**2. Basic material properties of rigid polyurethane foam**

Polyurethanes are characterized the urethane linkage (-NH-C(=O)-O-) which is formed by the reaction of organic isocyanate groups with hydroxyl groups as shown below

#### R-NCO+R -OH=R-NH-C(=O)-O-R

Polyurethanes can be turned into foam by means of blowing agents such as water. The cells created during the mixing process are filled and expanded with carbon dioxide gas, which is generated when water reacts with isocyanate group. The result is a closed foam structure, which is a cellular solid structure made up of interconnected network of solid struts or plates which form the edges and faces of cells. Thanks to its desirable material properties that give versatility and durability to the material, polyurethane has become one of the most adaptable materials that it is found everywhere such as carpet, sofa, beds, cars to name a few.

One unlikely place, however, is inside human body, that is human cancellous or spongy bone. The macroscopic structure of cancellous bone consists of a network of interconnecting rods and plates that forms complex struts and columns. Although this structure has strictly speaking open porosity structure, the overall macroscopic structure shows close resemblance to the closed foam structure of polyurethane foam (Figure 1)

Polyurethane foam microscopic structure Cancellous bone microscopic structure

**Figure 1.** Microstructures of cancellous bone and polyurethane foam.

The stress-strain curve of polyurethane foam exhibits similar pattern as cancellous bone. Figure 2 shows a schematic compressive stress-strain curve for polyurethane foams which shows three regions; firstly they show linear elasticity at low stresses followed by a long plateau, truncated by a regime of densification at which the stress rises steeply (Gibson and Ashby, 1988). Linear elasticity is controlled by cell wall bending while the plateau is associated with collapse of the cells by either elastic buckling or brittle crushing. When the cells have almost completely collapsed opposing cell walls touch and further strain compresses the solid itself, giving the final region of rapidly increasing stress.

**Figure 2.** Typical compressive stress-strain curve of polyurethane foam

172 Polyurethane

in this chapter.

osteosynthesis.

few.

highlight the use of polyurethane in orthopaedic biomechanical experiment will be included

Specifically, there will be three sections in this chapter. The first section will describe the basic material properties of rigid polyurethane foam. We will especially highlight the similarities and differences between the foam and human bone. The second section will then present the review of the literature focusing on the use of polyurethane foam in biomechanical experimentations. We will conclude the chapter with our use of polyurethane foam in bone grafting harvester design, fracture predictions and stability testing of

Polyurethanes are characterized the urethane linkage (-NH-C(=O)-O-) which is formed by

Polyurethanes can be turned into foam by means of blowing agents such as water. The cells created during the mixing process are filled and expanded with carbon dioxide gas, which is generated when water reacts with isocyanate group. The result is a closed foam structure, which is a cellular solid structure made up of interconnected network of solid struts or plates which form the edges and faces of cells. Thanks to its desirable material properties that give versatility and durability to the material, polyurethane has become one of the most adaptable materials that it is found everywhere such as carpet, sofa, beds, cars to name a

R-NCO+R -OH=R-NH-C(=O)-O-R

One unlikely place, however, is inside human body, that is human cancellous or spongy bone. The macroscopic structure of cancellous bone consists of a network of interconnecting rods and plates that forms complex struts and columns. Although this structure has strictly speaking open porosity structure, the overall macroscopic structure shows close

Polyurethane foam microscopic structure Cancellous bone microscopic structure

resemblance to the closed foam structure of polyurethane foam (Figure 1)

**Figure 1.** Microstructures of cancellous bone and polyurethane foam.

the reaction of organic isocyanate groups with hydroxyl groups as shown below

**2. Basic material properties of rigid polyurethane foam** 

The compressive stress-strain curve of cancellous bone has the similar three regimes of behaviour (Figure 3). Firstly the small strain, linear elastic region appears which is mainly from the elastic bending of the cell walls. Then the linear-elastic region ends when the cells begin to collapse and progressive compressive collapse gives the long horizontal plateau of the stress-strain curve which continues until opposing cell walls meat and touch, causing the stress rise steeply.

