Materials for Biomedical Engineering. Mohamed N. Rahaman

modulate the degradation rate of a polymer in tissue engineering applications to some optimal value. Incorporation of pores into strong materials such a Ti and hydroxyapatite is often used to bring their strength and elastic modulus closer to those of bone when they are used in healing bone defects. This is because a large difference in mechanical properties between the implant and bone can lead to adverse cell and tissue responses, resulting in bone resorption, loosening of the implant, bone fracture or the need for revision surgery (that is, replacement of the implant in a second surgery) (Chapter 17).

      Second, pores are often required to allow cells and nutrients to infiltrate an implant and create new tissue, resulting in healing of a tissue defect and integration of the implant with host tissue. When used in healing bone defects, for example, Ti implants often contain pores in order to achieve better bonding with bone. Lack of integration of an implant often results in unsatisfactory healing of a bone defect. In tissue engineering applications, pores are often incorporated into degradable biomaterials (called scaffolds) to allow cells to create new tissues or organs while the scaffold degrades away.

      The design and creation of a porous implant is important because the properties and performance of the implant depend strongly on a variety of pore characteristics. Furthermore, each application will have its own optimal pore characteristics. The important pore characteristics that require consideration are:

       The volume fraction of the pores in the biomaterial, that is, the porosity of the biomaterial;

       The average size of the pores, their shape and whether they are oriented in a given direction or not;

       How the pores are distributed within the solid, either randomly or in some ordered manner;

       Whether the pores are isolated, that is, disconnected from the surface of the material and from one another, or interconnected, that is, they from a continuous channel through the solid.

      An interconnected pore channel is desirable to allow cells and nutrients to migrate throughout an implant. For a random distribution of spherical pores of the same radius, the porosity should be at least ~16% for the pores to be interconnected. The porosity of implants used in healing bone defects and in tissue engineering, for example, should be well above this value, often greater than ~50%.

The majority of forming methods produce a random distribution of pores within the solid as well as pores that have a range of sizes (Figure 3.24a). On the other hand, the use of additive manufacturing (3D printing) techniques can provide pores with well‐controlled sizes and with a predesigned distribution within the solid (Figure 3.24b). As different cell types have different sizes and may require different environments for creating new tissue, controlling the size of the pores within some narrow range is often desirable for optimal healing or regeneration of some tissues. Implants for healing bone defects, for example, should have interconnected pores of size ~300–500 μm to provide an environment that is conducive to bone formation as well as angiogenesis, the formation of blood vessels that is essential for bone formation and growth (Karageorgiou and Kaplan 2005).

Figure 3.24 Examples of microstructures of porous biomaterials. (a) Bioactive glass with a microstructure approximating human trabecular bone; (b) composite composed of hydroxyapatite (HA) particles in a polycaprolactone (PCL) matrix.

      Source: From Russias et al. (2007)

      ; (c) oriented pores in collagen.

      Source: From Schoof et al. (2001)

      ; (d) bioactive glass with a gradient in pore size and porosity approximating human long bone of the limbs.

      At another level of complexity, we can envisage microstructures in which the pores are aligned in a given direction, have two or more discretely different pore sizes, or have a controlled gradient in porosity along a given direction. Implants containing pores that are oriented in a given direction (Figure 3.24c) are particularly important for directional growth of cells in some tissue engineering applications such as nerve regeneration. Porous implants (scaffolds) with a more complex microstructure may be required for engineered regeneration of some tissues and organs. The liver, for example, contains five cell types and a complex network of blood vessels. Consequently, the use of scaffolds with a more complex microstructure may be relevant for the regeneration of a liver. The long bones of human limbs are composed of a less porous, stronger outer region of cortical bone and a more porous, weaker inner region of trabecular bone. These bones are also subjected to significant physiological stresses during normal activity. Synthetic implants composed of a gradient microstructure may be relevant to healing segmental defects in these long bones (Figure 3.24d) In addition to mimicking the bone structure, such implants may be better able to provide the requisite mechanical properties.

3.6 Special Topic: Lattice Planes and Directions

      Different planes and directions in crystals can have a different packing of the atoms and, for crystals composed of compounds such as ceramics, they can also have a different composition of atoms or ions. Differences in atomic packing and composition can influence the properties of crystals in different planes and along different directions. Plastic deformation (slip) of metals, as noted earlier, occurs in planes and along directions that have the closest packing of the atoms and not just in any plane or along any direction. Consequently, in correlating properties of materials with their crystal structures, it is often necessary to identify specific atomic positions, planes, and directions in the crystal structure in a succinct manner.

      Unit Cell Geometry

The atomic positions, lattice planes, and directions in a crystal are specified with reference to the unit cell of the structure, as described in Figure 3.5. Directions opposite to the x, y, and z axes are taken to be negative.

      Lattice Positions

A point in the crystal lattice is denoted by its coordinates along the x, y, and z axes expressed as a ratio of the unit cell lengths a, b, and c in these directions (Figure 3.25). The origin of the unit cell is 0,0,0. Then, a point at the far corner of the unit cell, opposite the origin, with coordinates a,b,c is written 1,1,1 because each coordinate divided by the respective unit cell length is equal to 1. Similarly, 2,1/2,1 denotes a point in the lattice with coordinates 2a, b/2, and c in the x, y, and z directions, respectively.

Figure 3.25 Diagram illustrating the specification of lattice planes in a crystal.

      Lattice Planes

      Any plane A′B′C′ can be defined by the intercepts OA′, OB′, and OC′ with the three principal axes of the crystal system (Figure 3.25).