The dependence between the strength and stiffness of cancellous and cortical bone tissue for tension and compression: extension of a unifying principle

A strong positive correlation between the apparent ultimate strength and stiffness of bone tissue that can be expressed by a unified relationship has been observed for cortical bone in tension and low-density cancellous bone in compression. For practical purposes, the existence of a relationship between strength and stiffness is significant in that bone stiffness can be measured in vivo using non-invasive methods. It is generally accepted that bone strength is greater in compression than in tension whereas there is no substantial evidence that bone stiffness in compression is different from that in tension. This might suggest that compressive strength would relate to the stiffness, if at all, in a way that is different from tensile strength. In order to examine similarities and differences in the way strength is associated with stiffness between modes of loading and tissue type, we tested equine cortical bone and bovine cancellous bone in compression and examined these data together with previously reported data from compression testing of human cancellous bone as well as tensile testing of cortical bone from various sources. We have found for cortical bone that (i) the sensitivity of strength to stiffness is the same for tension and compression (p>0.75, ANCOVA), and (ii) the difference between the magnitudes of compressive and tensile strength for cortical bone is the result of an additive, rather than a multiplicative factor (52.1 MPa after adjusting to 1 microstrain/s, p<0.0001, ANOVA). High-density bovine tibial cancellous bone, on the other hand, has a steeper slope for its compressive strength-stiffness relationship than that for cortical bone and human cancellous bone, resulting in a transitional relationship between compressive strength and stiffness for a range of bone types and densities. Based on the current results and previous work, it is suggested that the offset strength in the compressive strength-stiffness relationship may be a direct manifestation of the difference between the compressive and tensile strengths of the bone material that constitutes the building blocks of the bone structure. Deviation of high-density cancellous bone compressive behavior from the other bone types and densities is attributed to stress distribution differences between the bone types.