Cancellous bone biomechanics

Cancellous bone is both a biological and a mechanical structure. The interaction between these two aspects of cancellous bone is sufficiently strong that understanding the mechanical properties of the tissue is not possible without consideration of the biology. This manuscript is a mathematical expansion of a portion of the first authorʹs Keynote lecture at the 1998 NACOB presentation. The cellular activity of cancellous bone proceeds in part by the transport of metabolites between trabecular hard tissue and marrow. The anatomical observation is that human trabeculae are seldom internally served by a blood supply, suggesting that the transport mechanisms for trabecular survival are diffusion and a collection of mechanisms for active transport of metabolites independent of blood flow. It will be demonstrated that metabolite transport by diffusion can explain two notable empirical relationships for bone: (a) the close relationship between the bone surface and the bone volume, and (b) the exponential decline in the bone volume fraction during periods of mechanical disuse. A mathematical model is also developed showing how mechanical loading can effect bone volume fraction by increasing metabolite transport between the tissue compartments.