A theory of fatigue damage accumulation and repair in cortical bone

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.