Lamellae that are assembled around a Haversian canal (Fig. 2.1) form concentric cylindrical units that run roughly in parallel to the long axis of bone making up the Haversian systems (200-250µm in diameter) [69]. Haversian canals contain bone cells, blood vessels and nerves and are connected to each other by Volkmann’s canals that run transversally to the long axis of bone ensuring radial blood flow. Haversian systems are more commonly known as osteons. The boundary between the osteon and interstitial bone is known as the cement line, a thin layer of mucopolysaccharides with a low min-eral and collagen content [57, 70]. Osteons form the bone structural unit (BSU) of cortical bone [24]. The periosteum covers the outer surface of bones, while the endosteum lines the inner surface.
Im-Bone
mediately beneath the periosteum and endosteum, the lamellae are arranged in parallel to the circumference of bone; these are called cir-cumferential lamellae. The spaces between adjacent osteons enclose interstitial lamellae, which are remnants of previously remodeled osteons. Over time, the osteons can be removed completely, leaving behind resorption cavities that are refilled by new osteons [57].
Cortical bone porosity is determined by the number and size of Haversian and Volkmann’s canals (12-200µm in diameter) as well as resorption cavities (200-300µm in diameter) [7, 71–74] excluding osteocyte lacunae and canaliculi [9, 75]. Average cortical porosity at typical fracture sites such as the radius, tibia and the femur in a healthy individual is low, ranging from 3% to 28% [55, 74, 76–78], which is why cortical bone is also referred to as compact bone. The porosity increases from the periosteum to the endosteum and forms a gradient with changing mechanical properties [35, 36, 38, 79]. The interface between the calcified matrix and porous network consti-tutes an internal surface with three compartments: the endocortical surface between the cortical bone and the medullary canal, the tra-becular surface, and the lesser-known intracortical surface (Haver-sian and Volkmann’s canals). Bone modeling and remodeling take place on these surfaces. As the surface area per calcified matrix
vol-ume is lower in cortical bone than in trabecular bone, metabolic activity is lower in cortical bone. Therefore, trabecular bone loss has been the main focus of research into bone fragility for the past 70 years [80]. However, a transitional zone that resides at locations comprising both cortical and trabecular bone has been recently iden-tified as a site with vigorous remodeling activity [81]. It has been reported that accurate segmentation of this transitional zone in X-ray based imaging methods minimizes errors associated with misclassifi-cations, e.g., ‘trabecularized’ areas of cortical bone being considered as the medullary compartment or as trabecular bone [81]. This has led to the appreciation that most bone loss occurs through remodel-ing on the intracortical surfaces after the age of 65 years, rather than by remodeling on trabecular surfaces [80].
Cortical bone covers most of the human skeleton and comprises
80% of its mass. It exclusively forms the diaphysis of long bones and the thin shells that surround the metaphyses [45]. Most long bones are hollow with a medullary cavity that contains marrow. The corti-cal shell essentially provides strength to resist compression, tension, bending, torsion and shearing. Its structure is optimized to favor stiffness while being as light as possible, leading to thicker cortices and wider diameters when more strength is needed [4, 68, 82–84].
Bi o m e c h a n i c a l p r o p e r t i e s o f c o r t i c a l b o n e
Long bones are often considered as levers with movements that are controlled through contraction and relaxation of muscles. A balance between strength and stiffness is required so that the bone may maintain its shape and resist deformation, while still being able to deform reversibly to absorb energy. These properties are commonly investigated by applying a load on a bone specimen and measuring its deformation (displacement) [47, 68]. To examine the properties of bone tissue, i.e., to eliminate the influence of the geometry into which the tissue is arranged, load and deformation may be converted to stress and strain, respectively. Here, the stiffness determined from the linear part of the stress-strain curve is referred to as the modulus of elasticity (Young’s modulus, E) [85, 86]. Bone’s Young’s modulus may depend on the rate of strain (change in strain divided by the time over which deformation occurs), doubling when the strain rate increases by a factor of 106 from extremely slow to high impact strain rates (0.001 to 1000 s−1) [87, 88]. This is one manifestation of viscoelastic behavior. The end of the linear part of the stress-strain curve is known as the yield point. After this point, increasing strain does not result in a linear stress response and bone is unable to return to its original shape. The bone finally fractures at a peak stress value, this is called the ultimate stress. The area under the stress-strain curve represents the amount of energy needed per unit volume to cause bone failure which is commonly described as its toughness.
The stress-strain curve yields the value of Young’s modulus in one specific direction, but due to the variation in osteonal
organi-Bone
zation of cortical bone [35, 36, 47], the modulus may be different in other directions. When the properties of a material are different in various directions, it is considered to be anisotropic. Analogically, the Young’s modulus may be thought of as the normalized propor-tionality constant in Hooke’s law. Hooke’s law can be expanded to three dimensions to relate stress, strain and the mechanical proper-ties of cortical bone. This representation includes six components of stress (three normal and transverse/shear stresses) and, likewise, six components of strain.
For a completely anisotropic material, 21 independent elastic con-stants are needed. In practice, however, cortical bone in the diaph-ysis of long bones has been successfully characterized by transverse isotropy (five independent elastic constants) [89–93]. This means that its mechanical properties can be considered to be equivalent in two directions (in a plane), and different along the third perpendicular di-rection. In the case where the mechanical properties are considered the same in all directions, only two independent elastic constants are required, namely Young’s modulus and Poisson’s ratio (ν). Poisson’s ratio describes the resulting ratio of strains parallel and perpendicu-lar to directions of uniaxial compression or tension [24, 47, 94].