This paper assembles current concepts about bone fatigue and osteonal remodeling into a mathematical theory of the repair of fatigue damage and the etiology of stress fracture. The model was used to address three questions. (a) How does the half-life of fatigue damage compare with the duration of the remodeling cycle? (b) Does the porosity associated with the remodeling response contribute to stress fracture? (c) To what extent is a periosteal callus response necessary to augment repair by remodeling? To develop the theory, existing experimental data were used to formulate mathematical relationships between loading, damage, periosteal bone formation, osteonal remodeling, porosity, and elastic modulus. The resulting nonlinear relationships were numerically solved in an iterative fashion using a computer, and the behavior of the model was studied for various loading conditions and values of system parameters. The model adapted to increased loading by increasing remodeling to repair the additional damage and by adding new bone periosteally to reduce strain. However, if too much loading was encountered, the porosity associated with increased remodeling caused the system to become unstable; i.e., damage, porosity, and strain increased at a very high rate and without limit. It is proposed that this phenomenon is the equivalent of a stress fracture and that its biological and mechanical elements are significant in the etiology of stress fractures. Additional experiments must be done to test the model and provide better values for its parameters. However, the instability characteristic is relatively insensitive to changes in model parameters.

There is a general, age-related reduction in the material strength and stiffness of bone in both men and women. Between the ages of 35 and 70, cortical bone strength in bending is diminished by about 15-20%, and cancellous bone strength in compression is reduced about 50%. In addition, bone becomes increasingly brittle and fractures with less energy. It is hypothesized that this tendency is driven by the need for remodeling to repair fatigue damage, and the fact that most osteonal and endotrabecular remodeling events fail to replace all the bone that they remove. Each remodeling event also introduces cement line interfaces, which although affording protection against fatigue failure, weaken bone for monotonic loading. Remodeling also affects collagen fiber orientation, mineralization, and the amount of unrepaired fatigue damage, which are additional determinants of bone strength and stiffness. Mechanical factors apparently inhibit age-related bone loss where stresses are higher by reducing remodeling rates and/or the deficit at each remodeling site. They may also stimulate modeling responses, primarily in the form of periosteal bone formation, which, in men more than women, alter bone size and shape to effectively compensate for loss of material strength. Suggested directions for future research include elucidation of the relationships between (1) histologically observable microcracks and bone fragility, (2) remodeling and the repair of fatigue damage, and (3) estrogen and other hormones and mechanically adaptive responses.

Platelet-derived growth factor (PDGF), an osteoblast mitogen, has been demonstrated to accelerate fracture healing and periodontal bone repair when applied locally in vivo. To explore whether PDGF could stimulate bone formation in intact bone, we administered it systemically to rats rendered acutely estrogen-deficient. Because PDGF may stimulate bone resorption in vitro, PDGF was administered with and without an antiresorptive agent (alendronate). All treatments were given by intravenous injection 3 times a week for 6 weeks. Spinal bone mineral density (BMD) decreased by 5% in the vehicle-treated ovariectomized (OVX) rats by the end of the study as determined by DXA. Treatment with PDGF prevented this bone loss and significantly (p < 0.05) increased the bone density in the spine (9%) and whole skeleton (5.8%). Combined treatment with PDGF and alendronate resulted in a greater increase at the spine (18%) and whole skeleton (12.8%) than either agent alone. Histomorphometric analysis demonstrated that treatment with PDGF increased the osteoblast number and osteoblast perimeter without consistent changes in osteoclast estimates. Biomechanical testing demonstrated that PDGF administration increased the vertebral body compressive strength and femoral shaft torsional stiffness and resulted in a trend for enhanced femoral head shearing strength. Coadministration of alendronate further increased these indices of bone strength. PDGF administration also caused premature closure of the growth plate, decreased body fat, and resulted in extraskeletal collagen deposition. We therefore demonstrate, for the first time, that systemic administration of PDGF can increase bone density and strength throughout the skeleton.

An analysis is presented of the balance between the accumulation and repair of fatigue damage in osteonal bone. Fatigue damage is defined in terms of cracks seen histologically when precautions are taken to avoid preparation artifact. The rate of occurrence of such damage is assumed to be proportional to the product of applied peak-to-peak stress, raised to a power, and the loading frequency. The rate of damage repair is assumed to be proportional to the activation rate for osteonal remodeling, and to the mean cross-sectional area of the resulting osteons. An additional factor is introduced to account for the possibility that damage provokes nearby remodeling. The theory is used to compare data from previous experiments of two types: fatigue-to-failure, and studies in which histologically observable cracks are made more numerous by repetitive loading. The analysis shows that there is a measure of agreement between the results of the two kinds of experiments, but the current data are too limited, and the results are too dependent on the mode of loading, to adequately test the theory. However, the analysis provides a framework for designing experiments to more efficiently clarify the relationships between fatigue failure, cracks seen in histologic sections, and the rate at which such cracks are repaired by osteonal remodeling.