Figure 2.

Conceptual diagram of the contribution of bone density and shape to bone stiffness and strength for a piece of bone of a given volume and length. Bone density is proportional to bone stiffness (E) and strength (yield stress). Dense bone is stiffer and stronger than less-dense bone, but it is also heavier. The overall shape of a bone affects its stiffness (but not necessarily its strength). For example, the shape axis illustrates sections though the shaft of a long bone that range from less rigid (solid cross-section) to more rigid (thin-walled, hollow cross-section). Diagonal lines within the figure represent isoclines of stiffness and strength; a given value of stiffness and strength can be achieved by different combinations of bone density and shape. If the weight of a bone is held constant, then stiffness can be optimized by adopting a more rigid shape. If shape is held constant and the volume of a bone is reduced, increased stiffness and strength can be achieved by increasing bone density.