It is generally presumed that compensation for the reduction of bone strength by progressive endosteal bone loss in adults is provided by continuing periosteal apposition (CPA) of new lamellar bone. However, the appropriate magnitude of compensatory bone growth, and the parameters that operate to determine that magnitude, are unknown. This paper examines the mechanical compensation hypothesis in a series of right-circular tubular bone analogues. Under this hypothesis, the stated objective of CPA is maintenance of the cross-sectional geometric properties of the element. These include the second and polar moments of area, as well as the cortical area of the section (I, J, and CA, respectively). This study assumes that, as resorption and apposition proceed, geometric change is isometric (shape preserving).
The analysis suggests that for a given rate of endosteal bone loss (the stimulus), the magnitude of periosteal growth (the response) required to maintain geometric strength is determined by the maximum ratio (CT0) of the radial distances from the section centroid to the endosteal and periosteal surfaces (i.e., cortical thickness prior to the onset of progressive endosteal bone loss, or peak bone mass). The analysis also indicates that, for any given individual, the amount of compensatory periosteal gain required may be very small. This is particularly true for individuals having a large CT0 and for whom the magnitude of dynamic loading imparted to the skeleton declines with advancing age. This finding is illustrated in a model that relates concepts of bone surface remodeling equilibria and age-related activity differentials.