Stiffness cortical bone

Keywords— Acoustic scanning microscope, cortical bone, stiffness, hydroxyapatite, osteon. 

There are two basic structural types of bone cancellous (trabecular, spongy) and cortical (dense) bones. Cancellous bone matter is less dense than that of cortical bone and is found across the ends of the long bones. Owing to its lower density, cancellous bone has also a much lower modulus of elasticity but higher strain-to-failure rate compared to cortical bone (Table 3.1). Bone has higher moduli of elasticity than soft connective tissues, such as tendons and ligaments. The difference in stiffness (elastic modulus) between the various types of connective tissues ensures a smooth gradient in mechanical stress across a bone, between bones and between muscles and bones (Hench, 2014). 

The anisotropy of cortical bone tissue has been described in two symmetry arrangements. Lang [1969], Katz and Ukraincik [1971], and Yoon and Katz [1976a,b] assumed bone to be transversely isotropic with the bone axis of symmetry (the 3 direction) as the unique axis of symmetry. Any small difference in elastic properties between the radial (1 direction) and transverse (2 direction) axes, due to the apparent gradient in porosity from the periosteal to the endosteal sides of bone, was deemed to be due essentially to the defect and did not alter the basic symmetry. For a transverse isotropic material, the stiffness matrix [Qj] is given by... 

Zioupos, P., and Currey, J. D. (1998), Changes in the stiffness, strength, and toughness of human cortical bone with age. Bone 22(l) 57-66. 

From an engineering perspective, PEEK has preferential mechanical properties as well as all the characteristics that would be expected of an implantable polymer. Unfilled PEEK has a Young s modulus of approximately 5 GPa, and the inclusion of short-chopped and continuous carbon fibres as well as carbon particles can result in a Young s modulus ranging from 20-150 GPa. Such a wide range of stiffness means that PEEK formulations can be produced with modulus values similar to that of cortical bone and hence can minimise or prevent bone resorption (caused by the disparity between metallic implant and bone). This is perhaps one of the main reasons why PEEK is so abundantly employed in hard tissue applications (Kurtz and Devine, 2007). 

The second material property adopted for tibia was transversely isotropic property of the elastic behavior. The stiffness matrix for cortical bone was assumed to have 5 independent constants as follows [5] ... 

Mechanical properties of cancellous (spongy) bone are dependent on the bone density and porosity, and therefore the strength and stiffness of spongy bone is much lower than that of cortical or osteonic bone. The axial compressive strength is related to the square of the bone density. 

The stiffness of a biomaterial should be comparable to that of cortical and trabecular bone to support loading at the fracture site (Nilsson 2003). Therefore, bone substitutes have to be designed in order to withstand long-term or short-term compressive and bending forces. The main drawback of CaPs materials is their brittleness and poor strength, limiting their use as implants in loaded situations. 

---