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Bone Biomechanics
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Types of Bone
Bone consists of two forms: woven and lamella
| Property | Woven Bone | Lamellar Bone |
|---|---|---|
| Definition | "Primitive", immature | "Mature" bone, remodelled from woven bone |
| Found in | Embryo and new-born, in fracture callus, metaphyseal region of growing bone, tumours, osteogenesis imperfecta, and pagetic bone. | Throughout the mature skeleton in both trabecular and cortical bone. |
| Composition | Dense coarse-fibred collagen, varied mineral content, greater turnover, more cells per unit volume with random arrangement, no lamellae. | Formed by intramembranous or endochondral ossification, contains collagen fibres. |
| Organisation | Randomly arranged collagen fibres, disorganised | Highly ordered, stress-oriented collagen fibres |
| Mechanical Properties | Isotropic | Anisotropic |
| Strength | Weaker, more flexible, more easily deformed | More stiffness and strength |
Woven and lamellar bone are organised structurally into trabecular (spongy or cancellous) bone and cortical (dense or compact) bone.
| Trabecular Bone | Cortical Bone | |
|---|---|---|
| Mass | Cortical bone has four times the mass of trabecular bone | |
| Metabolic turnover | Trabecular bone has 8 times greater metabolic turnover due to its high surface area as bone turnover happens at the surface. | |
| Found in | Metaphysis and epiphysis of long bones and in cuboid bones such as the vertebrae | Diaphysis of long bones, and envelope of cuboid bones. |
| Structure | Internal beams/spicules form a 3D branching lattice aligned along areas of mechanical stress. | Compact bone is formed by layers of lamellar bone.
Plexiform bone in larger animals is formed by layers of lamellar and woven bone. Haversian bone is composed of vascular channels circumferentially surrounded by lamellar bone, with a unit being an osteon. |
| Subjected forces | Compression predominates, but is subjected to complex set of stresses and strains | Bending, torsional, and compressive forces. |
| Density | Proximal tibial trabecular bone: 0.30 g/cm³
Greater percentage deviation in density compared to cortical bone. |
Femoral cortical bone: 1.85g/cm³ |
| Porosity | Typically 50% to 90% | Typically 10%. Densities of trabecular and cortical bone can overlap, cortical bone is usually defined as bone with less than approximately 30% porosity. |
| Architecture | Network of small, interconnected plates and rods of individual trabeculae with relatively large spaces between the trabeculae. Individual trabeculae contains only some of the voids found in cortical bone (canaliculi, lacunae, and rarely Haversian canals) | Solid containing a series of dense voids: Haversian and Volkmann's canals and to a lesser extent lacunae and canaliculi. |
Osteons in Haversian Bone
- Osteon: the major structural unit of cortical bone, is an irregular, branching, and anastomosing cylinder composed of a more or less centrally placed neurovascular canal surrounded by cell-permeated layers of bone matrix.
- Osteons are generally oriented in the long axis of the bone
- Haversian canal: The central canal of an osteon. This contains cells, vessels, and occasionally nerves
- Volkmann's canal: the canals connecting osteons
- Vessels: capillaries but smaller vessels resemble lymphatic vessels. Derived from th4e principal nutrient arteries of the bone or epiphyseal and metaphyseal arteries. A vascular network is formed.
Biomechanics of Bone
- The stress-strain curve has three regions: initial linear region, yield region, and postyield region
- Young's modulus is the slope of the linear region
- The strength properties are obtained from the yield and postyield regions
- Yielding (onset of permanent deformation) occurs at the junction of the linear and postyield regions
- Fracture occurs when the ultimate strength is reached.
Material Properties
- See also: Material Properties
Elastic Behaviour
- Isotropic materials: elastic properties do not depend on the orientation of the material with respect to the loading direction. Characterised by Young's modulus. Poisson's ratio measures how much a material bulges with compression or contracts with stretching.
- Anisotropic materials: elastic properties depend on their orientation with respect to the loading direction. Includes bone in the longitudinal direction. Cortical bone is transversely isotropic, i.e. it is isotropic with loading in the transverse plane. Transverse isotropy is a subset of anisotropy.
- Young's modulus of bone: modulus of cortical bone in longitudinal direction is 1.5 times the modulus in the transverse direction, and over 5 times the modulus in the shear direction.
- Poisson's ratio of bone: relatively high indicating that cortical bone bulges more than metals when subjected to uniaxial compression.
Strength
- The strength properties of bone also depends on
- The loading direction. Bone is transversely isotropic from both modulus and strength perspectives
- The method of loading: tension, compression, or torsion.
- Due to the above complexity it isn't possible to specify the strength of cortical bone with a single value.
- Cortical bone longitudinal strength: stronger in longitudinal compression (190 MPa) than tension (130 MPa)
- Cortical bone transverse strength: stronger in compression (130 MPa) than tension (50 MPa)
- Consistent with everyday loads where maximum compressive stresses are larger than maximum tensile stresses
- When cortical bone is loaded close to its yield point it is close to fracture as its yield strength is close to its ultimate strength. Before fracture cortical bone undergoes relatively large deformations.
Energy Absorption, Ductility, and Brittleness
- Toughness: a tough material is a material that absorbs substantial energy before failure.
- Fracture occurs if energy delivered is greater than the capacity of the bone to absorb energy
- Longitudinal loading
- Bone is tough in longitudinal loading
- Bone is relatively ductile in longitudinal loading, i.e. it undergoes a large amount of deformation prior to fracture.
- Transverse loading
- Bone is tougher under compressive than tensile loads. The ultimate strains are much larger than the yield strains.
- Ultimate strain is close to the yield strain for tensile loading in the transverse direction, i.e. it is relatively brittle for transverse loading.
- Therefore cortical bone can be relatively ductile or brittle depending on the loading direction and on whether tensile or compressive forces are applied
Viscoelastic Behaviour
- Cortical bone is viscoelastic because the mechanical properties are sensitive to both strain rate and duration of applied load.
