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Bone structure

Bone is composed of a cellular component and an extracellular matrix. The cellular component is made of osteoblasts, bone-forming cells, osteoclasts, bone-destroying cells, and osteocytes, bone-maintaining cells which are inactive osteoblasts trapped in the extracellular matrix. The matrix, which is responsible for the mechanical strength of the bone tissue, is formed by an organic and a mineral phase. The organic phase is mainly composed of collagen fibres and the mineral phase of hydroxyapatite crystals. A liquid component is also present.

The longitudinal section of human femur is shown in Figure 1. The bone is clearly not homogeneous. Two main types of bone can be individuated: the cortical bone tissue and the trabecular bone tissue.

 

Figure 1: Longitudinal section of human femur. The direction of principal stresses are shown in the scheme on the right.

 

Cortical bone is the more dense tissue usually found on the surface of bones. It is organised in cylindrical shaped elements called osteons composed of concentric lamellae (Figure 2).

 

Figure 2: Lamellar structure of osteons in cortical bone

 

Trabecular bone is quite porous and it is organized in trabecules oriented according to the direction of the physiological load, as shown in Figure 1. The configuration of the trabecular structures is highly variable and it depends on the anatomical site. Figures 3 and 4 show the difference between the structures of trabecules in the L1 vertebra (Figure 3) and in the calcaneus (Figure 4) in a 24 year old man.

 

Figure 3:Trabecular structures in the L1 vertebra of a 24 year old

 

Figure 4:Trabecular structures in the calcaneus of a 24 year old

 

The effect of aging is show below. Figure 5 shows the trabecular structure of vertebrae in a 36 year old woman and Figure 6 in a 74 year old woman.

 

Figure 5: Trabecular structures of vertebrae in a 36 year old woman

 

Figure 6: Trabecular structures of vertebrae in a 74 year old woman

 

 

Bone mechanical properties

The different structures of cortical bone and trabecular bone result in different mechanical properties. Bone mechanical properties are highly variable according to species, age (Table 1), anatomical site, liquid content, etc.

 

Table 1: Ultimate strength (MPa) and ultimate strain (%) of cortical bone from the human femur as a function of age

 

Cortical bone is an anisotropic material, meaning that its mechanical properties vary according to the direction of load (Figure 7). Cortical bone is often considered an orthotropic material. Orthotropic materials are a class of anisotropic materials characterized by three different Young's moduli E₁, E₂, E₃ according to the direction of load, three shear moduli G₁₂, G₁₃, G₂₃ and six Poisson's ratios ν₁₂, ν₁₃, ν₂₃, ν₂₁, ν₃₁, ν₃₂.

 

Figure 7: Comparison between the mechanical behaviour of isotropic and anisotropic materials

 

A few examples of elastic constants of cortical bone from different anatomical sites are reported in Tables 2,3,4.

 

Table 2: Average elastic constants of mandible bone in corpus and ramus

 

Table 3: Average elastic constants of corpus cortical bone in inferior, lingual and buccal zones

 

Table 4: Average elastic constants of human mandibular bone by tooth location

 

The mechanical characterization of trabecular bone is even more difficult. The mechanical properties of trabecular bone as a whole are due to the mechanical characteristics of single trabecules and to its highly porous structure. Figure 8 shows the dependence of the Young's modulus of trabecular bone from bone density.

 

Figure 8: Young's modulus of trabecular bone as a function of density of bone. Bone density ρ is expressed in g/cm³ and Young's modulus E in MPa.

 

 

Bone remodelling

Bone adapts and remodels in response to the stress applied. Wolff's law states that bones develop a structure most suited to resist the forces acting upon them, adapting both the internal architecture and the external conformation to the change in external loading conditions. This change follows precise mathematical laws.
When a change in loading pattern occurs stress and strain fields in the bone change accordingly. Bone tissue seems to be able to detect the change in strain on a local bases and then adapts accordingly. The internal architecture is adapted in terms of change in density and in disposition of trabecules and osteons and the external conformation in terms of shape and dimensions. When strain is intensified new bone is formed. On a microscopic scale bone density is raised and on a macroscopic scale the bone external dimensions are incremented. When strain is lowered bone resorption takes place. On a microscopic scale bone density is lowered and on a macroscopic scale the bone external dimensions are reduced (Figure 9).

 

Figure 9: Bone remodelling: effect of reduction (from A to B) and of intensification of strain (from B to A) on bone trabecules.

 

When the change in strain is due to a change in direction of load on a microscopic scale the structure of trabecules and osteons is rearranged and on a macroscopic scale a change in bone shape may occur.
remodelling is carried out by the cellular component of bone. When resorption takes place osteoclasts reabsorb collagen and mineral phase (Figure 10A) which are then taken into the circulatory system (Figure 10B). During deposition osteoblasts group on the deposition surface and build the collagen network of bone (Figure 11A). Mineralization takes place afterwards (Figure 11B).

Figure 10: Bone resorption

 

Figure 11: Bone deposition

 

Bone resorption and bone deposition processes are always active in bone. An equilibrium strain state exists in correspondence to which the two activities are perfectly balanced. When strain intensity is higher than the equilibrium strain deposition activity is more intense than resorption activity and net deposition occurs. When strain intensity is lower than the equilibrium strain deposition activity is less intense than resorption activity and net resorption occurs. Dynamical equilibrium between resorption and deposition is again achieved when the equilibrium strain state is newly established.

The cell-biology based model of Davy and Hart expresses functional dependence of bone remodelling on the strain field, based on cell activity (Figure 12). The load applied to the bone together with geometric and material properties determine the local strain. Strain is detected by a transducer which generates the strain remodelling potential (SRP). This signal is modulated by genetic, hormonal and metabolic factors, generating the remodelling potential which regulates the recruitment rate and the activity of osteoblasts and osteoclasts, stimulating bone formation and bone resorption. The balance between bone deposition and bone resorption determines the net bone remodelling. remodelling modifies bone geometric and material properties through a feedback loop.

Figure 12: Schematic diagram of the Davy and Hart model for bone remodelling