Mechanical properties

Mechanical properties of bone and bone grafts 1

Bone is a composite material consisting of organic and inorganic parts. An organic extracellular collagenous matrix is impregnated with inorganic materials, especially hydroxyapatite [ Ca10(PO4)6 (OH)2 ]. However, a bone’s strength is higher than that of either apatite or collagen because, similar to what happens with concrete, the softer component prevents the stiff one from brittle cracking, while the stiff component prevents the soft one from yielding. The organic material gives bone its flexibility, while the inorganic material gives bone its resilience. The mineral content of bone affects its mechanical property. Higher mineralization makes the bone stronger and stiffer (higher modulus of elasticity), but it lowers the toughness; that is, it is less capable of absorbing shock and strain energy. The organic phase makes it more pliable and shock-absorbing. The compressive strength of human cortical bone ranges between 90-230 MPa (tensile strengths ranging from 90-190 MPa), whereas the compressive strength of cancellous bone ranges between 2-45 MPa.

Bone is identified as either cancellous  (also referred to as trabecular or spongy) or cortical  (also referred to as compact). The porosity of cortical bone ranges from 5 to 30%, while cancellous bone’s porosity ranges from 30 to 90%. Bone porosity is not fixed and can change in response to altered loading, disease, and the aging process. Both cortical and cancellous bone may contain two types of basic architecture, woven  and lamellar.

Woven bone:

  • Characterized by a haphazard organization of collagen fibers and is mechanically weak
  • Woven bone is weaker, with a smaller number of randomly oriented collagen fibers, but forms quickly; it is for this appearance of the fibrous matrix that the bone is termed woven.
  • After a fracture, woven bone forms initially and is gradually replaced by lamellar bone during a process known as “bony substitution.”

Lamellar bone:

  • Characterized by regular parallel alignment of collagen into sheets (lamellae) and is mechanically strong
  • Is highly organized in concentric sheets with a much lower proportion of osteocytes to surrounding tissue
  • Characterized as filled with many collagen fibers parallel to other fibers in the same layer (these parallel columns are called osteons)
  • Compared to woven bone, lamellar bone formation takes place more slowly. The orderly deposition of collagen fibers restricts the formation of osteoid to about 1 to 2 µm per day.

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Mechanical properties of bone and bone grafts:

  • Structural properties characterize the bone, bone graft or biomaterials in its intact form. Important structural properties are represented by a relationship between force and deformation, or stress and strain.
  • Material properties characterize the behavior of the bone, bone graft or biomaterials comprising the tissue and they are commonly described in terms of the stress–strain relationship of the material.

The strength of a material, which is the breaking or ultimate strength under different modes of loading, such as tension, compression, torsion, or bending, will be different, as will the corresponding modulus of elasticity or stiffness, except bending. The stiffness of a material represents the material’s ability to resist deformation. Stiffness is commonly determined by the slope of the linear region of a stress– strain curve.  There can be different kinds of moduli depending on the loading types (e.g., shear modulus, compression modulus). The larger the stiffness, the greater the force required to cause a given deformation.

 

Visco-elasticity

Biological tissues are viscoelastic materials A viscoelastic material possesses characteristics of stress-relaxation, creep, strain-rate sensitivity, and hysteresis. Force-relaxation (or stress-relaxation ) is a phenomenon that occurs in a tissue stretched and held at a fi xed length. Over time the stress developed within the tissue continually declines. Stress-relaxation is force- or strain-rate–sensitive. In general, the higher the strain or loading rate, the larger the peak force/stress and subsequently the greater the magnitude of the force-relaxation. In contrast to stress- relaxation, which occurs when a tissue’s length is held fi xed, is creep. Creep occurs with time when a constant force/stress is applied across the tissue. If subjected to a constant tensile force, then a tissue elongates with time. The general shape of the displacement- time curve depends on the past loading history