SWARTZ, S.M.; KAY, N.; MIDDLETON, K.M.; BLUME, J. A.; Brown University, Providence, RI; Brown University, Providence, RI; Brown University, Providence, RI; Brown University, Providence, RI: The role of thickness and curvature in dictating subchondral bone stresses in mammalian joints

Most analyses of the design of mammal limb bones focus on the compact bone shaft or the cancellous bone of the joints. However, the subchondral bone, the compact layer sandwiched between the articular cartilage and the underlying epiphyseal trabecular bone, is a potentially important but poorly studied element of this structural system. Allometric analysis of subchondral bone in the mammal femoral head shows scaling that differs from that of long bone shafts, but is similar to that of individual bone trabeculae: subchondral bone thickness is of nearly constant absolute magnitude over a wide range of species. Because bone shaft dimensions scale in proportion to approximately (body mass)^0.33, the relative thickness of the subchondral bone and the shaft to which it connects varies greatly with body size. In small-bodied species, subchondral bone is similar in thickness to the shaft; in larger animals, it is a small fraction of the shaft thickness. We employed a abstracted finite-element model of a �femoral head� – three-quarters of a sphere – at the end of a cylindrical shaft to examine the mechanical consequences of this design variation. A 10X decrease in relative thickness of subchondral and diaphyseal bone, similar to that of small vs. large mammals, produces a significantly larger increase in peak shear stresses (13-15X). Notably, the peak stresses in the model subchondral bone, particularly for the relatively thin subchondral bone mimicking the condition in large mammals, are 15-20X greater than in the bone shaft, due to the curvature of the joint surface. Subchondral bone geometry may therefore be a significant constraint on the form of the skeleton in large mammals.