Structural Adaptations to Mechanical Usage. A Proposed “Three-Way Rule” for Bone Modeling

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Abstract
A collection of fundamental structural adaptations is defined for how compacta and spongiosa respond to overloading in compression, tension and flexure, alone and in combinations. Those adaptations underlie most physiological tissue- and organ-level structural adaptations of healthy intact bones to mechanical usage, so explaining them is a major task for models of mechanical determinants of bone architecture. A biomechanical function called the Gamma function is then devised to predict from a structure's net end-loads and the strain history of any given small bone surface domain, whether mechanically induced formation, resorption or neither will occur in that domain. A separate function is devised to predict local rates of modeling from local strain histories. These functions correctly predict varied details of all of the fundamental adaptations and they also suggest new laws for the mechanical control of bone architecture, some of which are presented. The threeway rule is a new way to analyse the mechanical determinants of bone architecture that accounts for bone-biological realities learned after 1960.

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