The prediction of stress fractures using a ‘stressed volume’ concept

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Abstract
This paper addresses an anomaly which exists in the current literature regarding stress fractures. Analysis of the data on fatigue strength of bone samples in vitro would conclude that these fractures should never occur at the strain levels known to occur in vivo. This anomaly can be resolved by including in the analysis the effect of stressed volume, whereby larger volumes of material are expected to have worse fatigue properties. A Weibull analysis was used to predict the probability of failure, Pf; this was an upperbound prediction because it did not include the effects of remodelling and adaptation. Combining this analysis with a finite element model of the human tibia, we predicted a Pf value of 21% after five weeks of strenuous exercise, which is comparable with reported incidences in military personnel. The high incidence of stress fractures in the cannon bone of racehorses could also be predicted (Pf = 62%, compared to 70% experimentally). The approach can be used to investigate the effect of variables in the exercise regime such as the distance run per day and the use of improved footwear. It can also predict the increased risk of stress fractures in elderly people. The results suggest certain simple rules which may be of clinical value in designing exercise regimes and in understanding the risk factors for this type of injury. © 2001 Orthopaedic Research Society. Punlished by Elsevier Science Ltd. All rights reserved.