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The effect of specimen geometry on the mechanical behaviour of trabecular bone specimens was studied by non-destructive uniaxial compression to 0.4% strain using cylindrical specimens with different sizes and length-to-diameter ratios, and by comparing cubic and cylindrical specimens with the same cross-sectional area. Both the length and the cross-sectional area of the specimen had a highly significant influence on the mechanical behaviour (p less than 0.0001). Within the actual range of length (2.75-11.0 mm) the normalized stiffness (Young's modulus) was related nearly linearly to the specimen length. This dependency on specimen length is suggested to be caused mainly by structural disintegrity of the trabecular specimens near the surface. The normalized stiffness (Young's modulus) was also positively correlated to the cross-sectional area. This dependency on cross-sectional area is probably due to friction-induced stress inhomogeneity at the platen-specimen interface. A cube with side length 6.5 mm or a cylindrical specimen with 7.5 mm diameter and 6.5 mm length are suggested as standard specimens for comparative studies on trabecular bone mechanics.

The effect of strain rate (e) and apparent density (ϱ) on stiffness (E), strength (σu), and ultimate strain (eu) was studied in 60 human trabecular bone specimens from the proximal tibia. Testing was performed by uniaxial compression to 5% specimen strain. Six different strain rates were used: 0.0001, 0.001, 0.01, 0.1, 1, and 10 s−1. Apparent density ranged between 0.23 and 0.59 g cm−3. Linear and non-linear regression analyses using strength, stiffness and ultimate strain as dependent variables (Y) and strain rate and apparent density as independent variables were performed using the following models: Y = aϱ b e c , Y = ϱ b (a+c e ; Y=(a+bϱ) e c , Y=aϱ 2 e c , E=aϱ 3 e c . The variations of strength and stiffness were explained equally well by the linear and the power function relationship to strain rate. The exponent was 0.07 in the power function relationship between strength and strain rate and 0.05 between stiffness and strain rate. The variation of ultimate strain was explained best using a power function relationship to strain rate (exponent =0.03). The variation of strength and stiffness was explained equally well by the linear, power function and quadratic relationship to apparent density. The cubic relationship between stiffness and apparent density showed a less good fit. Ultimate strain varied independently of apparent density.

The compressive axial strain distribution in cylindrical trabecular bone specimens was studied using digitized images of the specimen surface. Specimens were tested with strain rate 0.00015 s-1. Images were taken at 0, 1, 2, 3, 4, 6, 8 and 10% strain. Using an optical illusion of movement by rapidly changing succeeding images, failures were classified as transverse (33%) or oblique collapses (67%). The location of failure was not determined by the specimen density gradient. Local axial strain in the distal, intermediate and proximal third was measured throughout the compression in the transversely failing specimens, whereas local strain in the obliquely failing specimens was measured in the pre-failure phase only. Axial strain inhomogeneity was observed in the pre-failure as well as in the post-failure phase. In the pre-failure phase the intermediate third was strained significantly less than the thirds near the ends. In the post-failure phase specimen strain occurred solely in the collapsed part. Ultimate strain of the transversely failing specimens was 2.5% and ultimate strain of the failing third was 3.7%. At failure less than 1% strain was observed in the intermediate third and at 10% specimen strain 1.5% local strain was found in the intermediate third. The results indicate unreliability of conventional stiffness and strain measurements in trabecular bone specimens probably due to lack of trabecular constraint at the end surfaces. Conventional measurements tend to underestimate stiffness and, by giving an average value of strain in spite of considerable strain inhomogeneity, to underestimate failure strain.

The effect of the boundary conditions between trabecular bone specimens and the test columns of the testing machine was studied together with the effect of side-constraint on the mechanical behaviour of trabecular bone during axial compression. Cylindrical specimens taken from the upper tibial epiphysis of autopsy knees were tested non-destructively by cyclic compression to 0.8% strain under different conditions. Fixation of the specimens to the test columns by a thin layer of bone cement increased the stiffness by 40% and reduced the energy dissipation to 67% of those measured under unconstrained conditions (p less than 0.001). The thin cement layer alone increased the stiffness 19% and reduced energy dissipation to 86% (n.s.). When the machine was equipped with polished steel columns coated by a film of low-viscous oil, both the stiffness and the energy dissipation were reduced to 93% of those measured under standard conditions (p less than 0.005). Trabecular bone specimens tested side-constrained by the surrounding trabecular bone (in situ) showed a 19% larger stiffness than that measured during later testing of the corresponding machined specimens (p less than 0.005) whereas the energy dissipation was not altered significantly. The same specimens showed a 22% increase of stiffness and a 68% increase of energy dissipation when they were side-constrained by a closely fitting steel cylinder (p less than 0.005).

The prospects for the use of quantitative computed tomography (QCT) for evaluation of mechanical properties of tibial trabecular bone were investigated. Computed tomography (CT) data from the proximal tibial epi- and metaphysis of six human cadaver knees were correlated with mechanical data obtained from compression tests and penetration strength measurements. In addition CT and intraoperative penetration data were compared in 20 patients. If spatial agreement between CT and mechanical measurement sites is optimized, close correlations are found between the relative linear attenuation coefficient determined by CT and the ultimate strength (r = 0.84), the yield strength (r = 0.85), the elastic modulus (r = 0.78), the ultimate energy absorption (r = 0.83), the yield energy absorption (r = 0.81), and the penetration strength (r = 0.82). It is concluded that these correlations are sufficient to make QCT a valuable tool for non-invasive evaluation of the spatial distribution of bone properties in several clinical applications.

Cylindrical bone specimens from the proximal epiphysis of ten normal human proximal tibiae were randomly assigned to a destructive axial compression test-series (N=94) or to a protocol of standardized mechanical conditioning followed by non-destructive repeated testing to 0.6% strain and a final destructive test (N=121). Specimen X-ray quantitative computed tomography (QCT) obtained at different scanning energies (100, 120, and 140 kVp) yielded closely related results (r=1.00). Accordingly, predictions of physically measured densities or mechanical properties were not improved by using more than one scanning energy. QCT and physically measured densities were intimately related (QCT at 140 kVp to apparent density using linear regression: r=0.94, and to apparent ash density: r=0.95) and did not differ significantly in their ability to predict the mechanical properties, thus favouring the more easily implemented QCT for routine work. Evaluation of the relation of apparent density to Young's modulus and ultimate strength suggested that a power law regression model is preferable to a linear model, although linear model prediction of mechanical properties does not have significantly worse accuracy within the narrow density range investigated. The effect of conditioning on the behaviour of bone specimens subjected to destructive compression tests was to increase the stiffness and strength by approximately 50 and 20% respectively.

Trabecular bone specimens were tested by non-destructive technique with the purpose of investigating stiffness behaviour and optimizing stiffness determination. Cylindrical specimens (n = 25) were loaded repetitively (0.1 Hz, 30 cycles) by axial compression to 50% of predicted ultimate strength and finally compressed to failure. Analyses of single compression curves showed increasing stiffness (E') until a stress level about 50% of ultimate stress followed by decreasing stiffness. Curve fit analysis of the elastic part of the compression curve showed the best fit, when a second order polynomial was used (r = 0.94, p less than 0.001). The stiffness determined non-destructively at the 25% level of ultimate strength increased significantly to the tenth loading cycle followed by a steady state. The precision of stiffness determination as an average of five consecutive measurements at steady state was E' +/- less than 5% (95% confidence limits). A reproducibility test by repetition of the test sequence after 3 h rest showed qualitatively the same stiffness behaviour. The variation of stiffness determination between the two test sequences was +/- 27% at the first loading cycle falling to +/- 12% at steady state.