Such similarities have made polyurethane (PU) foams as popular testing substitutes for human cancellous bones and many researchers have quantitatively characterized material properties of polyurethane foam to investigate the suitability and usefulness of PU foams as bone analog. Szivek, Thomas and Benjamin (Szivek et al., 1993)conducted the first study on mechanical properties of PU foams with different microstructures. Compression testing was done to identify elastic modulus and compressive strength. The same group conducted further studies with three compositions of PU foams and evaluated their properties as well(Szivek et al., 1995). Thompson and co-workers(Thompson et al., 2003) analyzed compressive and shear properties of commercially available PU foams. They tested samples of four grades of rigid cellular foam materials and found out that elastic behaviour was similar to cancellous bones and an appropriate density of PU foams can be determined for a particular modulus value. However the shear response showed some discrepancy and concluded that caution is required when simulating other behaviours than elastic behaviour with these foams. Calvert and coworkers (Calvert et al.) evaluated cyclic compressive properties of PU foams and examined the mechanical properties in terms of microstructural features. They found that microstructural properties such as cell size and volume were uniform and increased with decreasing density. And their cyclic testing revealed hysteresis in the low density foams but consistent modulus up to 10 cycles.

Use of Polyurethane Foam in Orthopaedic Biomechanical Experimentation and Simulation 175

The number and variety of implants for osteosynthesis and joint replacement has increased dramatically over the past few decades along with the use of biomechanical testing of these implants to evaluate their performance. The most obvious material of choice will be fresh or embalmed cadaveric human or animal bones as they have the unique viscoelastic properties and internal structures of real bone. However such studies are often beset with a number of other problems such as issues in handling biological samples and huge variety in size, shape and material properties even in matched pairs to name a few. If reproducibility of experiments is important and comparable not absolute results are required, synthetic bones

made from PU-foam can provide a great alternative to the real bones (Figure 4).

**Figure 4.** Various synthetic bone material combinations with different types of PU foams and plastics

(c) transparaent plastic cortical shell with cellular PUfoam inside

(d) Solid PU-foam throughout

The major use of PU foam blocks is comparatives studies for quantitatively measuring some important functional parameters of orthopaedic implants such as pull out strength, stability and stiffness. Bredbenner et al. (Bredbenner and Haug, 2000) investigate the suitableness of synthetic bone made of PU-foam in testing rigidity of fracture fixations by comparing pull out strength from cadaveric bones, epoxy red oak and PU foams. They found out that PUfoam bone substitutes generated comparable results to cadaveric bones, concluding that PU-

Indeed many researchers have used PU-foam in comparative studies measuring pullout strength of fixation screws. Calgar et al.(Caglar et al., 2005) performed biomechanical comparative studies of different types of screws and cables using Sawbone models and found out that the load to failure of screws was significantly greater than that of the cables. Farshad et al. (Farshad et al., 2011)used PU foam blocks to test bone tunnels drilled during anterior cruciate ligament reconstruction. They found that screw embossed grafts achieved higher pull out strengths. Krenn et al. (Krenn et al., 2008)investigated the influence of thread

foams can be used in mechanical investigation of human bones.

(b) rigid PU-foam cortical shell with cellular PU-foam

inside

design on screw fixation using PU-foam blocks with different densities.

(from www.sawbones.com)

(a) plastic cortical shell with cellular PU-foam inside

**3. The use of PU foams in orthopaedic implant testing** 

**Figure 3.** Compressive stress-strain curves for several relative densities (ρ\* /ρs)of wet cancellous bone (modified from Figure 11-5 in Gibson and Ashyby, 1997)

As the use of PU foams in orthopaedic implant testing and their use as bone analogs increased, the American Society for Testing and Materials (ASTM) developed ASTM F1839- 97, "Rigid polyurethane foam for use as a standard material for testing orthopaedic devices and instruments." The aim of this standard is to provide a method for classifying foams as graded or ungraded based on the physical and mechanical behaviour with a given density. This standard has been revised twice since 1997 when it was originally introduced in order to include a wide range of properties and nominal densities(American Society for Testing and Materials, 2008a). As such the number of studies that used PU-foam in testing implant materials and function has increased dramatically after the introduction of the standard. The next section will give review of those studies.
