Figure 3.

Loading-induced addition of bone on the outer periosteal surface is functionally important, helping the skeleton meet its dual needs of being strong to resist injury, but lightweight for energy efficient motion. A) The polar moment of inertia (i.e. strength) of a bone is proportional to the radii of its outer periosteal (r_p) and inner endocortical (r_e) surfaces according to the relationship π(r_p⁴-r_e⁴)/2. This relationship illustrates that periosteal surface changes have a greater influence on strength than changes on the endocortical surface. B) For example, a 5% increase in r_p (equating to a 15% increase in bone mineral content [i.e. mass]) results in a disproportionate 24% increase in strength, assuming constant bone material properties (i.e. volumetric bone mineral density) and an initial r_p-to-r_e ratio of 1.8. C) If the same mass of bone added to the periosteal surface was simultaneously removed from the endocortical surface, r_e would increase by 15%, but the bone would still be 16% stronger than the bone with same mass in A) because of its greater size (i.e. 5% greater r_p). Broken lines in B) and C) indicate the original bone surfaces in A).