After 20 patients who had undergone primary hip arthroplasty gave written informed consent, we retrieved bone grafts from femoral heads, cut the heads into two halves, and randomly divided them into a large bone group (7–10 mm) and small slurry bone group (about 2 mm). The half-heads of the former group were cut into cubes of dimensions 7 × 7 × 7, 8 × 8 × 8, 9 × 9 × 9 and 10 × 10 × 10 mm; those of the latter group were reamed using an acetabular reamer (38 mm) of diameter ca. 2 mm. Both grafts were of pure cancellous bone. The bone grafts were mixed to minimize within-group differences, divided into 5-g samples (mean weight of 7–10 mm grafts 5.02 g, n = 10; mean weight of small slurry bone grafts 5.00 g, n = 10) and stored at –80℃. Before testing, grafts were thawed at room temperature for 2 h and then impacted in an apparatus resembling that of Bavadekar et al. , with minor modifications (Fig.1). Each sample was placed in a tube 14.7 mm in inner diameter and 24.3 mm in outer diameter; the tube wall was sufficiently thick to resist transverse expansion of the samples. Each sample was then intermittently impacted with a solid mass (1,220 g) dropped from a height of 40 cm to mimic the hammer/impactor system. The tube walls contained vents through which marrow and liquid could be extruded. We measured the elastic moduli (Z 2.5 apparatus; Zwick GmbH & Co., Ulm, Germany) at impactions 3, 5, 10, 20, 30, 40, and 50 . The compression velocity was set to 0.5 mm/min. The compression force was limited to 80 N and the graft displacement to 0.3 mm. Testing was immediately terminated when a plateau in either the compression force or displacement was achieved. Each elastic modulus (in MPa) was calculated by reference to the curve between 60 and 98% of the maximal load. As a bone graft is a visco-elastoplastic material exhibiting time-dependent creep and recoil, we delivered impacts at 1-min intervals [7, 15].
Changes in the elastic modulus were analyzed by two-way ANOVA, performed using GraphPad Prism software (version 5.0; GraphPad Software, Inc., San Diego, CA, USA). A P-value <0.05 was taken to reflect significance.
To obtain elastic moduli after impactions 3, 20, and 50, we first specified discrete thresholds (xi values; e.g., from 0 to 10 in steps of 2) and then recorded ni values (the numbers of samples) with test values X < xi,. Division of ni by N (the sample size) yielded an estimate of the probability distribution function, F(xi) = P (X < xi) = ni/N. The probability density function, f(x), was the derivative of F(x). The data were fitted using the Weibull function, F(x) = 1– exp [–(x/ß)m]. We plotted ln [–ln(1–F(x)] (the usual double-logarithmic form of the Weibull expression) versus ln(x), and determined the Weibull modulus m from the slope of the linear fit, and ß from the intercept [= –mln(ß)]. The fitting parameters, the mathematical expectation u = ßΓ(1+1/m), and the standard deviation (see Equation 1 in the Supplementary Files)