Skeletal structural adaptations to mechanical usage (SATMU): 2. Redefining Wolff's law: the remodeling problem.

Basic multicellular unit (BMU)-based remodeling of lamellar bone causes bone turnover, net gains and losses of bone on some bone surfaces or "envelopes," and a remodeling space comprising bone temporarily absent due to evolving resorption spaces and incomplete refilling of them by new bone. Those features depend a) on how many new BMU arise annually, b) on how much bone each BMU has resorbed and c) formed upon its completion, and d) on how long the typical BMU takes to become completed. Because a, b, and c have limiting or maximal values in life that direct and/or indirect effects of mechanical usage of the skeleton can change, the theory presented here derives mechanical usage functions that express what fractions of those maxima a given mechanical usage history allows to happen. The theory predicts some changes in bone formation, resorption, balance, turnover, and remodeling space that depend on how remodeling responds to the vigor of a subject's mechanical usage. The theory can predict specific effects of specific mechanical challenges that experiments can test, and it fits abundant published evidence. As the kernel of a new approach to the problem it awaits critique and refinement by others. It plus the 3-way rule can redefine Wolff's law conceptually and also in mathematical and quantifiable form.