Mechanical modeling of the stress adaptation process in bone.

The philosophy, techniques, and concepts involved in the mechanical modeling of the process of stress adaptation in bone are described here. First, the idea of a control surface, across which all mechanical forces and fluid transport are monitored, is introduced and employed to totally enclose a living whole bone. Then the mechanical forces are related to local tissue stresses and the fluid transport to the local microcirculation. The concepts of strain, stress, and elasticity are introduced next and the applications of these concepts to biological tissue are discussed. It is argued that biological tissue can only sense strain and not stress; thus baroreceptors are, in fact, strain receptors. The concept of remodeling or stress adaptive equilibrium is then introduced and associated with a particular range of strain values called the band of remodeling equilibrium strains. The deposition or resorption of bone tissue is hypothesized to be a function of the amount of strain by which the actual strain at an anatomical site differs from values of strain in the band of remodeling equilibrium strains. The form of this functional dependence is discussed with regard to a number of points, including its variance from anatomical site to site and the particular features of the strain history which are the most significant in enhancing bone remodeling. In the closing section of the paper, the basic mechanistic ideas underlying our models of bone stress adaptation are presented. These are mechanical models for internal bone remodeling (remodeling) and surface bone remodeling (modeling).