2.1 PU Foam Samples
PU foams, of three different densities, were used in this study. Closed cell PU foam of density 0.16 g.cm-3 and 0.32 g.cm-3 (American Society for Testing and Materials, ASTM, Grade 10 and Grade 20) [1] was used to model low and medium density cancellous bone respectively. Open cell rigid foam of density 0.09 g.cm-3 was used to model very low density cancellous bone. All PU foams were purchased in block form, with dimensions 130 × 180 × 40 mm, from Sawbones® Europe AB, Malmö, Sweden. The foam densities were supplied by Sawbones® Europe AB.
Using a sharpened tube, six cylindrical cores of 9 mm diameter were drilled from each of the three different density PU foam blocks. The cores were taken using the method described by Li and Aspden [14], in which the cylindrical axis of the core was roughly perpendicular to the surface of the PU block (this is the preferred orientation of the "trabeculae"). The exact diameter of the PU cylinders was determined as an average of four measurements; this was necessary to account for the inhomogeneity of the 0.09 g.cm-3 open cell PU foam in particular.
For this study, two different cylinder lengths were chosen to test for any buckling or shape effects. A cylinder, of length of 7.7 ± 0.2 mm, was chosen so that results could be compared with those from a published study of human OP cancellous bone [14]. In order to investigate the effect of specimen dimensions, a cylinder, of length 3.9 ± 0.1 mm, was also investigated. This length was obtained from a standard for testing rubbers [16]. The reason for choosing this standard was to ensure that the specimens did not bulge during compression; rubbers have a Poisson's value of about 0.5 and so maintain an almost constant volume during compression; as a result, they bulge more than most other materials [17, 18]. Dimensions were measured with digital vernier callipers (Fisher Scientific UK Ltd., Leicestershire).
Six cylinders were prepared for each cylinder length and each density of PU foam block. The required cylinder length was achieved by either using a small pair of scissors, for the 0.09 g.cm-3 PU foam, or by rubbing the PU foam cylinder on a sheet of sandpaper (medium grade M2, SupaDec, RS Components Ltd., Northamptonshire, UK), for the 0.16 g.cm-3 and 0.32 g.cm-3 PU foams.
2.2 Mechanical Testing
Quasi-static unconstrained compression tests were conducted using an ELF3200 (for the lowest density foam) or an ELF3300 (for other PU foams) materials testing machine (Bose Corporation, ElectroForce Systems Group, Minnetonka, MN, U.S.A.). The ELF3200 testing machine is fitted with a load cell of full scale 225 N (maximum error 0.21% of the full scale) and a displacement transducer with full scale 6.5 mm (maximum error 0.49% of the full scale). The ELF3300 testing machine is fitted with a load cell of full scale 5100 N (maximum error 0.1% of the full scale) and a displacement transducer with full scale 12.7 mm (maximum error 0.28% of the full scale). The manufacturer's tolerances on the hole alignments are ± 0.1 mm.
The lowest density foam was tested using a different machine, with a lower capacity load cell, because of its greater compliance and lower strength. All tests were video-recorded using a video camera (Sony Handycam DCR-DVD404E, Sony Corporation, Japan). No preload or preconditioning was applied to the specimens, which were compressed between two acetal plates (thickness 15 mm). For the 3.9 mm and 7.7 mm cylinder lengths, tests were performed under displacement control at a rate of 0.013 mm.s-1 and 0.026 mm.s-1 respectively, both of which are equivalent to a strain rate of 0.0033 s-1 [14]. Inspection of video recordings showed a repetitive cycle of trabeculae fracture and consolidation (particularly for the 0.09 g.cm-3 PU foam). All test cylinders experienced loads less than the critical load required for Euler buckling and no such buckling was observed in the video images. For each compression test, the engineering stress was calculated by dividing the load recorded at each data point by the original cross-sectional area of the PU foam cylinder, whilst the engineering strain was calculated by dividing the displacement of the machine actuator head (at each data point) by the original height of the PU foam cylinder [19]. A fifth-order polynomial was fitted to the stress-strain curves. The material properties determined were the Young's modulus, the yield strength, and the energy absorbed up to the yield point. A general expression for Young's modulus was found by differentiating the polynomial equation of the engineering stress-strain curve with respect to strain. This expression for Young's modulus was then plotted against strain and the Young's modulus was determined as the maximum value on the curve. It was necessary to determine the Young's modulus in this way because the stress-strain curves were non-linear. The yield strength was determined by the method described by Li and Aspden [14]; i.e. it was determined as the stress at which the Young's modulus had reduced by 3% from its maximum value. The energy absorbed to yield was calculated by integrating the polynomial equation of the engineering stress-strain curve between the limits of zero and the strain point at which the yield strength was determined.
2.3 Statistical Analysis
Statistical comparisons were made using MINITAB® Release 14.1 Statistical Software (Minitab Inc., Pennsylvania, USA). Normality of the distributions was assessed using the Anderson-Darling test. Data were compared using the two-sample t-test (normally distributed data) or the Mann-Whitney test (non-parametric data), with the significance level set at 0.05.