and higher trabecular thickness (138) Bone loss leading to increased fragility fractures is associated with loss of trabeculae, reduced connectivity and increased inter-trabecular spacing i.e. porosity (130).

 Cortical geometry.

Whilst whole bones are recognizable by their specific shape, their mechanical properties will be affected by differences in overall size and the relative proportions of their components. Although the overall size and shape of an individual’s bones is largely dictated by genetics (144) these can be modified to some degree by remodelling. Hip geometry plays a role in fracture etiology and examination of geometric factors in addition to BMD may improve identification of people at heightened fracture risk (145-147). The geometric parameters (Fig. 1.12) most relevant to hip strength are:

o HAL: hip axis length (mm). o Angle of femoral neck (Ө degrees).

o CSMI: cross sectional moment of inertia (mm4

) describes geometry and density in the femoral neck and is a measure of the distribution of material around the axis of the neck.

o CSA: cross sectional area (mm2

) of the minimum CSMI section within thefemoral neck.

These variables can be used to calculate the femur strength index (FSI) that provides an estimated ratio of the femoral neck yield strength against expected compressive stress from a fall on the greater trochanter (148).

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Fig. 1.12 Diagram showing geometric parameters of the proximal femur (149).

Leslie et al observed that in a cohort of 30,953 women with incident hip fractures and osteoporotic non-hip fractures, HAL and FSI made a small but significant contribution to hip fracture prediction independent of BMD and age (150). This result is corroborated by a previous study on 2506 women aged above 50 years in which HAL was significantly higher and FSI significantly lower in women with hip fracture (149).

Figure 1.13 shows the CSMI for two hollow cylinders with equal mass where one has a greater distribution of mass farther from the axis of bending (neutral axis) compared to the other. Although the walls are thinner in the right-hand structure, the distribution of material results in a substantially increased resistance to bending along its length. Larger bones have larger CSMI compared

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to smaller ones and greater resilience to fracture for any given value of BMD (151). The strength and stiffness of a hollow tubular shaped bone are proportional to the product of the CSMI and the elastic modulus (E) (33). Increasing CSMI therefore increases fracture resistance if E remains unchanged.

Fig. 1.13. Distribution of equal cortical mass in bones of different diameter (151).

In remodelling, expansion of long bones results from periostial apposition and endosteal resorption thereby increasing the outer cortical diameter over time. The femoral neck is an intracapsular structure not covered by periosteum. It is not therefore subject to periostial apposition and cortical thinning may consequently result (123). The potential effect of cortical thinning in the femoral neck with aging and osteoporotic conditions is an increased susceptibility to buckling fracture (152, 153). Mayhew et al (90) found that cortical thinning in this region is not uniform. Changes in physical activity with aging affect loading patterns in the proximal femur that can cause differential changes in the cortex, potentially altering its stability and exacerbating fracture risk (90). Kaptoge et al (154) concluded from a study of 7474 women, of whom 635 sustained incident

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hip fractures over a period of 13 years, that the proximal femurs of elderly women with hip fracture had lower bending and CSA strengths, thinner and more asymmetric cortices, wider bone diameters and more obtuse neck-shaft angles than non-fractured participants .

Although cortical bone is relatively non-porous compared to trabecular bone, it does have intrinsic qualities of porosity that increase with age. Chen et al (86) suggest that this relates to the enlargement of intracortical channels during osteonal remodelling. Increased cortical porosity is associated with reduced bone strength, although porosity in the endocortex has less structural impact than that in the outer cortex or periosteum (138).

1.4.4 CLINICAL PREDICTION OF FRACTURE AND FACTORS RELATING TO