The architecture of trabecular bone, the porous bone found in the spine and at articulating joints, provides the requirements for optimal load transfer, by pairing suitable strength and stiffness to minimal weight according to rules of mathematical design. But, as it is unlikely that the architecture is fully pre-programmed in the genes, how are the bone cells informed about these rules, which so obviously dictate architecture? A relationship exists between bone architecture and mechanical usage--while strenuous exercise increases bone mass, disuse, as in microgravity and inactivity, reduces it. Bone resorption cells (osteoclasts) and bone formation cells (osteoblasts) normally balance bone mass in a coupled homeostatic process of remodelling, which renews some 25% of trabecular bone volume per year. Here we present a computational model of the metabolic process in bone that confirms that cell coupling is governed by feedback from mechanical load transfer. This model can explain the emergence and maintenance of trabecular architecture as an optimal mechanical structure, as well as its adaptation to alternative external loads.

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Abstract--A chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from mixture theory. The model consists of an electrically charged porous solid saturated with a monovalent ionic solution. Incompressible and isothermal deformation is assumed. Hydration forces are neglected. The mixture as a whole is assumed locally electroneutral. Four phases following different kinematic paths are defined: solid, fluid, anions and cations. Balance laws are derived for each phase and for the mixture as a whole. A Lagrangian form of the second l~tw of thermodynamics is derived for incompressible porous media and is used to derive the constitutive relationships of the medium. It is shown that the theory is consistent with Biot's theory for the limiting case without ionic effects and with Staverman's results for the limiting case without deformation. ~) 1997 Elsevier Science Ltd.