Mechanical optimization of bone.

In bending, the mechanical strength of tubular bone can be estimated by the area moment of inertia (I) = 1/4 x pi x (R4 - r4) (R: external radius, and r: internal radius). Mechanical strength of bone is dissociated from bone density, since radiological density is different from inertia. When the cross-sectional area is constant (C = R2 - r2) in this equation, inertia can be expressed by the equation of (I) = 1/4 x pi x (2Cr2 + C2). Inertia increases with increases of the external and internal radii. According to the above equation, increase of inertia depending on the expansion of radii is inevitable 'optimization' of bone mass. Expansion of the radii of tubular bone with the decrease of wall thickness is an adaptation process rather than the 'decompensation' called osteoporosis. Senescence of individuals as manifested in conditions such as osteoporosis is a stampede of adaptations rather than decompensation of it.