Heterogeneity of yield strain in low-density versus high-density human trabecular bone

Abstract

Understanding the off-axis behavior of trabecular yield strains may lend unique insight into the etiology of fractures since yield strains provide measures of failure independent of elastic behavior. We sought to address anisotropy of trabecular yield strains while accounting for variations in both density and anatomic site and to determine the mechanisms governing this behavior. Cylindrical specimens were cored from vertebral bodies (n=22, BV/TV=0.11+/-0.02) and femoral necks (n=28, BV/TV=0.22+/-0.06) with the principal trabecular orientation either aligned along the cylinder axis (on-axis, n=22) or at an oblique angle of 15 degrees or 45 degrees (off-axis, n=28). Each specimen was scanned with micro-CT, mechanically compressed to failure, and analysed with nonlinear micro-CT-based finite element analysis. Yield strains depended on anatomic site (p=0.03, ANOVA), and the effect of off-axis loading was different for the two sites (p=0.04)-yield strains increased for off-axis loading of the vertebral bone (p=0.04), but were isotropic for the femoral bone (p=0.66). With sites pooled together, yield strains were positively correlated with BV/TV for on-axis loading (R(2)=58%, p<0.0001), but no such correlation existed for off-axis loading (p=0.79). Analysis of the modulus-BV/TV and strength-BV/TV relationships indicated that, for the femoral bone, the reduction in strength associated with off-axis loading was greater than that for modulus, while the opposite trend occurred for the vertebral bone. The micro-FE analyses indicated that these trends were due to different failure mechanisms for the two types of bone and the different loading modes. Taken together, these results provide unique insight into the failure behavior of human trabecular bone and highlight the need for a multiaxial failure criterion that accounts for anatomic site and bone volume fraction.

Figure 1

Renderings of 1 mm thick longitudinal cross-sections from representative cores of femoral neck (FN) and vertebral body (VB) trabecular bone for each of the on- and off-axis angles considered.

Figure 2

Experimental yield strains for on-axis and 45° off-axis femoral neck and vertebral trabecular bone. Yield strains were isotropic for the femoral bone (p>0.39), but slightly anisotropic for the vertebral bone (p=0.037). Data for the 15° off-axis femoral bone was omitted for clarity (yield strains were 0.76±0.10%).

Figure 3

Yield strain versus BV/TV for on-axis and 45° off-axis loading (anatomic sites are pooled together). A strong positive correlation existed for on-axis loading (p<0.0001), but not for off-axis loading (p=0.79).

Figure 4

Yield strains for (A) femoral neck and (B) vertebral trabecular bone from the parametrically altered finite element models (G.L.=geometrically linear, T/C Sym.=tissue failure strains were assumed to be tension-compression symmetric). Data for the 15° off-axis femoral bone was omitted for clarity (yield strains were 0.75±0.08%, 0.81±0.08%, 0.69±0.06%, and 0.73±0.08% for the original, G.L., T/C sym., and G.L.+T/C sym. models, respectively). Statistical isotropy was retained for all variations of the femoral bone FE analyses (p>0.64), while anisotropy was retained for all variations of the vertebral bone FE analyses (<0.0001).

Figure 5

(A) The percent of total tissue failed and (B) the ratio of tissue failed in tension to compression. Data for the 15° off-axis femoral bone was omitted for clarity (total failure was 11.1±7.5%, and ratio of tensile to compressive failure was 1.21±0.61).

Figure 6

Tissue failure distributions at the apparent yield point for typical on-axis and 45° off-axis femoral neck (FN) and vertebral body (VB) specimens. Red elements correspond to tissue failure in tension and blue correspond to failure in compression. Off-axis specimens tended to have less total tissue failure, increased failure in horizontal trabeculae, and a higher ratio of tensile to compressive tissue failure.

Figure 7

(Left) An off-axis, open-celled cellular solid structure shown with out-of-plane compressive loading. (Right) Free body diagram of an individual oblique beam with compressive force (P) and internal moment (M).