Predicting stress fractures using a probabilistic model of damage, repair and adaptation

This paper is concerned with the theoretical prediction of stress fractures in the bones of athletes, soldiers and others during periods of intensive exercise. Previously [J. Orthop. Res. 19 (2001) 919] we showed that test data on the fatigue strength of bone in vitro could be described using Weibull's probabilistic model, allowing predictions to be made of the probability of failure as a function of time under cyclic loading. This paper extends the earlier argument by including two living processes which act to reduce the incidence of failure: (i) repair of damage, and; (ii) adaptation by bone deposition. Having incorporated these aspects into the mathematical model, we applied the theory to a specific case: the human second metatarsal. We predicted a 17% incidence of stress fractures, all occurring within 6 weeks of commencement of the training programme. These predictions agreed well with clinical findings. Interestingly, we concluded that the major effect in preventing stress fractures comes from repair rather than from adaptation, which has a relatively minor role because it acts more slowly.